Introduction to Big Data/Machine Learning

Introduction to Machine Learning
2012-05-15
Lars Marius Garshol, larsga@bouvet.no, http://twitter.com/larsga
1

Agenda
• Introduction
• Theory
• Top 10 algorithms
• Recommendations
• Classification with naïve Bayes
• Linear regression
• Clustering
• Principal Component Analysis
• MapReduce
• Conclusion
2

The code
3
• I’ve put the Python source code for the
examples on Github
• Can be found at
– https://github.com/larsga/py-
snippets/tree/master/machine-learning/

What is big data?
7
Big Data is
any thing
which is
crash Excel.
Small Data is
when is fit in RAM.
Big Data is when is
crash because is
not fit in RAM.
Or, in other words, Big Data is data
in volumes too great to process by
traditional methods.
https://twitter.com/devops_borat

Data accumulation
• Today, data is accumulating at tremendous
rates
– click streams from web visitors
– supermarket transactions
– sensor readings
– video camera footage
– GPS trails
– social media interactions
– ...
• It really is becoming a challenge to store
and process it all in a meaningful way
8

From WWW to VVV
• Volume
– data volumes are becoming unmanageable
• Variety
– data complexity is growing
– more types of data captured than previously
• Velocity
– some data is arriving so rapidly that it must either
be processed instantly, or lost
– this is a whole subfield called “stream processing”
9

The promise of Big Data
• Data contains information of great
business value
• If you can extract those insights you can
make far better decisions
• ...but is data really that valuable?

13
“quadrupling the average cow's
milk production since your parents
were born”
"When Freddie [as he is known]
had no daughter records our
equations predicted from his DNA
that he would be the best bull,"
USDA research geneticist Paul
VanRaden emailed me with a
detectable hint of pride. "Now he is
the best progeny tested bull (as
predicted)."

Some more examples
14
• Sports
– basketball increasingly driven by data analytics
– soccer beginning to follow
• Entertainment
– House of Cards designed based on data analysis
– increasing use of similar tools in Hollywood
• “Visa Says Big Data Identifies Billions of
Dollars in Fraud”
– new Big Data analytics platform on Hadoop
• “Facebook is about to launch Big Data
play”
– starting to connect Facebook with real life
https://delicious.com/larsbot/big-data

Ok, ok, but ... does it apply to our
customers?
• Norwegian Food Safety Authority
– accumulates data on all farm animals
– birth, death, movements, medication, samples, ...
• Hafslund
– time series from hydroelectric dams, power prices,
meters of individual customers, ...
• Social Security Administration
– data on individual cases, actions taken, outcomes...
• Statoil
– massive amounts of data from oil exploration,
operations, logistics, engineering, ...
• Retailers
– seeTarget example above
– also, connection between what people buy, weather
forecast, logistics, ...
15

How to extract insight from data?
16
Monthly Retail Sales in New SouthWales
(NSW) Retail Department Stores

Types of algorithms
17
• Clustering
• Association learning
• Parameter estimation
• Recommendation engines
• Classification
• Similarity matching
• Neural networks
• Bayesian networks
• Genetic algorithms

Basically, it’s all maths...
18
• Linear algebra
• Calculus
• Probability theory
• Graph theory
• ...
18
Only 10% in
devops are know
how of work
with Big Data.
Only 1% are
realize they are
need 2 Big Data
for fault
tolerance

Big data skills gap
• Hardly anyone knows this stuff
• It’s a big field, with lots and lots of theory
• And it’s all maths, so it’s tricky to learn
19
http://wikibon.org/wiki/v/Big_Data:_Hadoop,_Business_Analytics_and_Beyond#The_Big_Data_Skills_Gap
http://www.ibmbigdatahub.com/blog/addressing-big-data-skills-gap

Two orthogonal aspects
20
• Analytics / machine learning
– learning insights from data
• Big data
– handling massive data volumes
• Can be combined, or used separately

Data science?
21 http://drewconway.com/zia/2013/3/26/the-data-science-venn-diagram

How to process Big Data?
22
• If relational databases are not enough,
what is?
Mining of Big
Data is
problem solve
in 2013 with
zgrep

MapReduce
23
• A framework for writing massively parallel
code
• Simple, straightforward model
• Based on “map” and “reduce” functions
from functional programming (LISP)

NoSQL and Big Data
24
• Not really that relevant
• Traditional databases handle big data sets,
too
• NoSQL databases have poor analytics
• MapReduce often works from text files
– can obviously work from SQL and NoSQL, too
• NoSQL is more for high throughput
– basically, AP from the CAP theorem, instead of CP
• In practice, really Big Data is likely to be a
mix
– text files, NoSQL, and SQL

The 4th V: Veracity
25
“The greatest enemy of knowledge is not
ignorance, it is the illusion of knowledge.”
Daniel Borstin, in The Discoverers (1983)
95% of time,
when is clean Big
Data is get Little
Data

Data quality
• A huge problem in practice
– any manually entered data is suspect
– most data sets are in practice deeply problematic
• Even automatically gathered data can be a
problem
– systematic problems with sensors
– errors causing data loss
– incorrect metadata about the sensor
• Never, never, never trust the data without
checking it!
– garbage in, garbage out, etc
26

27 http://www.slideshare.net/Hadoop_Summit/scaling-big-data-mining-infrastructure-twitter-experience/12

Conclusion
• Vast potential
– to both big data and machine learning
• Very difficult to realize that potential
– requires mathematics, which nobody knows
• We need to wake up!
28

Two kinds of learning
30
• Supervised
– we have training data with correct answers
– use training data to prepare the algorithm
– then apply it to data without a correct answer
• Unsupervised
– no training data
– throw data into the algorithm, hope it makes some
kind of sense out of the data

Some types of algorithms
• Prediction
– predicting a variable from data
• Classification
– assigning records to predefined groups
• Clustering
– splitting records into groups based on similarity
• Association learning
– seeing what often appears together with what
31

Issues
• Data is usually noisy in some way
– imprecise input values
– hidden/latent input values
• Inductive bias
– basically, the shape of the algorithm we choose
– may not fit the data at all
– may induce underfitting or overfitting
• Machine learning without inductive bias is
not possible
32

Underfitting
33
• Using an algorithm that cannot capture the
full complexity of the data

Overfitting
• Tuning the algorithm so carefully it starts
matching the noise in the training data
34

35
“What if the knowledge and data we have
are not sufficient to completely determine
the correct classifier?Then we run the risk of
just hallucinating a classifier (or parts of it)
that is not grounded in reality, and is simply
encoding random quirks in the data.This
problem is called overfitting, and is the
bugbear of machine learning. When your
learner outputs a classifier that is 100%
accurate on the training data but only 50%
accurate on test data, when in fact it could
have output one that is 75% accurate on both,
it has overfit.”
http://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf

Testing
36
• When doing this for real, testing is crucial
• Testing means splitting your data set
– training data (used as input to algorithm)
– test data (used for evaluation only)
• Need to compute some measure of
performance
– precision/recall
– root mean square error
• A huge field of theory here
– will not go into it in this course
– very important in practice

Missing values
37
• Usually, there are missing values in the
data set
– that is, some records have some NULL values
• These cause problems for many machine
learning algorithms
• Need to solve somehow
– remove all records with NULLs
– use a default value
– estimate a replacement value
– ...

Terminology
38
• Vector
– one-dimensional array
• Matrix
– two-dimensional array
• Linear algebra
– algebra with vectors and matrices
– addition, multiplication, transposition, ...

Top 10 machine learning algs
1. C4.5 No
2. k-means clustering Yes
3. Support vector machines No
4. the Apriori algorithm No
5. the EM algorithm No
6. PageRank No
7. AdaBoost No
8. k-nearest neighbours class. Kind of
9. Naïve Bayes Yes
10.CART No
40
From a survey at IEEE InternationalConference on Data Mining (ICDM) in December 2006. “Top 10
algorithms in data mining”, byX.Wu et al

C4.5
41
• Algorithm for building decision trees
– basically trees of boolean expressions
– each node split the data set in two
– leaves assign items to classes
• Decision trees are useful not just for
classification
– they can also teach you something about the
classes
• C4.5 is a bit involved to learn
– the ID3 algorithm is much simpler
• CART (#10) is another algorithm for
learning decision trees

Support Vector Machines
42
• A way to do binary classification on
matrices
• Support vectors are the data points nearest
to the hyperplane that divides the classes
• SVMs maximize the distance between SVs
and the boundary
• Particularly valuable because of “the kernel
trick”
– using a transformation to a higher dimension to
handle more complex class boundaries
• A bit of work to learn, but manageable

Apriori
43
• An algorithm for “frequent itemsets”
– basically, working out which items frequently
appear together
– for example, what goods are often bought
together in the supermarket?
– used forAmazon’s “customers who bought this...”
• Can also be used to find association rules
– that is, “people who buy X often buyY” or similar
• Apriori is slow
– a faster, further development is FP-growth
http://www.dssresources.com/newsletters/66.php

Expectation Maximization
44
• A deeply interesting algorithm I’ve seen
used in a number of contexts
– very hard to understand what it does
– very heavy on the maths
• Essentially an iterative algorithm
– skips between “expectation” step and
“maximization” step
– tries to optimize the output of a function
• Can be used for
– clustering
– a number of more specialized examples, too

PageRank
45
• Basically a graph analysis algorithm
– identifies the most prominent nodes
– used for weighting search results on Google
• Can be applied to any graph
– for example an RDF data set
• Basically works by simulating random walk
– estimating the likelihood that a walker would be
on a given node at a given time
– actual implementation is linear algebra
• The basic algorithm has some issues
– “spider traps”
– graph must be connected
– straightforward solutions to these exist

AdaBoost
46
• Algorithm for “ensemble learning”
• That is, for combining several algorithms
– and training them on the same data
• Combining more algorithms can be very
effective
– usually better than a single algorithm
• AdaBoost basically weights training
samples
– giving the most weight to those which are
classified the worst

Collaborative filtering
• Basically, you’ve got some set of items
– these can be movies, books, beers, whatever
• You’ve also got ratings from users
– on a scale of 1-5, 1-10, whatever
• Can you use this to recommend items to a
user, based on their ratings?
– if you use the connection between their ratings and
other people’s ratings, it’s called collaborative
filtering
– other approaches are possible
48

Feature-based recommendation
49
• Use user’s ratings of items
– run an algorithm to learn what features of items
the user likes
• Can be difficult to apply because
– requires detailed information about items
– key features may not be present in data
• Recommending music may be difficult, for
example

A simple idea
• If we can find ratings from people similar to
you, we can see what they liked
– the assumption is that you should also like it, since
your other ratings agreed so well
• You can take the average ratings of the k
people most similar to you
– then display the items with the highest averages
• This approach is called k-nearest neighbours
– it’s simple, computationally inexpensive, and works
pretty well
– there are, however, some tricks involved
50

MovieLens data
• Three sets of movie rating data
– real, anonymized data, from the MovieLens site
– ratings on a 1-5 scale
• Increasing sizes
– 100,000 ratings
– 1,000,000 ratings
– 10,000,000 ratings
• Includes a bit of information about the movies
• The two smallest data sets also contain
demographic information about users
51
http://www.grouplens.org/node/73

Basic algorithm
• Load data into rating sets
– a rating set is a list of (movie id, rating) tuples
– one rating set per user
• Compare rating sets against the user’s
rating set with a similarity function
– pick the k most similar rating sets
• Compute average movie rating within
these k rating sets
• Show movies with highest averages
52

Similarity functions
• Minkowski distance
– basically geometric distance, generalized to any
number of dimensions
• Pearson correlation coefficient
• Vector cosine
– measures angle between vectors
• Root mean square error (RMSE)
– square root of the mean of square differences
between data values
53

Data I added
54
User
ID
Movie
ID
Rating Title
6041 347 4 Bitter Moon
6041 1680 3 Sliding Doors
6041 229 5 Death and the Maiden
6041 1732 3 The Big Lebowski
6041 597 2 Pretty Woman
6041 991 4 Michael Collins
6041 1693 3 Amistad
6041 1484 4 The Daytrippers
6041 427 1 Boxing Helena
6041 509 4 The Piano
6041 778 5 Trainspotting
6041 1204 4 Lawrence of Arabia
6041 1263 5 The Deer Hunter
6041 1183 5 The English Patient
6041 1343 1 Cape Fear
6041 260 1 Star Wars
6041 405 1 Highlander III
6041 745 5 A Close Shave
6041 1148 5 The Wrong Trousers
6041 1721 1 Titanic
This is the 1M data set
https://github.com/larsga/py-snippets/tree/master/machine-learning/movielens
Note these. Later we’ll seeWallace &
Gromit popping up in recommendations.

Root Mean Square Error
• This is a measure that’s often used to judge
the quality of prediction
– predicted value: x
– actual value: y
• For each pair of values, do
– (y - x)2
• Procedure
– sum over all pairs,
– divide by the number of values (to get average),
– take the square root of that (to undo squaring)
• We use the square because
– that always gives us a positive number,
– it emphasizes bigger deviations
55

RMSE in Python
def rmse(rating1, rating2):
sum = 0
count = 0
for (key, rating) in rating1.items():
if key in rating2:
sum += (rating2[key] - rating) ** 2
count += 1
if not count:
return 1000000 # no common ratings, so distance is huge
return sqrt(sum / float(count))
56

Output, k=3
===== User 0 ==================================================
User # 14 , distance: 0.0
Deer Hunter, The (1978) 5 YOUR: 5
===== User 1 ==================================================
Close Shave, A (1995) 5 YOUR: 5
===== User 2 ==================================================
Big Lebowski, The (1998) 3 YOUR: 3
===== RECOMMENDATIONS =============================================
Chicken Run (2000) 5.0
Auntie Mame (1958) 5.0
Muppet Movie, The (1979) 5.0
'Night Mother (1986) 5.0
Goldfinger (1964) 5.0
Children of Paradise (Les enfants du paradis) (1945) 5.0
Total Recall (1990) 5.0
Boys Don't Cry (1999) 5.0
Radio Days (1987) 5.0
Ideal Husband, An (1999) 5.0
Red Violin, The (Le Violon rouge) (1998) 5.0
57
Distance measure: RMSE
Obvious problem: ratings agree perfectly,
but there are too few common ratings. More
ratings mean greater chance of disagreement.

RMSE 2.0
def lmg_rmse(rating1, rating2):
max_rating = 5.0
sum = 0
count = 0
for (key, rating) in rating1.items():
if key in rating2:
sum += (rating2[key] - rating) ** 2
count += 1
if not count:
return 1000000 # no common ratings, so distance is huge
return sqrt(sum / float(count)) + (max_rating / count)
58

Output, k=3, RMSE 2.0
===== 0 ==================================================
User # 3320 , distance: 1.09225018729
Highlander III: The Sorcerer (1994) 1 YOUR: 1
Boxing Helena (1993) 1 YOUR: 1
Pretty Woman (1990) 2 YOUR: 2
Michael Collins (1996) 4 YOUR: 4
Wrong Trousers, The (1993) 5 YOUR: 5
Amistad (1997) 4 YOUR: 3
===== 1 ==================================================
User # 2825 , distance: 1.24880819811
Amistad (1997) 3 YOUR: 3
English Patient, The (1996) 4 YOUR: 5
Death and the Maiden (1994) 5 YOUR: 5
Lawrence of Arabia (1962) 4 YOUR: 4
Piano, The (1993) 5 YOUR: 4
===== 2 ==================================================
User # 1205 , distance: 1.41068360252
Sliding Doors (1998) 4 YOUR: 3
English Patient, The (1996) 4 YOUR: 5
Michael Collins (1996) 4 YOUR: 4
Piano, The (1993) 4 YOUR: 4
===== RECOMMENDATIONS ==================================================
Patriot, The (2000) 5.0
Badlands (1973) 5.0
Blood Simple (1984) 5.0
Gold Rush, The (1925) 5.0
Mission: Impossible 2 (2000) 5.0
Gladiator (2000) 5.0
Hook (1991) 5.0
Funny Bones (1995) 5.0
Creature Comforts (1990) 5.0
Do the Right Thing (1989) 5.0
Thelma & Louise (1991) 5.0
59
Much better choice of users
But all recommended movies are 5.0
Basically, if one user gave it 5.0, that’s
going to beat 5.0, 5.0, and 4.0
Clearly, we need to reward movies that
have more ratings somehow

Bayesian average
• A simple weighted average that accounts
for how many ratings there are
• Basically, you take the set of ratings and
add n extra “fake” ratings of the average
value
• So for movies, we use the average of 3.0
60
(sum(numbers) + (3.0 * n))
float(len(numbers) + n)
>>> avg([5.0], 2)
3.6666666666666665
>>> avg([5.0, 5.0], 2)
4.0
>>> avg([5.0, 5.0, 5.0], 2)
4.2
>>> avg([5.0, 5.0, 5.0, 5.0], 2)
4.333333333333333

With k=3
===== RECOMMENDATIONS ===============
Truman Show,The (1998) 4.2
Say Anything... (1989) 4.0
Jerry Maguire (1996) 4.0
Groundhog Day (1993) 4.0
Monty Python and the Holy Grail (1974) 4.0
Big Night (1996) 4.0
Babe (1995) 4.0
What About Bob? (1991) 3.75
Howards End (1992) 3.75
Winslow Boy,The (1998) 3.75
Shakespeare in Love (1998) 3.75
61
Not very good, but k=3 makes us
very dependent on those specific 3
users.

With k=10
Groundhog Day (1993) 4.55555555556
Annie Hall (1977) 4.4
One Flew Over the Cuckoo's Nest (1975) 4.375
Fargo (1996) 4.36363636364
Wallace & Gromit:The Best of Aardman
Animation (1996) 4.33333333333
Do the RightThing (1989) 4.28571428571
Princess Bride,The (1987) 4.28571428571
Welcome to the Dollhouse (1995) 4.28571428571
Wizard of Oz,The (1939) 4.25
Blood Simple (1984) 4.22222222222
Rushmore (1998) 4.2
62
Definitely better.

With k=50
Wallace & Gromit:The Best of AardmanAnimation
(1996) 4.55
Roger & Me (1989) 4.5
Waiting for Guffman (1996) 4.5
Grand Day Out, A (1992) 4.5
Creature Comforts (1990) 4.46666666667
Fargo (1996) 4.46511627907
Godfather,The (1972) 4.45161290323
Raising Arizona (1987) 4.4347826087
City Lights (1931) 4.42857142857
Usual Suspects,The (1995) 4.41666666667
Manchurian Candidate,The (1962) 4.41176470588
63

With k = 2,000,000
• If we did that, what results would we get?
64

Normalization
• People use the scale differently
– some give only 4s and 5s
– others give only 1s
– some give only 1s and 5s
– etc
• Should have normalized user ratings before
using them
– before comparison
– and before averaging ratings from neighbours
65

Bayes’s Theorem
67
• Basically a theorem for combining
probabilities
– I’ve observed A, which indicates H is true with
probability 70%
– I’ve also observed B, which indicates H is true with
probability 85%
– what should I conclude?
• Naïve Bayes is basically using this theorem
– with the assumption that A and B are indepedent
– this assumption is nearly always false, hence
“naïve”

Simple example
68
• Is the coin fair or not?
– we throw it 10 times, get 9 heads and one tail
– we try again, get 8 heads and two tails
• What do we know now?
– can combine data and recompute
– or just use Bayes’sTheorem directly
http://www.bbc.co.uk/news/magazine-22310186
>>> compute_bayes([0.92, 0.84])
0.9837067209775967

Ways I’ve used Bayes
69
• Duke
– record deduplication engine
– estimate probability of duplicate for each property
– combine probabilities with Bayes
• Whazzup
– news aggregator that finds relevant news
– works essentially like spam classifier on next slide
• Tine recommendation prototype
– recommends recipes based on previous choices
– also like spam classifier
• Classifying expenses
– using export from my bank
– also like spam classifier

Bayes against spam
70
• Take a set of emails, divide it into spam and
non-spam (ham)
– count the number of times a feature appears in
each of the two sets
– a feature can be a word or anything you please
• To classify an email, for each feature in it
– consider the probability of email being spam given
that feature to be (spam count) / (spam count +
ham count)
– ie: if “viagra” appears 99 times in spam and 1 in
ham, the probability is 0.99
• Then combine the probabilities with Bayes
http://www.paulgraham.com/spam.html

Running the script
71
• I pass it
– 1000 emails from my Bouvet folder
– 1000 emails from my Spam folder
• Then I feed it
– 1 email from another Bouvet folder
– 1 email from another Spam folder

Code
72
# scan spam
for spam in glob.glob(spamdir + '/' + PATTERN)[ : SAMPLES]:
for token in featurize(spam):
corpus.spam(token)
# scan ham
for ham in glob.glob(hamdir + '/' + PATTERN)[ : SAMPLES]:
for token in featurize(ham):
corpus.ham(token)
# compute probability
for email in sys.argv[3 : ]:
print email
p = classify(email)
if p < 0.2:
print ' Spam', p
else:
print ' Ham', p
https://github.com/larsga/py-snippets/tree/master/machine-learning/spam

Classify
73
class Feature:
def __init__(self, token):
self._token = token
self._spam = 0
self._ham = 0
def spam(self):
self._spam += 1
def ham(self):
self._ham += 1
def spam_probability(self):
return (self._spam + PADDING) / float(self._spam + self._ham + (PADDING * 2))
def compute_bayes(probs):
product = reduce(operator.mul, probs)
lastpart = reduce(operator.mul, map(lambda x: 1-x, probs))
if product + lastpart == 0:
return 0 # happens rarely, but happens
else:
return product / (product + lastpart)
def classify(email):
return compute_bayes([corpus.spam_probability(f) for f in featurize(email)])

Ham output
74
Ham 1.0
Received:2013 0.00342935528121
Date:2013 0.00624219725343
<br 0.0291715285881
background-color: 0.03125
Received:Mar 0.0332667997339
Date:Mar 0.0362756952842
...
Postboks 0.998107494322
Postboks 0.998107494322
Postboks 0.998107494322
+47 0.99787414966
+47 0.99787414966
+47 0.99787414966
+47 0.99787414966
Lars 0.996863237139
Lars 0.996863237139
23 0.995381062356
So, clearly most of the spam
is from March 2013...

Spam output
75
Spam 2.92798502037e-16
Received:-0400 0.0115646258503
Received:-0400 0.0115646258503
Received-SPF:(ontopia.virtual.vps-host.net: 0.0135823429542
Received-SPF:receiver=ontopia.virtual.vps-host.net; 0.0135823429542
Received:<larsga@ontopia.net>; 0.0139318885449
Received:<larsga@ontopia.net>; 0.0139318885449
Received:ontopia.virtual.vps-host.net 0.0170863309353
Received:(8.13.1/8.13.1) 0.0170863309353
Received:ontopia.virtual.vps-host.net 0.0170863309353
Received:(8.13.1/8.13.1) 0.0170863309353
...
Received:2012 0.986111111111
Received:2012 0.986111111111
$ 0.983193277311
Received:Oct 0.968152866242
Received:Oct 0.968152866242
Date:2012 0.959459459459
20 0.938864628821
+ 0.936526946108
+ 0.936526946108
+ 0.936526946108
...and the ham from October 2012

More solid testing
76
• Using the SpamAssassin public corpus
• Training with 500 emails from
– spam
– easy_ham (2002)
• Test results
– spam_2: 1128 spam, 269 misclassified as ham
– easy_ham 2003: 2283 ham, 217 spam
• Results are pretty good for 30 minutes of
effort...
http://spamassassin.apache.org/publiccorpus/

Linear regression
78
• Let’s say we have a number of numerical
parameters for an object
• We want to use these to predict some
other value
• Examples
– estimating real estate prices
– predicting the rating of a beer
– ...

Estimating real estate prices
79
• Take parameters
– x1 square meters
– x2 number of rooms
– x3 number of floors
– x4 energy cost per year
– x5 meters to nearest subway station
– x6 years since built
– x7 years since last refurbished
– ...
• a x1 + b x2 + c x3 + ... = price
– strip out the x-es and you have a vector
– collect N samples of real flats with prices = matrix
– welcome to the world of linear algebra

Our data set: beer ratings
80
• Ratebeer.com
– a web site for rating beer
– scale of 0.5 to 5.0
• For each beer we know
– alcohol %
– country of origin
– brewery
– beer style (IPA, pilsener, stout, ...)
• But ... only one attribute is numeric!
– how to solve?

Example
81
ABV .se .nl .us .uk IIPA Black
IPA
Pale
ale
Bitter Rating
8.5 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 3.5
8.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0 3.7
6.2 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 3.2
4.4 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 3.2
... ... ... ... ... ... ... ... ... ...
Basically, we turn each category into a column of 0.0 or 1.0 values.

Normalization
82
• If some columns have much bigger values than
the others they will automatically dominate
predictions
• We solve this by normalization
• Basically, all values get resized into the 0.0-1.0
range
• For ABV we set a ceiling of 15%
– compute with min(15.0, abv) / 15.0

Adding more data
83
• To get a bit more data, I added manually a
description of each beer style
• Each beer style got a 0.0-1.0 rating on
– colour (pale/dark)
– sweetness
– hoppiness
– sourness
• These ratings are kind of coarse because all
beers of the same style get the same value

Making predictions
84
• We’re looking for a formula
– a * abv + b * .se + c * .nl + d * .us + ... = rating
• We have n examples
– a * 8.5 + b * 1.0 + c * 0.0 + d * 0.0 + ... = 3.5
• We have one unknown per column
– as long as we have more rows than columns we can
solve the equation
• Interestingly, matrix operations can be used to
solve this easily

Matrix formulation
85
• Let’s say
– x is our data matrix
– y is a vector with the ratings and
– w is a vector with the a, b, c, ... values
• That is: x * w = y
– this is the same as the original equation
– a x1 + b x2 + c x3 + ... = rating
• If we solve this, we get

Enter Numpy
86
• Numpy is a Python library for matrix
operations
• It has built-in types for vectors and matrices
• Means you can very easily work with matrices
in Python
• Why matrices?
– much easier to express what we want to do
– library written in C and very fast
– takes care of rounding errors, etc

Quick Numpy example
87
>>> from numpy import *
>>> range(10)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> [range(10)] * 10
[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5,
6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1,
2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8,
9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]
>>> m = mat([range(10)] * 10)
>>> m
matrix([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]])
>>> m.T
matrix([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[3, 3, 3, 3, 3, 3, 3, 3, 3, 3],
[4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
[5, 5, 5, 5, 5, 5, 5, 5, 5, 5],
[6, 6, 6, 6, 6, 6, 6, 6, 6, 6],
[7, 7, 7, 7, 7, 7, 7, 7, 7, 7],
[8, 8, 8, 8, 8, 8, 8, 8, 8, 8],
[9, 9, 9, 9, 9, 9, 9, 9, 9, 9]])

Numpy solution
88
• We load the data into
– a list: scores
– a list of lists: parameters
• Then:
x_mat = mat(parameters)
y_mat = mat(scores).T
x_tx = x_mat.T * x_mat
assert linalg.det(x_tx)
ws = x_tx.I * (x_mat.T * y_mat)

Does it work?
89
• We only have very rough information about
each beer (abv, country, style)
– so very detailed prediction isn’t possible
– but we should get some indication
• Here are the results based on my ratings
– 10% imperial stout from US 3.9
– 4.5% pale lager from Ukraine 2.8
– 5.2% German schwarzbier 3.1
– 7.0% German doppelbock 3.5
http://www.ratebeer.com/user/15206/ratings/

Beyond prediction
90
• We can use this for more than just prediction
• We can also use it to see which columns
contribute the most to the rating
– that is, which aspects of a beer best predict the rating
• If we look at the w vector we see the following
– Aspect LMG grove
– ABV 0.56 1.1
– colour 0.46 0.42
– sweetness 0.25 0.51
– hoppiness 0.45 0.41
– sourness 0.29 0.87
• Could also use correlation

Did we underfit?
• Who says the relationship between ABV
and the rating is linear?
– perhaps very low and very high ABV are both
negative?
– we cannot capture that with linear regression
• Solution
– add computed columns for parameters raised to
higher powers
– abv2, abv3, abv4, ...
– beware of overfitting...
91

Scatter plot
92
Freeze-distilled Brewdog beers
Rating
ABV in %Code in Github, requires matplotlib

Matrix factorization
94
• Another way to do recommendations is
matrix factorization
– basically, make a user/item matrix with ratings
– try to find two smaller matrices that, when
multiplied together, give you the original matrix
– that is, original with missing values filled in
• Why that works?
– I don’t know
– I tried it, couldn’t get it to work
– therefore we’re not covering it
– known to be a very good method, however

Clustering
• Basically, take a set of objects and sort
them into groups
– objects that are similar go into the same group
• The groups are not defined beforehand
• Sometimes the number of groups to create
is input to the algorithm
• Many, many different algorithms for this
96

Sample data
• Our sample data set is data about aircraft from
DBpedia
• For each aircraft model we have
– name
– length (m)
– height (m)
– wingspan (m)
– number of crew members
– operational ceiling, or max height (m)
– max speed (km/h)
– empty weight (kg)
• We use a subset of the data
– 149 aircraft models which all have values for all of these
properties
• Also, all values normalized to the 0.0-1.0 range
97

Distance
• All clustering algorithms require a distance
function
– that is, a measure of similarity between two objects
• Any kind of distance function can be used
– generally, lower values mean more similar
• Examples of distance functions
– metric distance
– vector cosine
– RMSE
– ...
98

k-means clustering
• Input: the number of clusters to create (k)
• Pick k objects
– these are your initial clusters
• For all objects, find nearest cluster
– assign the object to that cluster
• For each cluster, compute mean of all
properties
– use these mean values to compute distance to
clusters
– the mean is often referred to as a “centroid”
– go back to previous step
• Continue until no objects change cluster
99

First attempt at aircraft
• We leave out name and number built when
doing comparison
• We use RMSE as the distance measure
• We set k = 5
• What happens?
– first iteration: all 149 assigned to a cluster
– second: 11 models change cluster
– third: 7 change
– fourth: 5 change
– fifth: 5 change
– sixth: 2
– seventh: 1
– eighth: 0
100

Cluster 5
101
cluster5, 4 models
ceiling : 13400.0
maxspeed : 1149.7
crew : 7.5
length : 47.275
height : 11.65
emptyweight : 69357.5
wingspan : 47.18
The Myasishchev M-50 was a Soviet
prototype four-engine supersonic
bomber which never attained service
TheTupolevTu-16 was a twin-engine
jet bomber used by the Soviet Union.
The Myasishchev M-4 Molot is a
four-engined strategic bomber
TheConvair B-36 "Peacemaker” was a
strategic bomber built by Convair and
operated solely by the United StatesAir
Force (USAF) from 1949 to 1959
3 jet bombers, one
propeller bomber.
Not too bad.

Cluster 4
102
cluster4, 56 models
ceiling : 5898.2
maxspeed : 259.8
crew : 2.2
length : 10.0
height : 3.3
emptyweight : 2202.5
wingspan : 13.8
TheAvia B.135 was a Czechoslovak
cantilever monoplane fighter aircraft
The NorthAmerican B-25 Mitchell was
anAmerican twin-engined medium
bomber
TheYakovlev UT-1 was a single-seater
trainer aircraft
TheYakovlev UT-2 was a single-seater
trainer aircraft
The Siebel Fh 104 Hallore was a small
German twin-engined transport,
communications and liaison aircraft
The Messerschmitt Bf 108Taifun was a
German single-engine sports and touring
aircraft
TheAirco DH.2 was a single-seat
biplane "pusher" aircraft
Small, slow propeller aircraft.
Not too bad.

Cluster 3
103
cluster3, 12 models
ceiling : 16921.1
maxspeed : 2456.9
crew : 2.67
length : 17.2
height : 4.92
emptyweight : 9941
wingspan : 10.1
The Mikoyan MiG-29 is a fourth-
generation jet fighter aircraft
TheVought F-8 Crusader was a
single-engine, supersonic [fighter]
aircraft
The English Electric Lightning is a
supersonic jet fighter aircraft of the
ColdWar era, noted for its great
speed.
The Dassault Mirage 5 is a supersonic
attack aircraft
The NorthropT-38Talon is a two-
seat, twin-engine supersonic jet
trainer
The Mikoyan MiG-35 is a further
development of the MiG-29
Small, very fast jet planes.
Pretty good.

Cluster 2
104
cluster2, 27 models
ceiling : 6447.5
maxspeed : 435
crew : 5.4
length : 24.4
height : 6.7
emptyweight : 16894
wingspan : 32.8
The Bartini BerievVVA-14 (vertical
take-off amphibious aircraft)
TheAviationTradersATL-98
Carvair was a large piston-engine
transport aircraft.
The Junkers Ju 290 was a long-range transport,
maritime patrol aircraft and heavy bomber
The Fokker 50 is a turboprop-
powered airliner
The PB2Y Coronado was a large
flying boat patrol bomber
The Junkers Ju 89 was a heavy
bomber
The Beriev Be-200 Altair is a
multipurpose amphibious aircraft
Biggish, kind of slow planes.
Some oddballs in this group.

Cluster 1
105
cluster1, 50 models
ceiling : 11612
maxspeed : 726.4
crew : 1.6
length : 11.9
height : 3.8
emptyweight : 5303
wingspan : 13
TheAdamA700AdamJet was a
proposed six-seat civil utility aircraft
The Learjet 23 is a ... twin-engine,
high-speed business jet
The Learjet 24 is a ... twin-engine,
high-speed business jet
TheCurtiss P-36 Hawk was an American-
designed and built fighter aircraft
The Kawasaki Ki-61 Hien was a
Japanese WorldWar II fighter aircraft
TheGrumman F3F was the last
American biplane fighter aircraft
The English ElectricCanberra is a
first-generation jet-powered light
bomber
The Heinkel He
100 was a
German pre-
WorldWar II
fighter aircraft
Small, fast planes. Mostly
good, though the Canberra is
a poor fit.

Clusters, summarizing
• Cluster 1: small, fast aircraft (750 km/h)
• Cluster 2: big, slow aircraft (450 km/h)
• Cluster 3: small, very fast jets (2500 km/h)
• Cluster 4: small, very slow planes (250 km/h)
• Cluster 5: big, fast jet planes (1150 km/h)
106
For a first attempt to sort through the data,
this is not bad at all
https://github.com/larsga/py-snippets/tree/master/machine-learning/aircraft

Agglomerative clustering
• Put all objects in a pile
• Make a cluster of the two objects closest to
one another
– from here on, treat clusters like objects
• Repeat second step until satisfied
107 There is code for this, too, in the Github sample

Principal
component analysis
108

PCA
109
• Basically, using eigenvalue analysis to find
out which variables contain the most
information
– the maths are pretty involved
– and I’ve forgotten how it works
– and I’ve thrown out my linear algebra book
– and ordering a new one fromAmazon takes too
long
– ...so we’re going to do this intuitively

An example data set
110
• Two variables
• Three classes
• What’s the longest
line we could draw
through the data?
• That line is a vector in two dimensions
• What dimension dominates?
– that’s right: the horizontal
– this implies the horizontal contains most of the
information in the data set
• PCA identifies the most significant
variables

Dimensionality reduction
111
• After PCA we know which dimensions
matter
– based on that information we can decide to throw
out less important dimensions
• Result
– smaller data set
– faster computations
– easier to understand

Trying out PCA
112
• Let’s try it on the Ratebeer data
• We know ABV has the most information
– because it’s the only value specified for each
individual beer
• We also include a new column: alcohol
– this is the amount of alcohol in a pint glass of the
beer, measured in centiliters
– this column basically contains no information at
all; it’s computed from the abv column

Complete code
113
import rblib
from numpy import *
def eigenvalues(data, columns):
covariance = cov(data - mean(data, axis = 0), rowvar = 0)
eigvals = linalg.eig(mat(covariance))[0]
indices = list(argsort(eigvals))
indices.reverse() # so we get most significant first
return [(columns[ix], float(eigvals[ix])) for ix in indices]
(scores, parameters, columns) =
rblib.load_as_matrix('ratings.txt')
for (col, ev) in eigenvalues(parameters, columns):
print "%40s %s" % (col, float(ev))

Output
114
abv 0.184770392185
colour 0.13154093951
sweet 0.121781685354
hoppy 0.102241100597
sour 0.0961537687655
alcohol 0.0893502031589
United States 0.0677552513387
....
Eisbock -3.73028421245e-18
Belarus -3.73028421245e-18
Vietnam -1.68514561515e-17

University pre-lecture, 1991
116
• My first meeting with university was Open
University Day, in 1991
• Professor Bjørn Kirkerud gave the computer
science talk
• His subject
– some day processors will stop becoming faster
– we’re already building machines with many processors
– what we need is a way to parallelize software
– preferably automatically, by feeding in normal source
code and getting it parallelized back
• MapReduce is basically the state of the art on
that today

MapReduce
117
• A framework for writing massively parallel
code
• Simple, straightforward model
• Based on “map” and “reduce” functions
from functional programming (LISP)

118
http://research.google.com/archive/mapreduce.html
Appeared in:
OSDI'04: Sixth Symposium on Operating System Design and
Implementation,
San Francisco, CA, December, 2004.

map and reduce
119
>>> "1 2 3 4 5 6 7 8".split()
['1', '2', '3', '4', '5', '6', '7', '8']
>>> l = map(int, "1 2 3 4 5 6 7 8".split())
>>> l
[1, 2, 3, 4, 5, 6, 7, 8]
>>> import operator
>>> reduce(operator.add, l)
36

MapReduce
120
1. Split data into fragments
2. Create a Map task for each fragment
– the task outputs a set of (key, value) pairs
3. Group the pairs by key
4. Call Reduce once for each key
– all pairs with same key passed in together
– reduce outputs new (key, value) pairs
Tasks get spread out over worker nodes
Master node keeps track of completed/failed tasks
Failed tasks are restarted
Failed nodes are detected and avoided
Also scheduling tricks to deal with slow nodes

Communications
121
• HDFS
– Hadoop Distributed File System
– input data, temporary results, and results are
stored as files here
– Hadoop takes care of making files available to
nodes
• Hadoop RPC
– how Hadoop communicates between nodes
– used for scheduling tasks, heartbeat etc
• Most of this is in practice hidden from the
developer

Does anyone need MapReduce?
122
• I tried to do book recommendations with
linear algebra
• Basically, doing matrix multiplication to
produce the full user/item matrix with
blanks filled in
• My Mac wound up freezing
• 185,973 books x 77,805 users =
14,469,629,265
– assuming 2 bytes per float = 28 GB of RAM
• So it doesn’t necessarily take that much to
have some use for MapReduce

The word count example
123
• Classic example of using MapReduce
• Takes an input directory of text files
• Processes them to produce word frequency
counts
• To start up, copy data into HDFS
– bin/hadoop dfs -mkdir <hdfs-dir>
– bin/hadoop dfs -copyFromLocal <local-dir> <hdfs-
dir>

WordCount – the mapper
124
public static class Map extends Mapper<LongWritable,
Text,Text, IntWritable> {
private final static IntWritable one = new IntWritable(1);
privateText word = newText();
public void map(LongWritable key,Text value, Context
context) {
String line = value.toString();
StringTokenizer tokenizer = new StringTokenizer(line);
while (tokenizer.hasMoreTokens()) {
word.set(tokenizer.nextToken());
context.write(word, one);
}
}
}
By default, Hadoop will scan all text files in input directory
Each line in each file will become a mapper task
And thus a “Text value” input to a map() call

WordCount – the reducer
125
public static class Reduce extends Reducer<Text,
IntWritable,Text, IntWritable> {
public void reduce(Text key,
Iterable<IntWritable> values, Context context) {
int sum = 0;
for (IntWritable val : values)
sum += val.get();
context.write(key, new IntWritable(sum));
}
}

The Hadoop ecosystem
126
• Pig
– dataflow language for setting up MR jobs
• HBase
– NoSQL database to store MR input in
• Hive
– SQL-like query language on top of Hadoop
• Mahout
– machine learning library on top of Hadoop
• Hadoop Streaming
– utility for writing mappers and reducers as
command-line tools in other languages

Word count in HiveQL
CREATETABLE input (line STRING);
LOAD DATA LOCAL INPATH 'input.tsv' OVERWRITE INTOTABLE
input;
-- temporary table to hold words...
CREATETABLE words (word STRING);
add file splitter.py;
INSERT OVERWRITETABLE words
SELECTTRANSFORM(text)
USING 'python splitter.py'
AS word
FROM input;
SELECT word, COUNT(*)
FROM input
LATERALVIEW explode(split(text, ' ')) lTable as word
GROUP BY word;
127

Word count in Pig
input_lines = LOAD '/tmp/my-copy-of-all-pages-on-internet'AS (line:chararray);
-- Extract words from each line and put them into a pig bag
-- datatype, then flatten the bag to get one word on each row
words = FOREACH input_lines GENERATE FLATTEN(TOKENIZE(line))AS word;
-- filter out any words that are just white spaces
filtered_words = FILTER words BY word MATCHES 'w+';
-- create a group for each word
word_groups = GROUP filtered_words BY word;
-- count the entries in each group
word_count = FOREACH word_groups GENERATE COUNT(filtered_words)AS
count, groupAS word;
-- order the records by count
ordered_word_count = ORDER word_count BY count DESC;
STORE ordered_word_count INTO '/tmp/number-of-words-on-internet';
128

Applications of MapReduce
129
• Linear algebra operations
– easily mapreducible
• SQL queries over heterogeneous data
– basically requires only a mapping to tables
– relational algebra easy to do in MapReduce
• PageRank
– basically one big set of matrix multiplications
– the original application of MapReduce
– the SON algorithm
• ...

Apache Mahout
130
• Has three main application areas
– others are welcome, but this is mainly what’s there
now
– several different similarity measures
– collaborative filtering
– Slope-one algorithm
• Clustering
– k-means and fuzzy k-means
– Latent Dirichlet Allocation
• Classification
– stochastic gradient descent
– SupportVector Machines
– Naïve Bayes

SQL to relational algebra
131
select lives.person_name, city
from works, lives
where company_name = ’FBC’ and
works.person_name = lives.person_name

Translation to MapReduce
132
• σ(company_name=‘FBC’, works)
– map: for each record r in works, verify the condition,
and pass (r, r) if it matches
– reduce: receive (r, r) and pass it on unchanged
• π(person_name, σ(...))
– map: for each record r in input, produce a new record r’
with only wanted columns, pass (r’, r’)
– reduce: receive (r’, [r’, r’, r’ ...]), output (r’, r’)
• ⋈(π(...), lives)
– map:
• for each record r in π(...), output (person_name, r)
• for each record r in lives, output (person_name, r)
– reduce: receive (key, [record, record, ...]), and perform
the actual join
• ...

Lots of SQL-on-MapReduce tools
133
• Tenzing Google
• Hive Apache Hadoop
• YSmart Ohio State
• SQL-MR AsterData
• HadoopDB Hadapt
• Polybase Microsoft
• RainStor RainStor Inc.
• ParAccel ParAccel Inc.
• Impala Cloudera
• ...

Big data & machine learning
135
• This is a huge field, growing very fast
• Many algorithms and techniques
– can be seen as a giant toolbox with wide-ranging
applications
• Ranging from the very simple to the
extremely sophisticated
• Difficult to see the big picture
• Huge range of applications
• Math skills are crucial

136
https://www.coursera.org/course/ml

Books I recommend
137
http://infolab.stanford.edu/~ullman/mmds.html

Introduction to Big Data/Machine Learning

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