DogDogFish

Data Science, amongst other things.

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Markov Clustering – What is it and why use it?

Hi all,

Bit of a different blog coming up – in a previous post I used Markov Clustering and said I’d write a follow-up post on what it was and why you might want to use it. Well, here I am. And here you are. So let’s begin:

In the simplest explanation, imagine an island. The island is connected to a whole bunch of other islands by bridges. The bridges are made out of bricks. Nothing nasty so far – apart from the leader of all the islands. They’re a ‘man versus superman’, ‘survival of the fittest’ sort and so one day the issue a proclamation. “Every day a brick will be taken from every bridge connected to your island and the bricks will be reapportioned on your island back to the bridges, in proportion to the remaining number of bricks in the bridge.”

At first, nobody is especially worried – each day, a brick disappears and then reappears on a different bridge on the island. Some of the islands notice some bridges getting three or four bricks back each day. Some hardly ever seem to see a brick added back to their bridge. Can you see where this will lead in 1000 years? In time, some of the bridges (the smallest ones to start off with) fall apart and end up with no bricks at all. If this is the only way between two islands, these islands become cut off entirely from each other.

This is basically Markov clustering.

For a more mathematical explanation:

Let’s start with a (transition) matrix:

import numpy as np
transition_matrix = np.matrix([[0,0.97,0.5],[0.2,0,0.5],[0.8,0.03,0]])

Transition Matrix = begin{matrix}  0 & 0.97 & 0.5 \  0.2 & 0 & 0.5 \  0.8 & 0.03 & 0  end{matrix}

In the above ‘islands’ picture those numbers represent the number of bricks in the bridges between islands A, B and C. In the random-walk interpretation, those are the probabilities that you’ll end up at each node as the number of random walks tends to infinity. In my previous post on house prices, I used a correlation matrix.

First things first – I’m going to stick a one in each of the identity areas. If you’re interested in why that is, have a read around self-loops and, even better, try this out both with and without self-loops. It sort of fits in nicely with the above islands picture but that’s more of a fluke than anything else – there’s always the strongest bridge possible between an island and itself. The land. Anyway…

np.fill_diagonal(transition_matrix, 1)

Transition Matrix = begin{matrix}  1 & 0.97 & 0.5 \  0.2 & 1 & 0.5 \  0.8 & 0.03 & 1  end{matrix}

Now let’s normalize – make sure each column sums to 1:

transition_matrix = transition_matrix/np.sum(transition_matrix, axis=0)

Transition Matrix = begin{matrix}  0.5 & 0.485 & 0.25 \  0.1 & 0.5 & 0.25 \  0.4 & 0.015 & 0.5  end{matrix}

Now we perform an expansion step – that is, we raise the matrix to a power (I’ll use two – you can change this parameter – in the ‘random-walk’ picture this can be thought of as varying how far a person can walk from their original island).

transition_matrix = np.linalg.matrix_power(transition_matrix, 2)

Expanded Matrix = begin{matrix}  0.3985 & 0.48875 & 0.37125 \  0.2 & 0.30225 & 0.275 \  0.4015 & 0.209 & 0.35375  end{matrix}

Then we perform the inflation step – This involves multiplying each element in the matrix by itself (to a power) and then normalizing on column again. Again, I’ll be using two as a power – increasing this leads to a greater number of smaller clusters:

for entry in np.nditer(transition_matrix, op_flags=['readwrite']):
    entry[...] = entry ** 2

Inflated Matrix = begin{matrix}  0.15880225 & 0.23887556 & 0.13782656 \  0.04 & 0.09135506 & 0.075625 \  0.16120225 & 0.043681 & 0.12513906  end{matrix}

Finally (for this iteration) – we’ll normalize by row.

transition_matrix = transition_matrix/np.sum(transition_matrix, axis=0)

Normalized Matrix = begin{matrix}  0.44111185 & 0.63885664 & 0.40705959 \  0.11110972 & 0.24432195 & 0.22335232 \  0.44777843 & 0.11682141 & 0.36958809  end{matrix}

And it’s basically that simple. Now all we need to do is rinse and repeat the expansion, inflation and normalization until we hit a stable(ish) solution i.e.

Normalized Matrix_{n+1} - Normalized Matrix_n < epsilon
for some small epsilon.

Once we’ve done this (with this particular matrix) we should see something like this:

Final Matrix = begin{matrix}  1 & 1 & 1 \  0 & 0 & 0 \  0 & 0 & 0  end{matrix}

Doesn’t look like a brilliant result be we only started with a tiny matrix. In this case we have all three nodes belonging to one cluster. The first node (the first row) is the ‘attractor’ – as it has values in its row it is attracting itself and the second and third row (the columns). If we were to end up with the following result (from a given initial matrix):

Final Matrix = begin{matrix}  1 & 0 & 1 & 0 & 0\  0 & 1 & 0 & 1 & 0\  0 & 0 & 0 & 0 & 0\  0 & 0 & 0 & 0 & 0\  0 & 0 & 0 & 0 & 1\  end{matrix}

This basically says that we have three clusters {1,3} (with 1 as the attractor), {2,4} (with 2 as the attractor) and {5} on its lonesome.

Instead of letting you piece all that together here’s the code for Markov Clustering in Python:

import numpy as np
import math
## How far you'd like your random-walkers to go (bigger number -> more walking)
EXPANSION_POWER = 2
## How tightly clustered you'd like your final picture to be (bigger number -> more clusters)
INFLATION_POWER = 2
## If you can manage 100 iterations then do so - otherwise, check you've hit a stable end-point.
ITERATION_COUNT = 100
def normalize(matrix):
    return matrix/np.sum(matrix, axis=0)

def expand(matrix, power)
    return np.linalg.matrix_power(matrix, power)

def inflate(matrix, power):
    for entry in np.nditer(transition_matrix, op_flags=['readwrite']):
        entry[...] = math.pow(entry, power)
    return matrix

def run(matrix):
    np.fill_diagonal(matrix, 1)
    matrix = normalize(matrix)
    for _ in range(ITERATION_COUNT):
        matrix = normalize(inflate(expand(matrix, EXPANSION_POWER), INFLATION_POWER))
    return matrix

If you were in the mood to improve it you could write something that’d check for convergence for you and terminate once you’d achieved a stable solution. You could also write a function to perform the cluster interpretation for you.

As you were.

Stock Prices and Python – Pandas to the rescue

Hi all,

Today I fancy a bit of a play around with stock prices – I recently took the plunge into the world of stocks & shares and have been getting more and more interested in the financial world as I’ve become more and more exposed to it through savings. I’m a bit sceptical as to being able to find anything ‘new’ or any real arbitrage opportunities – mostly because there’s a billion (trillion?) dollar industry built off of the back of stock trading. It attracts some really smart people with some really powerful gear and a whole lot of money to invest. However, there’s no harm in having a look around and seeing what interesting things we can do with the data.

R is well good but I want a bit more freedom with this little project and I’m missing Python. I find that with R, I spend a lot of my time getting data into the right format to be able to use the tools that already exist. With Python, if I’m silly enough to decide on a strange data structure then I can. I shouldn’t, but I can.

Ordinarily I like the Python & SQL combination and tend not to rely too heavily on the ‘Python analysis stack’ of Pandas/iPython/Scipy/Matplotlib, only pulling things in when necessary. I was going to follow the same pure Python & SQL route for this project until I found an awesome little feature of Pandas – in-built Google and Yahoo stock data integration. It’s not that much work to build this sort of thing yourself but why reinvent the wheel? 🙂

So – I guess we should start with some sort of question, shall we see if we can plot some of the big tech players (AMZ, GOOGL, FB e.t.c.) against the whole tech sector. Given the recent headlines in that area it should be interesting and at least give us some ideas about future work.

As a lazy person, I’m not necessarily inclined to manually go through a list of stock symbols and decide if they’re tech or even go through a list of tech stock and type them into a text file. A quick google shows me that there’s nothing (that I could find) in the way of a regularly updated text file of what I’m after but it shouldn’t be too difficult to coax Python into doing this for me – let’s start off with the NASDAQ site.

If you have a look, you’ll see it’s fairly regular in its URL structure and the URLs are easily craftable – there’s an annoying amount of pagination but you can’t have everything. Actually, hold the phone. You can download the list as a CSV – winner winner chicken dinner.

Downloading all the company information we get a CSV with the following headers:

Symbol Name LastSale MarketCap ADR TSO IPOyear Sector Industry Summary Quote

All I’m really after for now is the sector and symbol – market cap will prove useful but basically I think I can agree we’ve hit the jackpot!

Time for the Python:

from pandas.io.data import DataReader
import pandas as pd
from datetime import datetime
import numpy as np
company_information = pd.read_csv('allcompany.csv')
mega_frame = [DataReader(company.strip(),  "yahoo", datetime(2014,1,1), datetime.now().date()) for company in company_information[company_information.Sector == 'Technology']['Symbol']]
symbol_list = [symbol for symbol in company_information[company_information.Sector == 'Technology']['Symbol']]

At this point we’ve got all the data since the start of the year on every tech stock listed on the NASDAQ, NYSE and AMEX and it’s taken us 6 lines. Note that the population of mega_frame takes a fairly long time. In retrospect, we should have filtered further

20 minutes later and I’m regretting my decision to get all of them.

Cancelled it and switched to the first 50 – will just prove concept first.

Right, now I’ve got a list containing data frames – one for each of the first 50 tech stocks. Let’s throw in a percentage change column and make sure all our data frames are of the same length to avoid problems at a later date:

mega_frame = [stock for stock in mega_frame if len(stock) == 79]
symbol_list = [symbol_list[index] for index in len(symbol_list) if len(mega_frame[i]) == 79]
for stock_index in range(len(mega_frame)):
    mega_frame[stock_index]['perc_change'] = 100*((mega_frame[stock_index]['Close'] - mega_frame[stock_index]['Open'])/mega_frame[stock_index]['Open'])
## The modal value is 79 hence 79
percentage_change_list = [stock['perc_change'] for stock in mega_frame]

Now we’re going to create a correlation matrix out of those lists to see the most strongly correlated tech stocks over that time period (and in our subset). I’m also going to look at the negatively correlated stocks – you wouldn’t expect to see a strong negative correlation for two stocks in the same sector and region but it won’t hurt to look:

correlation_matrix = np.corrcoef(percentage_change_list)
## Correlation with yourself is no big deal
for i in range(np.shape(correlation_matrix)[0]):
    for j in range(np.shape(correlation_matrix)[1]):
        if i == j:
             correlation_matrix[i][j] = 0
maximum_indices = np.argmax(correlation_matrix, axis=1)
minimum_indices = np.argmin(correlation_matrix, axis=1)
for index in range(np.shape(correlation_matrix)[0]):
    print "Stock %s is best correlated with stock %s: %.3g" % (my_list[index], my_list[maximum_indices[index]], correlation_matrix[index][maximum_indices[index]])
    print "Stock %s is worst correlated with stock %s: %.3g" % (my_list[index], my_list[minimum_indices[index]], correlation_matrix[index][minimum_indices[index]])

So there we have it (I’ll leave it to run over all the tech stocks overnight) – a fairly quick and simple way to find the most correlated tech stocks in America over a given time period.

Now this isn’t a particularly great way of doing this, as I said earlier, there are people who dedicate their lives to this. If the fancy takes me, I’ll have a look at a few of these (maximal spanning trees, stability of eigenvectors of correlation matrices e.t.c) and see what improvements we can make to our very simple model.

Installing Hadoop 2.4 on Ubuntu 14.04

Hey all,

Another of my ‘getting my new operating system set up with all the bits of kit I use’ – this time we’ll be on Hadoop (and HDFS). There’s a very strong chance that this post will end up a lot like Sean’s post – Hadoop from spare-change. If there are any differences it’ll be for these reasons three:
1.) He was using Ubuntu Server 13.04 not Ubuntu Desktop 14.04
2.) He was using Hadoop 2.2 not Hadoop 2.4
3.) He was setting up a whole bunch of nodes – I’m stuck with this oft-abused laptop

Anywho – on with the show.

Step 1:

Download Hadoop from Apache: I’ll be using this mirror but I trust that if you’re not in England, you can likely find a more suitable one:
http://mirror.ox.ac.uk/sites/rsync.apache.org/hadoop/common/hadoop-2.4.0/hadoop-2.4.0.tar.gz

If you’re trying to stick to the terminal/don’t have a GUI then go with this:

wget http://mirror.ox.ac.uk/sites/rsync.apache.org/hadoop/common/hadoop-2.4.0/hadoop-2.4.0.tar.gz

Find your way to wherever you downloaded the tar.gz file and untar it using the following command:

tar -xzf hadoop-2.4.0.tar.gz

Sorry if I’m teaching you to suck eggs – everybody has to start somewhere right?

Has it worked up till here?

Run the following command in the same directory you ran the above tar command:

ls | grep hadoop | grep -v *.gz

If there’s at least one line returned (ideally hadoop-2.4.0) then you’re good up till here.

Step 2:

Let’s move everything into a more appropriate directory:

sudo mv hadoop-2.4.0/ /usr/local
cd /usr/local
sudo ln -s hadoop-2.4.0/ hadoop

We create that link to allow us to write scripts/programs that interact with Hadoop that won’t need changing if we upgrade our Hadoop version. All we’ll do is install the new version and point the Hadoop folder to the new version instead. Ace.

Has it worked up to here?

Run this command anywhere:

whereis hadoop

If the output is:
hadoop: /usr/local/hadoop
you may proceed.

Step 3:

Righty, now we’ll be setting up a new user and permissions and all that guff. I’ll steal directly from Michael Noll’s tutorial here and go with:

sudo addgroup hadoop
sudo adduser --ingroup hadoop hduser
sudo adduser hduser sudo
sudo chown -R hduser:hadoop /usr/local/hadoop/

Has it worked up to here?

Type:

ls -l /home/ | grep hadoop

If you see a line then you’re in the money.

Step 4:

SSH is a biggy – possibly not so much for the single node tutorial but when we were setting up our first cluster, SSH problems probably accounted for about 90% of all head-scratching with the remaining 10% being nits.


su - hduser
sudo apt-get install ssh
ssh-keygen -t rsa -P ""
cat ~/.ssh/id_rsa.pub >> ~/.ssh/authorized_keys

So we switch to our newly created user, generate an SSH key and get it added to our authorized keys. Unfortunately, Hadoop and ipv6 don’t play nice so we’ll have to disable it – to do this you’ll need to open up /etc/sysctl.conf and add the following lines to the end:


net.ipv6.conf.all.disable_ipv6 = 1
net.ipv6.conf.default.disable_ipv6 = 1
net.ipv6.conf.lo.disable_ipv6 = 1

Fair warning – you’ll need sudo privileges to modify the file so might want to open up your file editor like this:

sudo apt-get install gksu
gksu gedit /etc/sysctl.conf

If you’re set on using terminal then this’ll do it:

echo "net.ipv6.conf.all.disable_ipv6 = 1" | sudo tee -a /etc/sysctl.conf
echo "net.ipv6.conf.default.disable_ipv6 = 1" | sudo tee -a /etc/sysctl.conf
echo "net.ipv6.conf.lo.disable_ipv6 = 1" | sudo tee -a /etc/sysctl.conf

Rumour has it that at this point you can run
sudo service networking restart
and kapeesh – ipv6 is gone. However, Atheros and Ubuntu seem to have a strange sort of ‘not working’ thing going on and so that command doesn’t work with my wireless driver. If the restart fails, just restart the computer and you should be good.

(if you’re terminal only : sudo shutdown -r now )

Has it worked up to here?

If you’re stout of heart, attempt the following:

su - hduser
ssh localhost

If that’s worked you be greeted with a message along the lines of ‘Are you sure you want to continue connecting?’ The answer you’re looking for at this point is ‘yes’.

If it hasn’t worked at this point run the following command:
cat /proc/sys/net/ipv6/conf/all/disable_ipv6

If the value returned is 0 then you’ve still not got ipv6 disabled – have a re-read of that section and see if you’ve missed anything.

Step 5:
I’m going to assume a clean install of Ubuntu on your machine (because that’s what I’ve got) – if this isn’t the case, it’s entirely likely you’ll already have Java installed. If so, find your JAVA_HOME (lots of tutorials on this online) and use that for the upcoming instructions. I’m going to be installing Java from scratch:

sudo apt-get update
sudo apt-get install default-jdk

Given a bit of luck, you’ll now have Java on your computer (I do on mine) and you’ll be able to set your environment variables. Open up your bashrc file:

su - hduser
gksu gedit .bashrc

and add the following lines:

export HADOOP_HOME=/usr/local/hadoop
export JAVA_HOME=/usr

and follow up with this command:
source ~/.bashrc

If you’ve deviated from any of the instructions above, those lines are likely to be different. You can find what your java home should be by running the following command:
which java | sed -e 's/(.*)/bin/java/1/g'

Your Hadoop home will be wherever you put it in step 2.

Has it worked up to here?

So many different ways to test – let’s run our first Hadoop command:

/usr/local/hadoop/bin/hadoop version

If that worked with no error (and gave you your Hadoop version) then you’re laughing.

Step 6:

Configuration of Hadoop (and associated bits and bobs) – we’re going to be editing a bunch of files so pick your favourite file editor and get to work. First things first though, you’re going to want some place for HDFS to save your files. If you’ve going to be storing anything big/bought external storage for this purpose now is the time to deviate from this tutorial. Otherwise, this should do it:


su - hduser
mkdir /usr/local/hadoop/data

Now for the file editing:

(only necessary when running a multi-node cluster, but let’s do it in case we ever get more nodes to add)
1.) /usr/local/hadoop/etc/hadoop/hadoop-env.sh
Change export JAVA_HOME=${JAVA_HOME} to match the JAVA_HOME you set in your bashrc (for us JAVA_HOME=/usr).
Also, change this line:
export HADOOP_OPTS="$HADOOP_OPTS -Djava.net.preferIPv4Stack=true
to be

export HADOOP_OPTS="$HADOOP_OPTS -Djava.net.preferIPv4Stack=true -Djava.library.path=$HADOOP_PREFIX/lib"

And finally, add the following line:
export HADOOP_COMMON_LIB_NATIVE_DIR=${HADOOP_PREFIX}/lib/native

2.) /usr/local/hadoop/etc/hadoop/yarn-env.sh
Add the following lines:

export HADOOP_CONF_LIB_NATIVE_DIR=${HADOOP_PREFIX:-"/lib/native"}
export HADOOP_OPTS="-Djava.library.path=$HADOOP_PREFIX/lib"

3.) /usr/local/hadoop/etc/hadoop/core-site.xml
Change the whole file so it looks like this:

<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="configuration.xsl"?>
<configuration>
<property>
  <name>fs.default.name</name>
  <value>hdfs://localhost:9000</value>
</property>
<property>
  <name>hadoop.tmp.dir</name>
  <value>/usr/local/hadoop/data</value>
</property>
</configuration>

4.) /usr/local/hadoop/etc/hadoop/mapred-site.xml
Change the whole file so it looks like this:

<?xml version="1.0"?>
<?xml-stylesheet type="text/xsl" href="configuration.xsl"?>

<configuration>
    <property>
        <name>mapreduce.framework.name</name>
        <value>yarn</value>
    </property>
</configuration>

5.) /usr/local/hadoop/etc/hadoop/hdfs-site.xml
Change the whole file so it looks like this:

<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="configuration.xsl"?>

<configuration>
    <property>
        <name>dfs.replication</name>
        <value>3</value>
    </property>
</configuration>

6.) /usr/local/hadoop/etc/hadoop/yarn-site.xml
Change the whole file so it looks like this:

<?xml version="1.0"?>
<configuration>
    <property>
        <name>yarn.nodemanager.aux-services</name>
        <value>mapreduce_shuffle</value>
    </property>
    <property>
        <name>yarn.nodemanager.aux-services.mapreduce_shuffle.class</name>
        <value>org.apache.hadoop.mapred.ShuffleHandler</value>
    </property>
    <property>
        <name>yarn.resourcemanager.resource-tracker.address</name>
        <value>localhost:8025</value>
    </property>
    <property>
        <name>yarn.resourcemanager.scheduler.address</name>
        <value>localhost:8030</value>
    </property>
    <property>
        <name>yarn.resourcemanager.address</name>
        <value>localhost:8050</value>
    </property>
</configuration>

Annnd we’re done 🙂 Sorry about that – if I could guarantee that you’d be using the same file paths and OS as me then I’d let you wget those files from a Github somewhere but alas, I think that’s likely to cause more headaches than it solves. Don’t worry, we’re nearly there now 🙂

Has it worked up to here?

Run the following command:

/usr/local/hadoop/bin/hadoop namenode -format

If that works, you’re 20% of the way there.

Then, run:

/usr/local/hadoop/sbin/start-dfs.sh

If that seems to work without throwing up a bunch of errors:

/usr/local/hadoop/sbin/start-yarn.sh

If that’s worked, you can safely say you’ve got Hadoop running on your computer 🙂 Get it on the LinkedIn as a strength as soon as possible 😉

Conclusion
Now you’ve got Hadoop up and running on your computer, what can you do? Well, unfortunately with that single node and single hard disk, not much you couldn’t have done without it. However, if you’re just getting started with Linux and Hadoop you’ll have hopefully learnt a bit on the way to setting up your cluster.

UK House Sales – When should estate agents go on holiday?

Hi all,

If you’ve been following all of these blog posts then you’re in a minority of one. However, you’ll also know that we’ve taken all of the UK house sales in the last 18 years or so and have found a bunch of things out. We’ve seen the spread of average house price by region, we’ve seen seasonality in the average house price, we’ve seen the impact the housing crash had on average house price (not that much) and on number of houses sold (an awful lot). Finally, we investigated seasonality of number of house sales by region and in doing so, found that London suffered the housing crash worse than other areas but almost immediately picked itself up and is in fact (relative to the rest of the country) better off than it was before the crash.

I had a couple of ideas for investigations in my last post – one of which was finding the most sold house in the UK and seeing if there was a correlation between the times a house has sold and its price. I’ll briefly tackle this because it’s one line of bash – working with our file pp-all.csv (all of our data in one big text file) the following command will give us the top 100 most sold properties in the UK in the last 18 years:


cut -d ',' -f5,9-15 pp-all.csv | tr -d '"' | tr ',' ' ' | sort | uniq -c | sort -k1 -n -r | head -n 100

The top 10 are as follows (with the format: # of sales | postcode | address ) :

24 L17 3BP 48 FLAT 5-19 ULLET ROAD LIVERPOOL LIVERPOOL MERSEYSIDE
19 W8 6JE 126 FLAT 1-10 LEXHAM GARDENS LONDON KENSINGTON AND CHELSEA GREATER LONDON
19 LS2 7LY 31 EASTGATE LEEDS LEEDS LEEDS WEST YORKSHIRE
16 SE1 3FF 41 FLAT 67 MALTBY STREET LONDON SOUTHWARK GREATER LONDON
16 PL2 1RR 48 HADDINGTON ROAD PLYMOUTH CITY OF PLYMOUTH CITY OF PLYMOUTH
16 BN43 5AR SHOREHAM COURT 3-10 THE CLOSE SHOREHAM-BY-SEA ADUR WEST SUSSEX
15 IP1 3PW 54 ANGLESEA ROAD IPSWICH IPSWICH IPSWICH SUFFOLK
14 WA16 6JD TATTON LODGE 1-6 MOORSIDE KNUTSFORD CHESHIRE EAST CHESHIRE EAST
14 M3 6DE FRESH 138 APARTMENT 1008 CHAPEL STREET SALFORD SALFORD SALFORD
14 M19 2HF 35 CENTRAL AVENUE MANCHESTER MANCHESTER GREATER MANCHESTER

I decided against pursuing this investigation as a quick hunt on Zoopla tells me that flats 5-19 Ullet Road were sold individually and so we’re just seeing the results of grouping and nothing overly interesting. I guess there are certain houses in there of interest – why has 48 Haddington Road been sold 16 times since 1995?

Sale prices of 48 Haddington Road since 1995

Sale prices of 48 Haddington Road since 1995

I don’t really know and I’m not going to investigate – I think I’d rather look at the age old question:

“When should estate agents take holidays?”

Of course, this is every bit as much a question of where national estate agents should have their staff distributed throughout the year, which region removal companies should target throughout the year, where travelling housing surveyors are most likely to pick up business e.t.c.

In the last post we were able to create time series of the percentage of UK house sales a region was responsible for. Now we’re going to create a whole bunch of time series (one for each region) and perform clustering on them to see when each region peaks and troughs. Note we’re looking at a percentage of total sales here and not absolute numbers – I’m also not looking at the saturation of the market or anything like that.

I’m going to use Markov Clustering in this example – don’t worry too much about this (if you don’t want to), I’ll do a post on Markov Clustering at a later point. For now, all you need to know is that it’ll cluster our data in a sensible way.

So, down to business:

## Get the data I need in a small(er) table
library(reshape2)
library(rEMM)
mini_frame <- data.frame(newFrame$Datey, newFrame$Region, newFrame$Percent)
colnames(mini_frame) <- c("Datey", "Region", "Percent")
ts_frame <- dcast(mini_frame, Datey ~ Region, sum)
## Have found I need to initialize this before I kick off
seasonal_ts_frame <- data.frame(matrix(0, nrow=12, ncol=length(colnames(ts_frame)))
colnames(seasonal_ts_frame) <- colnames(ts_frame)
row.names(seasonal_ts_frame) <- factor(month.name, levels=month.name)
for (i in 1:ncol(ts_frame)) {
    decomposed_ts <- decompose(ts(ts_frame[,i], frequency=12, start=c(1995,1)))$seasonal[c(1:12)]
    seasonal_ts_frame[[colnames(ts_frame)[i]]] <- decomposed_ts
}
cor(seasonal_ts_frame)
emm <- EMM(threshold=0.2, measure="eJaccard")
build(emm, cor(seasonal_ts_frame))
cluster_centres <- data.frame(cluster_centers(emm))
cluster_frame <- data.frame(lapply(cluster_centres, which.max))
row.names(cluster_frame) <- c("Cluster")
cluster_frame <- data.frame(t(cluster_frame))
colnames(cluster_frame) <- c("Region", "Cluster")
cluster_one <- subset(cluster_frame, Cluster==1)
cluster_two <- subset(cluster_frame, Cluster==2)
## A list of all the cluster one regions
seasonal_ts_frame[,(names(seasonal_ts_frame) %in% row.names(cluster_one))]
## Now the biggie - let's see the points on a map
library(maps)
library(mapdata)
library(RCurl)
library(RJSONIO)

## A couple of functions allowing us to dynamically get the longitude and latitude of regions
construct.geocode.url <- function(address, return.call = "json", sensor = "false") {
  root <- "http://maps.google.com/maps/api/geocode/"
  u <- paste(root, return.call, "?address=", address, "&sensor=", sensor, sep = "")
  return(URLencode(u))
}

gGeoCode <- function(address,verbose=FALSE) {
  if(verbose) cat(address,"n")
  u <- construct.geocode.url(address)
  doc <- getURL(u)
  x <- fromJSON(doc,simplify = FALSE)
  if(x$status=="OK") {
    lat <- x$results[[1]]$geometry$location$lat
    lng <- x$results[[1]]$geometry$location$lng
    return(c(lat, lng))
  } else {
    return(c(NA,NA))
  }
}

## Plot a UK map
map('worldHires', c('UK', 'Ireland', 'Isle of Man','Isle of Wight'), xlim=c(-8,2), ylim=c(51.8,54.2))

longitude_and_latitude <- data.frame(sapply(paste(row.names(cluster_one), ", UK", sep=''), function(x) gGeoCode(x)))
row.names(longitude_and_latitude) <- c("Latitude", "Longitude")
longitude_and_latitude <- data.frame(t(longitude_and_latitude))
points(longitude_and_latitude$Longitude, longitude_and_latitude$Latitude, col=1, pch=4)

O.K, so there’s an awful lot of R code in there and all to produce a slightly underwhelming graph. Where does the great divide come in seasonality of house sales? Why, in South Wales and North East England of course:

Seasonality Cluster

Regions that break the national housing seasonality pattern

Semi-ignoring our ability to get accurate latitude and longitude using what was at best, a wildly optimistic attempt at doing so, we have some fairly believable (if confusing clusters). The bulk of the country follows the trend set by London:

Seasonal Variations in London's Percent of the UK Housing Market (by number sold)

Seasonal Variations in London’s Percent of the UK Housing Market (by number sold)

with lots of houses being bought in the summer and many fewer being bought in the winter. However, 6 regions in South Wales (including all of Glamorgan), 2 regions in the North East of England and Avon all follow this trend:

Seasonal Variations in Humberside's Percent of the UK Housing Market (by number sold)

Seasonal Variations in Humberside’s Percent of the UK Housing Market (by number sold)

This struck me as very strange indeed and so I looked at the original data and what should I discover? That almost all of the above analysis is wrong. If only we’d have performed the following query the folly of all that I’ve done would have become clear:

colSums(ts_frame==0) > 200

Every single one of the regions that didn’t follow our pattern had substantial missing data. One with more knowledge of British geography may have been able to spot that those counties had ceased to exist in 1995/6. The reason why I’ve left all that analysis in, aside from the fact that there are a few useful bits of code in there (plotting the regions on a UK map may well be helpful to somebody), is to show that it’s really really important to check your data when you’ve got an unexpected result. It’s also important to check it whatever the result, but in data analysis, if something seems dodgy there’s a good chance it is.

When I strip out all regions with missing data, we in fact see that all of the regions follows the same pattern as Greater London. Bugger.

Going to draw this one to a close – what have we discovered? Well, we now know that every single region in the UK follows the same seasonality pattern when it comes to house sales: lots more in summer than winter. We also know that the average house price follows the same trend. I’ve not shown that the regionality isn’t a factor in the increasing average house price (you could imagine the scenario where the more expensive areas see a greater surge in house sales in the summer than the less expensive areas). I’m not sure what I’m going to work on next – I’m getting a bit sick of house prices.

It’ll likely either be:
1.) Regional variations in average house price.
2.) Which regions see the greatest increase in number of house sales in summer – clustering as before.
3.) Seasonality of any other variable (type of house, new versus old, freehold versus leasehold)
4.) Build a predictive model to calculate something specific (number of old detached houses sold in Derbyshire every month for the next year).
5.) Identify towns with the fastest growing (and falling) average house price over the last x years. Try to use this to predict which areas will see similar areas of growth/decline in the future.
6.) Finding correlated stock opening/closing prices over historical data and using this to make £££££. Obviously that one is a bit different but does involve ££££.

Hadoop From Spare Change

A Data Scientist happened upon a load of stuff – junk, at first glance – and wondered, as was his wont, “what can I get out of this?”

Conceded: as an opening line this is less suited to a tech blog than an old-fashioned yarn. In an (arguably) funny way, this isn’t far from the truth. My answer: get some holism down your neck. Make it into a modest, non-production Hadoop cluster and enjoy a large amount of fault-tolerant storage, faster processing of large files than you’d get on a single high-spec machine, the safety of not having placed all your data-eggs in one basket, and an interesting challenge. Squeeze the final, and not inconsiderable, bit of business value out of it.

To explain, when I say “stuff”, what I mean is 6 reasonable but no longer DC-standard rack servers, and more discarded dev desktops than you can shake a duster at. News of the former reached my Data Scientist colleague and I by way of a last call before they went into the skip; I found the latter buried in the boiler room when looking for bonus cabling. As a northerner with a correspondingly traumatic upbringing, instinct won out and, being unable to see it thrown away, I requested to use the hardware.

I’m not gonna lie. They were literally dumped at my feet, “unsupported”. Fortunately, the same qualities of character that refused to see the computers go to waste saw me through the backbreaking physical labour of racking and cabling them up. Having installed Ubuntu Server 13 on each of the boxes, I had soon pinged my desktop upstairs successfully and could flee the freezing server room to administrate from upstairs. Things picked up from here, generally speaking.

The hurdle immediately ahead was the formality of installing and correctly configuring Hadoop on all of the boxes, and this, you may be glad to know, brings me to the point of this blog post. Those making their first tentative steps into the world of Hadoop may be interested to know how exactly this was achieved, and indeed, I defy anyone to point me towards a comprehensive Hadoop-from-scratch quick start which leaves you with a working version of a recent release of Hadoop. Were it not for the fact that Hadoop 2.x has significant configuration differences to Hadoop 1.x, Michael Noll’s excellently put-together page would be ideal. It’s still a superb pointer in itself and was valuable to me during my first youthful fumblings with Hadoop 18 months ago. The inclusion of important lines of bash neatly quashes the sorts of ambiguity that may arise from instructions like “move the file to HDFS” which you sometimes find.

In any case, motivated by the keenness to see cool technology adopted as easily and widely as possible, I propose in this to briefly explain the configuration steps necessary to get me into a state of reverse cartography. (Acknowledged irony: there will probably be a time when someone reads this and it’s out of date. Apologies in advance.) Having set up a single node, it’s actually more of a hassle to backtrack over your configuration to add more nodes than to just go straight to a multi-node cluster. Here’s now to do the latter.

Setting the Scene

The Hadoop architecture can be summarised in saying that it elegantly facilitates doing two things in a distributed manner: storing files, and processing files. The two poles of the Hadoop world which respectively deal with these are known as the DFS (distributed file system) layer, and the MapReduce layer. Each layer knows about the other, but can, and indeed must, be configured, administrated and used fairly independently across a cluster. There’s an interesting history to both of these computing paradigms, and many papers written by the likes of Google and Facebook describing their inner workings. A quick Youtube yields some equally illuminating talks. My personal favourites on the two layers are this for HDFS and this for MapReduce.

Typically a cluster of computers (nodes) will have 1 master node, which coordinates the distribution of storage and processing, and (n-1) slave nodes which do the actual stuff. The modules (daemons) in Hadoop 2.x which control all of these are as below.

Master Slaves
DFS  Namenode  Datanode
MR  Resourcemanager  Nodemanager

Obligatory diagram:

Hadoop Architecture
Illuminating.

Based on your current cluster setup, Hadoop makes a bunch of intelligent decisions about where to put files, and which machines to do certain bits of processing on, motivated by maximising redundancy and fault tolerance by clever replication choices, minimising network overhead, optimally leveraging each bit of hardware, and so on. The way that the architecture makes these decisions in such a way that you, the Hadoop developer, don’t have to worry about them, is where the real beauty and power of Hadoop lies. We’ll see later in this blog how, whilst HDFS and MapReduce are breathtakingly complex and scalable under the bonnet, leveraging their power is no more difficult than performing normal straightforward file system operations and file processing in Linux.

So. At this stage, all you have is a collection of virginal, disparate machines that can see each other on the network, but beyond that share no particular sense of togetherness. Each must undergo the same setup procedure before it’s ready to pull its weight in the cluster. In a production environment, this would be achieved by means of an automated deployment script, so that nodes could be added easily and arbitrarily, but that is both overkill and an unnecessary complication here. Good old-fasioned Bash elbow grease will see us through.

Having said that, one expedient whose virtues I will extol is a little gem of software called SuperPutty, which will send the same command from any single Windows PC to all the Linux boxes simultaneously, in so doing greatly reducing repetitiveness and cutting out chances for human error:

SuperPutty
Using SuperPutty to send commands en-masse is only the same as doing the same thing on each box in sequence.

Connect to all the boxes and make sure you’re at the same bash prompt on all of them. SuperPutty will let you store connection authentication details to save you even more time in swiftly connecting to every  machine in your cluster. (Disclaimer: if you do store passwords, anyone with Linux knowledge who finds your unattended, unlocked PC could connect to your cluster and perform wild-rogue Hadoop operations on your data. Think carefully.)

Masters and Slaves

One of your computers will be the master node, and the rest slaves. The master’s disks are the only ones that need to have an appropriate RAID configuration, since Hadoop itself handles replication in a better way in HDFS: choose JBOD for the slaves. If one of your machines stands above the rest in terms of RAM and/or processing power, choose this as the master.

Since Hadoop juggles data around amongst nodes like there’s no tomorrow, there are a few networking prerequisites to sort, to make sure it can do this unimpeded and all nodes can communicate freely with each other.

Hosts

Working with IPs is a lot like teaching cats to read: it quickly becomes tedious. The file /etc/hosts enables you to specify names for IP addresses, then you can just use the names. Every node needs to know about every other node. You’ll want your hosts file on each of the boxes to look something like this so you can refer to (eg) slave 11 without having to know (or calculate!) slave 11’s IP:
123.1.1.25 master
123.1.1.26 slave001
123.1.1.27 slave002
123.1.1.28 slave003
123.1.1.29 slave004
... etc

It’s also a good idea to disable IPv6 on the Hadoop boxes to avoid potential confusion regarding localhost addresses… Fire every box the below commands to append the necessary lines to /etc/sysctl.conf…
sean@node:~$ echo "#disable ipv6" | sudo tee -a /etc/sysctl.conf
sean@node:~$ echo "net.ipv6.conf.all.disable_ipv6 = 1" | sudo tee -a /etc/sysctl.conf
sean@node:~$ echo "net.ipv6.conf.default.disable_ipv6 = 1" | sudo tee -a /etc/sysctl.conf
sean@node:~$ echo "net.ipv6.conf.lo.disable_ipv6 = 1" | sudo tee -a /etc/sysctl.conf

The machines need to be rebooted for the changes to come into effect…
sean@node:~$ sudo shutdown -r now

Once they come back up, run the following to check whether IPv6 has indeed been disabled. A value of 1 would indicate that all is well.
sean@node:~$ cat /proc/sys/net/ipv6/conf/all/disable_ipv6

Setting up the Hadoop User

For uniformity across your cluster, you’ll want to have a dedicated Hadoop user with which to connect and do work…
sean@node:~$ sudo addgroup hadoop
sean@node:~$ sudo adduser --ingroup hadoop hduser
sean@node:~$ sudo adduser hduser sudo

We’ll now switch users and work as the new Hadoop user…
sean@node:~$ su - hduser
hduser@node:~$

SSH Promiscuity

Communication between nodes take place by way of the secure shell (SSH) protocol. The idea is to enable every box to passwordlessly use an SSH connection to itself, and then copy those authentication details to every other box in the cluster, so that any given box is on familiar terms with any other and Hadoop is unshackled to work its magic!

Firstly, send every box the instruction to make a passwordless SSH key to itself for hduser:
hduser@node:~$ ssh-keygen -t rsa -P ""

Bash will prompt you for a location in which to store this newly-created key. Just press enter for default:
Generating public/private rsa key pair.
Enter file in which to save the key (/home/hduser/.ssh/id_rsa): Created directory '/home/hduser/.ssh'.
Your identification has been saved in /home/hduser/.ssh/id_rsa.
Your public key has been saved in /home/hduser/.ssh/id_rsa.pub
The key fingerprint is: 9b:82...................:0e:d2 hduser@ubuntu
The key's randomart image is: [weird ascii image]

Copy this new key into the local list of authorised keys:
hduser@node:~$ cat $HOME/.ssh/id_rsa.pub >> $HOME/.ssh/authorized_keys

The final step in enabling local SSH is to connect – this will save the fingerprint of the host to the list of familiar hosts.
hduser@node:~$ ssh hduser@localhost
The authenticity of host 'localhost (::1)' can't be established.
RSA key fingerprint is d7:87...............:36:26
Are you sure you want to continue connecting? yes
Warning: permanently added 'localhost' (RSA) to the list of known hosts.

Now, to allow all the boxes to enjoy the same level of familiarity with each other, fire them all this command:
hduser@node:~$ ssh-copy-id -i $HOME/.ssh/id_rsa.pub hduser@master

This will make every box send its SSH key to the master node. Unfortunately, you have to repeat this to tell every box to send its key to every node…
hduser@node:~$ ssh-copy-id -i $HOME/.ssh/id_rsa.pub hduser@slave001
hduser@node:~$ ssh-copy-id -i $HOME/.ssh/id_rsa.pub hduser@slave002
hduser@node:~$ ssh-copy-id -i $HOME/.ssh/id_rsa.pub hduser@slave003
etc...

Finally, and this is also a bit tedious, via SuperPutty make every box SSH to each box in turn and check that all’s well. Ie, send them all:
hduser@node:~$ ssh master

…check that they all have…
hduser@node:~$ ssh slave001

… check that they all have… etc.

This is a one-time thing; after any box has connected to any other one time, the link between them remains.

Java

The next prerequisite to sort is a Java environment, as the Hadoop core is written Java (although you can harness the power of MapReduce in any language you please, as we shall see). If you’re fortunate, your machines will have internet access, in which case fire the following command to them all using SuperPutty:
hduser@node:~$ sudo apt-get install openjdk-6-jre
If like mine, however, your machines were considered ticking chemical time bombs by infrastructure and hence weren’t granted internet access, what you’ll want to do is download a JDK to a computer that does have internet access and can also see your Hadoop boxes on the network, and fire the files over from there. So on your internet-connected box:
32 bit version:
hduser@node:~$ wget --no-cookies --no-check-certificate --header "Cookie: gpw_e24=http://www.oracle.com/" http://download.oracle.com/otn-pub/java/jdk/6u34-b04/jre-6u34-linux-i586.bin

64 bit version:
hduser@node:~$ wget --no-cookies --no-check-certificate --header "Cookie: gpw_e24=http://www.oracle.com/" http://download.oracle.com/otn-pub/java/jdk/6u45-b06/jdk-6u45-linux-x64.bin

Now then! Each of your Hadoop nodes wants to connect to this box and pull over the Java files. Find its IP by typing ifconfig, and then fire this command to all of your Hadoop nodes:
hduser@node:~$ scp user@internetbox:/locationoffile/rightarchtecturefile.bin $HOME

Be careful to get the edition matching the machine, be it 32bit or 64bit.

Now execute the following on the Hadoop machines to install Java…

32 bit machines:
hduser@node:~$ chmod u+x jre-6u34-linux-i586.bin
hduser@node:~$ ./jre-6u34-linux-i586.bin
hduser@node:~$ sudo mkdir -p /usr/lib/jvm
hduser@node:~$ sudo mv jre1.6.0_34 /usr/lib/jvm/
hduser@node:~$ sudo update-alternatives --install "/usr/bin/java" "java" "/usr/lib/jvm/jre1.6.0_34/bin/java" 1
hduser@node:~$ sudo update-alternatives --install "/usr/lib/mozilla/plugins/libjavaplugin.so" "mozilla-javaplugin.so" "/usr/lib/jvm/jre1.6.0_34/lib/i386/libnpjp2.so" 1
hduser@node:~$ sudo update-alternatives --install "/usr/bin/javaws" "javaws" "/usr/lib/jvm/jre1.6.0_34/bin/javaws" 1
hduser@node:~$ sudo update-alternatives --config java
hduser@node:~$ sudo update-alternatives --config javac
hduser@node:~$ export JAVA_HOME=/usr/lib/jvm/jre1.6.0_34/

64 bit machines:
hduser@node:~$ chmod u+x jdk-6u45-linux-x64.bin
hduser@node:~$ ./jdk-6u45-linux-x64.bin
hduser@node:~$ sudo mv jdk1.6.0_45 /opt
hduser@node:~$ sudo update-alternatives --install "/usr/bin/java" "java" "/opt/jdk1.6.0_45/bin/java" 1
hduser@node:~$ sudo update-alternatives --install "/usr/bin/javac" "javac" "/opt/jdk1.6.0_45/bin/javac" 1
hduser@node:~$ sudo update-alternatives --install "/usr/lib/mozilla/plugins/libjavaplugin.so" "mozilla-javaplugin.so" "/opt/jdk1.6.0_45/jre/lib/amd64/libnpjp2.so" 1
hduser@node:~$ sudo update-alternatives --install "/usr/bin/javaws" "javaws" "/opt/jdk1.6.0_45/bin/javaws" 1
hduser@node:~$ sudo update-alternatives --config java
hduser@node:~$ sudo update-alternatives --config javac
hduser@node:~$ export JAVA_HOME=/opt/jdk1.6.0_45/

Finally, test by firing all machines
hduser@node:~$ java --version

You should see something like this:
hduser@node:~$ java -version
java version "1.6.0_45"
Java(TM) SE Runtime Environment (build 1.6.0_45-b06)
Java HotSpot(TM) 64-Bit Server VM (build 20.45-b01, mixed mode)

Installing Hadoop

Download Hadoop 2.2.0 into the directory /usr/local from the best possible source:
hduser@node:~$ cd /usr/local
hduser@node:~$ wget http://mirror.ox.ac.uk/sites/rsync.apache.org/hadoop/core/hadoop-2.2.0/hadoop-2.2.0.tar.gz

If your boxes don’t have internet connectivity, use the same workaround we used above to circuitously get Java.

Unzip, tidy up and make appropriate ownership changes:
hduser@node:~$ sudo tar xzf hadoop-2.2.0.tar.gz
hduser@node:~$ sudo mv hadoop-2.2.0 hadoop
hduser@node:~$ sudo chown -R hduser:hadoop hadoop

Finally, append the appropriate environment variable settings and aliases to the bash configuration file:
hduser@node:~$ echo "" | sudo tee -a $HOME/.bashrc
hduser@node:~$ echo "export HADOOP_HOME=/usr/local/hadoop" | sudo tee -a $HOME/.bashrc
hduser@node:~$ echo "" | sudo tee -a $HOME/.bashrc

#32 bit version:
hduser@node:~$ echo "export JAVA_HOME=/usr/lib/jvm/jre1.6.0_34" | sudo tee -a $HOME/.bashrc

#64 bit version:
hduser@node:~$ echo "export JAVA_HOME=/opt/jdk1.6.0_45" | sudo tee -a $HOME/.bashrc

hduser@node:~$ echo "" | sudo tee -a $HOME/.bashrc
hduser@node:~$ echo "unalias fs &> /dev/null" | sudo tee -a $HOME/.bashrc
hduser@node:~$ echo "alias fs &>"hadoop fs"" | sudo tee -a $HOME/.bashrc
hduser@node:~$ echo "unalias hls &> /dev/null" | sudo tee -a $HOME/.bashrc
hduser@node:~$ echo "alias hls="fs -ls" | sudo tee -a $HOME/.bashrc
hduser@node:~$ echo "" | sudo tee -a $HOME/.bashrc
hduser@node:~$ echo "export PATH=$PATH:$HADOOP_HOME/bin" | sudo tee -a $HOME/.bashrc

There are a few changes that must be made to the configuration files in /usr/local/hadoop/etc/hadoop which inform the HDFS and MapReduce layers. Editing these on every machine at once via SuperPutty requires skill, especially when, having made the changes, you realise that you can’t send an “escape” character to every machine at once. There’s a solution involving mapping other, sendable, characters to the escape key, but that’s “out of scope” here 😉 Here’s what the files should look like.

core-site.xml

It needs to look like this on all machines, master and slave alike:

[code language=”xml”]
<configuration>
<property>
<name>fs.default.name</name>
<value>hdfs://master:9000</value>
</property>
<property>
<name>hadoop.tmp.dir</name>
<value>/usr/local/hadoop/tmp</value>
</property>
</configuration>[/code]

hadoop-env.sh

There’s only one change that needs to be made to this mofo; locate the line which specifies JAVA_HOME (helpfully commented with “the Java implementation to use”). Assuming a Java setup like that described above, this should read

32 bit machines:

export JAVA_HOME=/usr/lib/jvm/jre1.6.0_34/

64 bit machines:
export JAVA_HOME=/opt/jdk1.6.0_45/

hdfs-site.xml

This specifies the replication level of file blocks. Note that your physical storage size will be divided by this number to give the storage you’ll have in HDFS.

[code language=”xml”]
<configuration>
<property>
<name>dfs.replication</name>
<value>3</value>
</property>
</configuration>[/code]

Additionally, it’s necessary to create a local directory on each box for Hadoop to use:
hduser@node:~$ sudo mkdir -p /app/hadoop/tmp
hduser@node:~$ sudo chown hduser:hadoop /app/hadoop/tmp

mapred-site.xml

Which MapReduce implementation to use. At the moment we’re on YARN (“Yet Another Resource Negotiator”…………).

[code language=”xml”]
<configuration>
<property>
<name>mapreduce.framework.name</name>
<value>yarn</value>
</property>
</configuration>[/code]

yarn-site.xml

Controls the actual MapReduce configuration. Without further ado, this is what you want:

[code language=”xml”]
<configuration>
<property>
<name>yarn.nodemanager.aux-services</name>
<value>mapreduce_shuffle</value>
</property>
<property>
<name>yarn.nodemanager.aux-services.mapreduce_shuffle.class</name>
<value>org.apache.hadoop.mapred.ShuffleHandler</value>
</property>
<property>
<name>yarn.resourcemanager.resource-tracker.address</name>
<value>master:8025</value>
</property>
<property>
<name>yarn.resourcemanager.scheduler.address</name>
<value>master:8030</value>
</property>
<property>
<name>yarn.resourcemanager.address</name>
<value>master:8040</value>
</property>
</configuration>[/code]

Slaves

In short, the master needs to consider itself and every other node a slave. Each slave needs to consider itself, and itself only, a slave. The entirety of your slaves file ought to look like this:

Master:
master
slave001
slave002
slave003
etc

Slave xyz:
slavexyz

Formatting the Filesystem

Much like manually deleting your data, formatting a HDFS filesystem containing data will delete any data you might have in it, so don’t do that if you don’t want to delete your data. Warnings notwithstanding, execute the following on the master node to format the HDFS namespace:
hduser@master:~$ cd /usr/local/hadoop
hduser@master:~$ bin/hadoop namenode -format

Bringing up the Cluster

This is the moment that the band strikes up. If you’re not already there, switch to the Hadoop directory…
hduser@master:~$ cd /usr/local/hadoop

Fire this shizz to start the DFS layer:
hduser@master:/usr/bin/hadoop$ sbin/start-dfs.sh

You should see this kind of thing:
WARN util.NativeCodeLoader: Unable to load native-hadoop library for your platform... using builtin-java classes where applicable
starting namenodes on [master]
master: starting namenode, logging to /usr/local/hadoop/logs/hadoop-hduser-namenode-master.out
slave001: starting datanode, logging to /usr/local/hadoop/logs/hadoop-hduser-datanode-slave001.out
slave002: starting datanode, logging to /usr/local/hadoop/logs/hadoop-hduser-datanode-slave002.out
slave003: starting datanode, logging to /usr/local/hadoop/logs/hadoop-hduser-datanode-slave003.out
...etc

Now start the MapReduce layer:
hduser@master:/usr/local/hadoop$ sbin/start-yarn.sh

Expect to be greeted by something like this:
starting yarn daemons
starting resourcemanager, logging to /usr/local/hadoop/logs/yarn-hduser-resourcemanager-master.out
slave001: starting nodemanager, logging to /usr/local/hadoop/logs/yarn-hduser-nodemanager-slave001.out
slave002: starting nodemanager, logging to /usr/local/hadoop/logs/yarn-hduser-nodemanager-slave002.out
slave003: starting nodemanager, logging to /usr/local/hadoop/logs/yarn-hduser/nodemanager-slave003.out
...

Also start the job history server…
hduser@master:/usr/local/hadoop$ sbin/mr-jobhistory-daemon.sh start historyserver

Surveying One’s Empire

By this stage your Hadoop cluster is humming like a dynamo. There are several web interfaces which provide a tangible window into the specification of the cluster as a whole…

For the DFS layer, have a look at http://master:50070.

DFS Interface

And for a breakdown of the exact condition of each node in your DFS layer,

DFS Interface 2

And for the MapReduce layer, look at http://master:8088,

YARN Interface

The First Distributed MapReduce

MapReduce is nothing more than a certain way to phrase a script to process a file, which is friendly to distributed computing. There’s a mapper, and a reducer. The “mapper” must be able to process any arbitrary fragment of the file (eg, count the number of occurrences of something within that fragment), independently and obliviously of the contents of the rest of the file. This is why it’s so scalable. The “reducer” aggregates the outputs of the mappers to give the final result (eg, sum up the occurrences of something reported by each of the mappers to give the total number of occurrences). Again, the way that you only have to write the mapper and reducer, and Hadoop handles the rest (deploying a copy of the mapper to every worker node, “shuffling” the mapper outputs for the reducer, re-allocating failed maps etc), is why Hadoop is well good. Indeed, a well-maintained cluster is much like American dance/rap duo LMFAO: every day it’s shuffling.

Later in this blog we’ll address how to write MapReduces; for now let’s just perform one and let the cluster stretch its legs for the first time.

Make a cheeky text file (example.txt):
Example text file
Contains example text

Make a directory in HDFS, lob the new file in there, and check that it’s there:
hduser@master:/usr/local/hadoop$ bin/hadoop fs -mkdir /test
hduser@master:/usr/local/hadoop$ bin/hadoop fs -put example.txt /test
hduser@master:/usr/local/hadoop$ bin/hadoop fs -ls /test
WARN util.NativeCodeLoader: Unable to load native-hadoop library for your platform... using builtin-java classes where applicable
Found 1 items
-rw-r--r-- 3 hduser supergroup 50 2013-12-23 09:09 /test/example.txt

As you can see, the Hadoop file system commands are very similar to the normal Linux ones. Now run the example MapReduce:
hduser@master:/usr/local/hadoop$ bin/hadoop jar share/hadoop/mapreduce/hadoop-mapreduce-examples-2.2.0.jar wordcount /test /testout

Hadoop will immediately inform you that a load of things are now deprecated – ignore these warnings, it seems that deprecation is the final stage in creating new Hadoop modules – and then more interestingly keep you posted on the progress of the job…
INFO mapreduce.JobSubmitter: Submitting tokens for job: job_1387739551023_0001
INFO impl.YarnClientImpl: Submitted application application_1387739551023_0001 to ResourceManager at master/1.1.1.1:8040
INFO mapreduce.Job: The url to track the job: http://master:8088/proxy/application_1387739551023_0001/
INFO mapreduce.Job: Running job: job_1387739551023_0001
INFO mapreduce.Job: Job job_1387739551023_0001 running in uber mode : false
INFO mapreduce.Job: map 0% reduce 0%
INFO mapreduce.Job: map 100% reduce 0%
INFO mapreduce.Job: map 100% reduce 100%
INFO mapreduce.Job: Job job_1387739551023_0001 completed successfully
INFO mapreduce.Job: Counters: 43
File System Counters
FILE: Number of bytes read=173
FILE: Number of bytes written=158211
FILE: Number of read operations=0
FILE: Number of large read operations=0
FILE: Number of write operations=0
HDFS: Number of bytes read=202
HDFS: Number of bytes written=123
HDFS: Number of read operations=6
HDFS: Number of large read operations=0
HDFS: Number of write operations=2
Job Counters
Launched map tasks=1
Launched reduce tasks=1
Rack-local map tasks=1
Total time spent by all maps in occupied slots (ms)=7683
Total time spent by all reduces in occupied slots (ms)=11281
Map-Reduce Framework
Map input records=2
Map output records=11
Map output bytes=145
Map output materialized bytes=173
Input split bytes=101
Combine input records=11
Combine output records=11
Reduce input groups=11
Reduce shuffle bytes=173
Reduce input records=11
Reduce output records=11
Spilled Records=22
Shuffled Maps =1
Failed Shuffles=0
Merged Map outputs=1
GC time elapsed (ms)=127
CPU time spent (ms)=2570
Physical memory (bytes) snapshot=291241984
Virtual memory (bytes) snapshot=1030144000
Total committed heap usage (bytes)=181075968
Shuffle Errors
BAD_ID=0
CONNECTION=0
IO_ERROR=0
WRONG_LENGTH=0
WRONG_MAP=0
WRONG_REDUCE=0
File Input Format Counters
Bytes Read=101
File Output Format Counters
Bytes Written=123
hduser@master:/usr/local/hadoop$

GLORY. We can examine the output thus:
hduser@master:/usr/local/hadoop$ bin/hadoop fs -ls /testout
WARN util.NativeCodeLoader: Unable to load native-hadoop library for your platform... using builtin-java classes where applicable
Found 2 items
-rw-r--r-- 3 hduser supergroup 50 2013-12-23 09:10 /testout/_SUCCESS
-rw-r--r-- 3 hduser supergroup 50 2013-12-23 09:10 /testout/part-r-00000
hduser@master:/usr/local/hadoop$ bin/hadoop fs -cat /testout/part-r-00000
WARN util.NativeCodeLoader: Unable to load native-hadoop library for your platform... using builtin-java classes where applicable
Contains 1
Example 1
example 1
file 1
text 2

Business value, delivered. If you want to retrieve the output file from HDFS back to your local filesystem, run
hduser@master:/usr/local/hadoop$ bin/hadoop fs -get /testout
hduser@master:/usr/local/hadoop$ ls | grep testout
testout

And there it is! Now that your Hadoop cluster is essentially a self-aware beacon of supercomputing, stay tuned for further posts on using Hadoop to do interesting/lucrative things! 🙂

UK House Sales – More Seasonality in Time Series with R

So the average sale price of houses in the UK is seasonal. Does that mean it’s sensible to advise house buyers to only purchase in the winter months? Let’s try to see.

I’m going to have a look and see if the data we have implies that the change in average sale price of a house with the month is actually just a function of some other monthly variation. I don’t really know how to go about doing this but it’s probably best to not let things like that stop me – I’m thinking the first port of call is likely calculate the correlation between the month each of the other factors (excluding price). If there’s a decent correlation (positive or negative) then we might be in trouble and will have to investigate that variable with a bit more seriousness.

Again, that’d be a delightfully easy task if I could hold the entire dataset in memory. Unfortunately I’m not that lucky and so I’ll have to do a bit of aggregation before importing the data to R/Python.

So my independent variables:

1.) Region
2.) Type of house
3.) New or old house
4.) Freehold or leasehold

I’m thinking of the work we did in the last blog post in Python and that that might be the best way to proceed; to generate vectors containing the average proportion of sales due to each ‘test group’ (the factors of the independent variable in question) in each of the relevant years. Once I’ve got that, I’m initially thinking of a twelve variant paired t-test. We’ve got 12 different months – in each month we’ve got a year for which each of the other test groups have a corresponding year, hence the choice of paired t-test. However, previously when I grievously abused the normality assumption required to run a t-test I had a whole bunch of data (800,000 points) and so I was sort of O.K with it. Now, I’ve got 18. We may have to investigate other options – Kruskal-Wallis being at the forefront of those. Anyway – let’s worry about that when we have to.

First things first, let’s get this data into a format we can load into memory:

awk -F, '{print $4"-"$(NF-1)}' pp-all.csv | cut -d '-' -f1,2,4 | tr -d '"' | tr '-' ' ' | sed -e 's/s+/-/' | sed -e 's/s+/,/' | sort | uniq -c | sort -s -nk2 | sed 's/^ *//' | sed -e 's/s+/,/' | awk -F, '{if ($3 != "2014-01") print $0}' > number_of_sales_by_region.txt

Again, a horrible one-liner that I’ll have to apologise for. All it does is give me an output file with the format: Count | Month | Region – off of the back of that I can now use R:

library(plyr)
library(ggplot2)
library(scales)
myData <- read.csv('number_of_sales_by_region.txt', header=F, sep=',', col.names=c("Sales", "Datey", "Region"))
## To store as a date object we need a day - let's assume the first of the month
myData$Datey <- as.Date(paste(myData$Datey, 1, sep="-"), format="%Y-%m-%d")
## I'm not too worried about January 2014 - it makes the lengths of the 'month vectors' uneven and ruins the below graphs
myData <- myData[format(myData$Datey, "%Y") < 2014,]
byYear <- data.frame(aggregate(Sales ~ format(Datey, "%Y"), data = myData, FUN=sum))
colnames(byYear) <- c("Year", "houseSales")
ggplot(byYear, aes(x=Year, y=houseSales)) + geom_bar(stat="identity") + ggtitle("Number of UK House Sales") + theme(axis.text.x = element_text(angle=90, hjust=1)) + scale_y_continuous(name="Houses Sold", labels=comma)
byMonth <- data.frame(aggregate(Sales ~ format(Datey, "%m"), data = myData, FUN=sum))
colnames(byMonth) <- c("Month", "houseSales")
byMonth$Month <- factor(month.name, levels=month.name)
ggplot(byMonth, aes(x=Month, y=houseSales)) + geom_bar(stat="identity") + ggtitle("Number of UK House Sales") + theme(axis.text.x = element_text(angle=90, hjust=1)) + scale_y_continuous(name="Houses Sold", labels=comma)

Giving us what’d I’d class as a couple of very interesting graphs:

Number of UK House Sales by Year

Number of UK House Sales by Year

and:

UK House Sales by Month

Number of UK House Sales by Month

In terms of the housing crash, we saw it a bit in the average house sale price but we can see the main impact was a complete slow-down on the number of houses sold. There are potentially hints of a re-awakening in 2013 but I guess we’ll have to see how this year ends up panning out. The monthly variation is interesting and at first glance, counter-intuitive when viewed alongside the average house price data. Naively, you’d expect the average house price to be highest when fewer houses were being sold (what with number of houses being the denominator and all). I’m not too bothered in digging into the relationship between number of houses sold and average house sale price (I’ve got the feeling that it’s the sort of thing economists would concern themselves with) so won’t really be looking at that. I am however now at least a bit interested in the most sold houses in the UK – I don’t know what I’ll uncover but I’m marking it down as something to look at in the future.

Anyway, now we’ve had a first look at our data let’s see if we can track the proportion of UK house sales made by each region. There are likely a few ways to do this in R; I’ll be picking the SQL-esque way because I use SQL a lot more than I use R and so am more familiar with the ideas behind it. I’d be glad to be shown a more paradigmically R way to do it (in the comments):

myData$Year <- format(myData$Datey, "%Y")
myData <- merge(x=myData, y=byYear, by = "Year")
myData$Percent <- 100*(myData$Sales/myData$houseSales)
## I'm not very London-centric but given that they're the biggest house sellers in the UK...
londontimeseries <- ts(myData[myData$Region == 'GREATER LONDON',]$Percent, frequency=12, start=c(1995, 1))
london_decomposed <- decompose(londontimeseries)
plot(london_decomposed)
seasonality <- data.frame(london_decomposed$seasonal[c(1:12)])
colnames(seasonality) <- c("Sales", "Month")
ggplot(seasonality, aes(x=Month, y=Sales)) + geom_bar(stat="identity") + ggtitle("Seasonal variations in London's proportion of UK House Sales") + theme(axis.text.x = element_text(angle=90, hjust=1)) + scale_y_continuous(name="$ of London's % of total UK house sales", labels=percent)

giving:

London's proportion of UK House Sales

The percent of UK house sales that were made in Greater London between 1995 and 2014 and inferences around the overall trend and seasonality

and the bit we were after:

Seasonal Variations in London's Percent of the UK Housing Market (by number sold)

Seasonal Variations in London’s Percent of the UK Housing Market (by number sold)

Well, I don’t really know if that’s good news or bad. It’s good in the fact that we thought to check the factors behind seasonal variations in house price. It’s bad because I can no longer advise people to buy houses in the winter (I’ve checked and there’s a seasonal variation for every region I tried). In all honesty, I think the two graphs above are really interesting. I’m saying that the housing crash effected London more strongly than the rest of the country, but that the market in London bounced back within a year and is now above pre-crash levels. The size of the seasonal variations is pretty marked as well, with 20% swings either way from London’s mean value of percent of total house sales (sorry if the language seems verbose – I’m being careful to be precise).

What does this mean for our investigation into the seasonality of the average house price? Well, I’m confident that the average house price is seasonal but I’m also confident that we can’t use that to advise people when they should be selling their house (just yet).

There are a couple of pieces of analysis I’d now like to do on this data. I think it’d be really interesting to get an idea of the ‘most-sold’ house in the UK since 1995. I also think there may be surprises around the correlation between the number of times a house is sold and its selling price. However, this seasonality by region is also really interesting and I think I’d like to try to cluster regions based on the seasonality of their housing market. It’d be interesting to graph the clusters and see if the divide is North/South, City/Country or something else entirely. Additionally, the (G.C.S.E) economist in me is screaming out for the same investigation as above but with total sale price instead of number sold.

UK House Prices – Seasonality in Time Series with R

Hi All,

After work over one year (approximately 800,000 data points) it’s time to start ramping things up a bit and we’ll be heading into the realms of big data. There are a bunch of definitions of big data floating around but I’m going to go with the one I like the most: “Big data is the point at which the size of your data becomes part of the problem.” That of course depends entirely on the hardware you’ve got and given my current hardware situation, as soon as we start looking at multiple years of house sale data, we’re firmly in ‘big data’ territory. In fact, the size of the data isn’t really that large – only ~20 million rows with a total size of 3.2GB. I could upgrade my RAM for a small amount and we’d be fine to deal with this in the usual ways. However, I’m cheap, the shops are closed and I’d rather think of a less hardware bound way of doing it.

Unfortunately for me, while working at home on my own projects, I don’t have access to any cluster of computers so won’t be throwing my data into HDFS and getting my mappers and reducers polished. At work we’re soon to be adding 40TB of storage and 10 more nodes to our existing cluster and that set up would chew through this sort of thing like nobody’s business. Given an i5 and 6GB of RAM, we’re going to have to be a tad more creative 😉 It’s also worth noting that, for 3.2GB of data, distributing the problem isn’t likely the most efficient solution. Just because I’m talking about big data, there’s no reason we can’t use R, Python, SQL or anything else that will solve the problem.

I liked what we were able to do in R and don’t feel I’ve had a sufficiently deep dive into the statistical functions it offers and so will be trying to use it again. Fitting all the data in memory isn’t going to work but R offers a number of packages for working with data that exceeds the RAM you’d be willing to give it; I’ll be using bigmemory.

First things first, all the data is split across text files. If we want to have them read into a single table I think we’ll be best creating that text file in bash and adding a new column with the year – bash to the rescue:


for file in pp-*.csv
do
echo "Processing $file...";
year=${file:3:4};
awk -F, -v year=$year '{print year","$0}' $file >> pp-all.csv;
done

At the risk of stating the obvious, that will loop over all the relevant files, extract the year from the title of the file, prepend it to the start of the line and then append the line to pp-all.

O.K – originally I was going to use bigmemory but have found it unsuitable for the task (namely, I couldn’t even get it to load the file from disk). I’m sure that’s more a damning indictment of my own ability rather than bigmemory but I’ll proceed in a different way for now.


cut -d ',' -f3,4 pp-all.csv | tr -d '"' | cut -d '-' -f1,2 | awk -F, '{ total_array[$2] += $1; count_array[$2] += 1} END {for (region in total_array) print region"t"total_array[region]/count_array[region]}' | tr '-' ' ' | sort -nk1 -nk2 | sed -e 's/s+/-/' > price_summary_by_month.txt

OK – it’s a bit of a nasty one-liner but it basically:
1.) Gets the date and house sale price
2.) Formats the output
3.) Create an array of the count and sum of sale prices per month
4.) Sort by date and format
5.) Output to price_summary_by_month.txt

Now I’ve got myself a lovely text file – I decided to have a dig into Python and especially, Matplotlib. As it’s not really relevant to the overall direction of this analysis I won’t include the code here but it’s available on my Github. As a summary, this script looks at the percentage of total value of the year’s sales made in each month. A vector is built for each month and then the Gaussian density is calculated for that month. This is plotted versus the surrounding months. I’m aware that’s likely a poor explanation but if you’re interested, have a look at the code and feel free to drop me a comment. The output is something like this:

Python sample figure

% of value of house sales since 1995, by month.

Anyway, back to the main thread of the investigation. I’ve got a relatively small time-series and I’m investigating the periodicity of the data – I’m right back in native R territory.

priceSummary <- read.table('price_summary_by_month.txt', header=F, col.names=c("date", "price"))
pricetimeseries <- ts(priceSummary$price, frequency=12, start=c(1995,1))
plot(pricetimeseries, ylab="Average sale price (£)", main="UK House Prices")

Giving us:

UK House Prices

Average UK House Price (by month)

That’s pretty much as you’d expect – generally rising prices with a bit of a wobble around the housing crash. Disappointingly, there doesn’t seem to be that much evidence of seasonality being a factor. However, R provides us the tools to see whether or not that’s the case:

library(ggplot2)
library(scales)
pricetimeseriescomponents <- decompose(pricetimeseries)
plot(pricetimeseriescomponents)
seasonality <- data.frame(pricetimeseriescomponents$seasonal[c(1:12)])
seasonality$Month <- factor(month.name, levels=month.name)
colnames(seasonality) <- c("Price", "Month")
ggplot(seasonality, aes(x=Month, y=Price)) + geom_bar(stat="identity") + ggtitle("Seasonal variations in house sale price") + theme(axis.text.x = element_text(angle=90, hjust=1)) + scale_y_continuous(name="Price difference (£)", labels=comma)
orderedSeasonality <- transform(seasonality, Month = reorder(Month, Price))
ggplot(orderedSeasonality, aes(x=Month, y=Price)) + geom_bar(stat="identity") + ggtitle("Seasonal variations in house sale price") + theme(axis.text.x = element_text(angle=90, hjust=1)) + scale_y_continuous(name="Price difference (£)", labels=comma)

This gives us our first hint at some real cyclicity to the housing market:

Decomposition of UK House Prices

Decomposition of UK House Prices

 

House price seasonality

Seasonality of House Prices – the amount above/below average you’ll pay for a house based on the month

and a perhaps more helpful, sorted version:

Ordered house price seasonality

Ordered seasonality of House Prices – the amount above/below average you’ll pay for a house based on the month

Well well well. Time to throw the cowboy hat into the air, unholster our pistol and start firing wildly into the sky? Or at least quietly inform those who I know who are looking to buy/sell a house that they can likely save/make themselves an extra £10,000 or so if only they’re willing to wait until summer before selling?

Unfortunately, I’m not confident enough to say that just yet. I’ve already fairly conclusively shown that there are a bunch of factors that affect the sale price of a house. Now while I’m happy to say that the month of the year is significant in determining the sale price, I don’t really know why. It could be that people are more inclined to buy houses in the south during summer. As these houses are more expensive, we see the average house price rise in the summer months. It could be that people are less inclined to buy terraced houses during the summer (heating concerns?) and, as terraced houses are generally cheaper, the average sale price is inflated.

If either of those statements, or indeed, any other like it that I’ve not thought of are true it could lead to me giving bad advice in specific cases. To be able to report anything especially useful (and ultimately, actionable) we’ll need to look a bit closer at the causes of seasonality. My next post will hopefully address these issues and will try to determine whether or not the average UK house buyer is better off waiting until winter before buying.

Monthly House Price Variation – an adventure in R

So we’ve got our data set, we’ve had a cursory investigation and now we’re ready to see if we can find anything interesting. I’m going to proceed in a fairly methodical way and be precise in the way I do things – let’s do this scientific like.

So let’s start with a null hypothesis: “The month alone has no impact on the average selling price of houses“.

At this point, I don’t really know whether or not that’s true but it seems likely that it’s not. I can imagine that the housing market is, to some extent, cyclical. The first thing I’ll do is plot the data – there are a number of reasons why this is a good idea and I’d advise plotting your data wherever possible as a first step.

I’ll run this example investigation in R – it’s great for exploratory analysis and it allows me to produce graphics that I can share really easily.

housingData <- read.csv('pp-2013.csv', header=TRUE)
housingData$date <- as.Date(housingData$date, "%Y-%m-%d %H:%M")
# We're only interested in the month at this point
housingData$month <- strftime(housingData$date, "%m")
housingDataSummary <- data.frame(aggregate(housingData$price, by=list(housingData$month), FUN=mean)
colnames(housingDataSummary) <- c("Month", "Price")
# It's nice to have a look at the data before we perform our test on it, just to get an idea of how it looks and to check we think what we've done up to this point is reasonable.
# Let's take advantage of a very commonly used R library - ggplot2
library(ggplot2)
ggplot(housingDataSummary, aes(x=housingDataSummary$Month, y=housingDataSummary$Price, fill=housingDataSummary$Price)) + geom_bar(stat="identity", width=0.4, position=position_dodge(width=0.5)) + guides(fill=FALSE) + xlab("Month") + ylab("Average price") + ggtitle("Average GB house sale price in 2013")+ scale_y_continuous(labels=comma) + coord_fixed(ratio=0.000035)

Giving us:

Average house price by month in the UK in 2013

Average house price by month in the UK in 2013

O.K – I don’t know about you but looking at the graph I’d say it looks like there might be something to the theory that the month is important in house sales. In this year, we can see a dip in the early months and then a peak when we get to summer.

Let’s shore up the mathematics behind this – I’m going to imagine the situation where I’ve got twelve test groups (one for each month) where my values are the sold house prices. There’s a whole lot of statistical tests designed for this situation. To compare the means of these groups with each other I’d perform a one-way ANOVA (analysis of variance) – a multivariate extension of the t-test. Technically, the assumptions made in performing a one-way are independence of measurements (I’m happy that the sale price of one house is independent of the sale of another), continuity of the dependent variable (house price is continuous) and the dependent variables come from a normal distribution. A simple density plot shows us that the house prices aren’t normally distributed:

2013 house price density plot

2013 house price density plot

However, fear not. The t-test is still a good choice of test under violations of normality, especially so when there are lots of data points (we’ve got over 700,000) . As a little check, let’s also have a go at comparing the medians of the test groups. To do this we can use the Mann-Whitney U test and its multivariate brother, the Kruskal-Willis test. These are non-parametric tests (don’t require normally distributed data) and so if these say the medians of the groups are significantly different and the one-way ANOVA has shown the means of the groups are significantly different, we can be fairly confident they are!

month_aov <- aov(price ~ month, data=housingData)
summary(month_aov)
print(model.tables(month_aov, "means"), digits=2)
kruskal.test(price ~ as.factor(month), data=housingData)

Giving us:


Df Sum Sq Mean Sq F value Pr(>F)
month 11 4.463e+13 4.057e+12 46.38 <2e-16 ***
Residuals 781167 6.834e+16 8.748e+10
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Tables of means
Grand mean

246834.8

month
01 02 03 04 05 06 07 08 09 10 11 12
245200 234879 235136 242679 237509 243942 257421 256289 256988 249722 245077 246392
rep 43404 45238 54692 51025 66357 66175 73526 79119 69314 76042 80986 75301


Kruskal-Wallis rank sum test

data: price by as.factor(month)
Kruskal-Wallis chi-squared = 1642.505, df = 11, p-value < 2.2e-16

There’s an awful lot of that that we’re not interested in – the key bits for us to pick out are the p-values on the ANOVA and the Kruskal-Wallis tests – both of which are < 2e-16. We can fairly conclusively say that there are statistically significant differences between the mean and median of the average house prices by month.

However, let’s have a think what assumptions we’re making and whether we’re comfortable making them. Firstly, a previous investigation has hinted that the region the house is in makes a difference to the sale price. This could impact our data in any number of ways – it could be that each region sells their houses at different times and as average house value per region is different then the average house value per month ends up being different. Obviously, region isn’t the only concern – I singled that out as I’ve previously looked at it and know it’s a contributing factor to house price.

Additionally, we’re only looking in one year. That means that any overall change in house prices (ala the property market crash) will completely throw our results off and give us the (possibly false) impression of a cyclical housing market.

There’s an awful lot more we’ll have to consider if we’re to answer our question satisfactorily: does the month impact the selling price of a house? In the next post in this series I’ll be looking at ways of unpicking dependencies (MANOVA and MANCOVA) and will likely have to do bits of the analysis in a distributed way as there’s no way the entire dataset (since 1995) is going to fit in my RAM!

Installing R on Ubuntu 14.04

A quick break from our analysis of UK Government house sale data – I’ve decided that I’d like to do the analysis in R (reasons for this will be explained in a later post). A new version of Ubuntu is out (Trusty Tahr) and, after updating, I realised I didn’t have R on my computer. So, a quick and simple guide to installing R:

Step 1:

Assuming you’ve got the internet and everything set up as it should be run:
sudo apt-get install r-base-core

Go ahead and accept the new 147MB (or thereabouts) and you should now be able to type R at the terminal and see R (verion 3.0.2 at the time of writing) fire up. If this hasn’t worked, drop me a comment and I’ll see what we can do about it.

Step 2:

Now – assuming you’re going to want a bit more than the standard packages (I’d strongly advise ggplo2 – it’s well good), you’ll want r-base-dev. I’d give the following command a go:

sudo apt-get install r-base-dev

Fortunately, it looks to me like this is bundled with r-base-core now so that command didn’t do anything so might not be necessary. But no harm done, eh?

Now, open up R with sudo privileges (if you don’t do this and have the standard permissions and install locations, R won’t have permissions to write to /usr/lib – you can use your personal library if you like, but I won’t):

sudo R

and (for here in on, we’re in the R terminal) run:

update.packages()

There are a bunch of libraries you may be interested in, but for me (and indeed, for the next bit of data analysis I’m going to do) ggplot2 will suffice.

install.packages('ggplot2', dependencies=TRUE)

If that worked you should now be able to type library(ggplot2) without errors.

Step 3:

While I’m sure you’re a big fan of just bashing out your R code in the terminal, sometimes it’s nice to have an IDE and RStudio is at the front of the pack when it comes to R IDEs. Getting this on Ubuntu is a doddle.

Head on over to the R Studio download site and download the version with Ubuntu in the name (RStudio 0.98.501 – Debian 6+/Ubuntu 10.04+ (64-bit) for my system at the time of writing). You can then open this file using Ubuntu Software Centre (it should open in this by default) – click install and you’re on your way!

Now, everything being OK you should be able to open up R Studio and develop away to your heart’s content 🙂 If there are any problems with this, I’d encourage you to leave comments and we’ll see if we can get to the bottom of this. As a point of interest, if you need any more packages installing, you’ll need to pop into terminal, open up R in sudo mode and install them from there. There are fixes for this (check out the official R documentation for this) but I don’t think it’s that much of a problem that it’s worth bothering with.

Average House Price Visualization using Python and Google Charts

Hi all,

Only yesterday I came across a rich store of data that I had hitherto been unaware of; namely, data.gov.uk. Giddy with joy, I perused the mountains of interesting data and thought it’d be fun to pull together a visualization based on some of it. One particular set caught my eye: all of the house sales in the UK in the last 19 years (link to the data at the bottom).

So,  the first question that sprung to mind was “How does the average house price vary by region?”

First things first, let’s calculate the average house price per locale using (only) Python:


def average_price(year):
    with open('pp-' + str(year) + '.csv', 'rb') as f:
        lines = f.readlines()[1:]
        for line in lines:
            try:
                identifier, price, date, postcode, type_of_house, new, freehold_or_leasehold, address_1, address_2, address_3, address_4, address_5, address_6, address_7, letter = line.split(',')
            except:
                continue
            try:
                data_dictionary[address_7.strip('"').lower()].append(int(price.strip('"')))
            except:
                data_dictionary[address_7.strip('"').lower()] = [int(price.strip('"'))]
        final_results = dict((key, sum(value)/float(len(value))) for key,value in data_dictionary.iteritems())
        return final_results

So, we’ve built ourselves a nice little function that’ll take the year as an input, open up the relevant data file, calculate the average house price by region and return the result in a dictionary. Easy does it.

Please note at this point that there are a million ways to do what we’ve just done ranging from sticking the raw CSV into Excel and using pivot tables, loading the data into R and performing an aggregate on the region, using Panda’s excellent data frames or in fact using a bash one-liner (a favourite of mine):
cut -d ',' -f2,14 pp-2014.csv | tr -d '"' | awk '{region[$2] += $1; region_count[$2]++;} END { for (area in region) print area"t"region[area]/region_count[area]}' .
However, I’m sticking to Python for reasons hopefully soon to become clear.

So now we can see that Stoke-on-Trent is very cheap and London is very expensive. Can we see this data changing over time?

I decided the nicest way of piecing this together was using a jQuery slider to select the year, a Google Geocharts frontend to visualize the data and then a lightweight Python web framework to hold the whole thing together. I chose web.py because I’ve used it before and think it’s great for work with AJAX and is also useful when you’ve already written your Python functions and just need something that won’t get in your way too much.

I’m not going to show all the code here but you can find my finished versions on my Github:
Back end
Front end

There are a couple of details that are contained in that code that I’ve not dealt with.

Firstly, Google Charts API doesn’t work with the place names listed in the Government data. As such, you’ll see I’ve written a little lookup function to map Government place names to ISO-3166 Codes as required by Google. There’s a bit of fuzzy matching going on here but if you navigate around in that repo, you’ll find I tested a few things and settled on a decent solution. When I can be bothered I’ll go and tidy that up by filling in the missing ISO codes manually.

Secondly, you’ll notice (if you get this running on your own computer) that the visualization is fairly slow. It runs calculations over the entire data set each time a query is run. What’s more, it then tries to render around 100 points on the Google Chart. Given that there are only a limited number of ways you’d ever want the user to be able to query the data and that the data doesn’t change day on day, you’d want to pre-aggregate the results and store them in a database somewhere.

Thirdly, you’ll note that this blog doesn’t contain the visualization. Pretty shoddy on my part, just haven’t got around to doing that yet.

That’s one of the problems with this data science malarkey, I could spend my time building my own blog platform that allows me to serve simple web apps. I could spend my time sticking in a simple database caching solution to speed up the apps on localhost. I could tidy up the fuzzy matching on the ISO codes to create an 100% correct mapping. However, it seems much more interesting to head off and see what else this data contains.

Next stop – is there a better time to buy/sell a house? Do house prices go up in certain months? I’ll try to answer that question fairly thoroughly with due consideration to statistical significance along the way.

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