Introduction to Mahout

1©MapR Technologies 2013- Confidential
Introduction to Mahout
And How To Build a Recommender

Me, Us
 Ted Dunning, Chief Application Architect, MapR
Committer PMC member, Mahout, Zookeeper, Drill
Bought the beer at the first HUG
 MapR
Distributes more open source components for Hadoop
Adds major technology for performance, HA, industry standard API’s
 Tonight
Hash tag - #tchug
See also - @ApacheMahout @ApacheDrill
@ted_dunning and @mapR

Sidebar on Drill
 Apache Drill
– SQL on Hadoop (and other things)
– Intended to solve problems for 1-5 years from now
Not the problems from 1-10 years ago
– Multiple levels of API supported
• SQL-2003
• Logical plan language (DAG in JSON)
• Physical plan language (DAG with push-down, exchange markers)
• Execution plan language (many DAG’s)
 Current state
– SQL 2003 support in place
– Logical plan interpreter useful for testing
– Value vectors near completion
– High performance RPC working

More on Drill
 Just completed OSCON workshop
 Workshop materials available shortly
– Extracted technology demonstrators
– Sample queries
 Send me email or tweet for more info

What’s Up?
 What is Mahout?
– Math library
– Clustering, classifiers, other stuff
 Recommendation
– Generalities
– Algorithm Specifics
– System Design
– Important things never mentioned
 Final thoughts

What is Mahout?
 “Scalable machine learning”
– not just Hadoop-oriented machine learning
– not entirely, that is. Just mostly.
 Components
– math library
– clustering
– classification
– decompositions
– recommendations

Mahout Math

Mahout Math
 Goals are
– basic linear algebra,
– and statistical sampling,
– and good clustering,
– decent speed,
– extensibility,
– especially for sparse data
 But not
– totally badass speed
– comprehensive set of algorithms
– optimization, root finders, quadrature

Matrices and Vectors
 At the core:
– DenseVector, RandomAccessSparseVector
– DenseMatrix, SparseRowMatrix
 Highly composable API
 Important ideas:
– view*, assign and aggregate
– iteration
m.viewDiagonal().assign(v)

Assign? View?
 Why assign?
– Copying is the major cost for naïve matrix packages
– In-place operations critical to reasonable performance
– Many kinds of updates required, so functional style very helpful
 Why view?
– In-place operations often required for blocks, rows, columns or diagonals
– With views, we need #assign + #views methods
– Without views, we need #assign x #views methods
 Synergies
– With both views and assign, many loops become single line

Assign
 Matrices
 Vectors
Matrix assign(double value);
Matrix assign(double[][] values);
Matrix assign(Matrix other);
Matrix assign(DoubleFunction f);
Matrix assign(Matrix other, DoubleDoubleFunction f);
Vector assign(double value);
Vector assign(double[] values);
Vector assign(Vector other);
Vector assign(DoubleFunction f);
Vector assign(Vector other, DoubleDoubleFunction f);
Vector assign(DoubleDoubleFunction f, double y);

Views
 Matrices
 Vectors
Matrix viewPart(int[] offset, int[] size);
Matrix viewPart(int row, int rlen, int col, int clen);
Vector viewRow(int row);
Vector viewColumn(int column);
Vector viewDiagonal();
Vector viewPart(int offset, int length);

Aggregates
 Matrices
 Vectors
double zSum();
double aggregate(
DoubleDoubleFunction reduce, DoubleFunction map);
double aggregate(Vector other,
DoubleDoubleFunction aggregator,
DoubleDoubleFunction combiner);
double zSum();
Vector aggregateRows(VectorFunction f);
Vector aggregateColumns(VectorFunction f);
double aggregate(DoubleDoubleFunction combiner,
DoubleFunction mapper);

Predefined Functions
 Many handy functions
ABS LOG2
ACOS NEGATE
ASIN RINT
ATAN SIGN
CEIL SIN
COS SQRT
EXP SQUARE
FLOOR SIGMOID
IDENTITY SIGMOIDGRADIENT
INV TAN
LOGARITHM

Examples
double alpha; a.assign(alpha);
a.assign(b, Functions.chain(
Functions.plus(beta),
Functions.times(alpha));
A =a
A =aB+ b

Sparse Optimizations
 DoubleDoubleFunction abstract properties
 And Vector properties
public boolean isLikeRightPlus();
public boolean isLikeLeftMult();
public boolean isLikeRightMult();
public boolean isLikeMult();
public boolean isCommutative();
public boolean isAssociative();
public boolean isAssociativeAndCommutative();
public boolean isDensifying();
public boolean isDense();
public boolean isSequentialAccess();
public double getLookupCost();
public double getIteratorAdvanceCost();
public boolean isAddConstantTime();

More Examples
 The trace of a matrix
 Set diagonal to zero
 Set diagonal to negative of row sums

Examples
m.viewDiagonal().zSum()

Examples
m.viewDiagonal().assign(0)

Examples
 Set diagonal to negative of row sums excluding the diagonal
m.viewDiagonal().assign(0)
Vector diag = m.viewDiagonal().assign(0);
diag.assign(m.rowSums().assign(Functions.MINUS));

Iteration
 Matrices are Iterable in Mahout
 Vectors are densely or sparsely iterable
// compute both row and columns sums in one pass
for (MatrixSlice row: m) {
rSums.set(row.index(), row.zSum());
cSums.assign(row, Functions.PLUS);
}
double entropy = 0;
for (Vector.Element e: v.nonZeroes()) {
entropy += e.get() * Math.log(e.get());
}

Random Sampling
 Samples from some type
 Lots of kinds
ChineseRestaurant Missing Normal
Empirical Multinomial PoissonSampler
IndianBuffet MultiNormal Sampler
public interface Sampler<T> {
T sample();
}
public abstract class AbstractSamplerFunction
extends DoubleFunction
implements Sampler<Double>

Clustering and Such
 Streaming k-means and ball k-means
– streaming reduces very large data to a cluster sketch
– ball k-means is a high quality k-means implementation
– the cluster sketch is also usable for other applications
– single machine threaded and map-reduce versions available
 SVD and friends
– stochastic SVD has in-memory, single machine out-of-core and map-reduce
versions
– good for reducing very large sparse matrices to tall skinny dense ones
 Spectral clustering
– based on SVD, allows massive dimensional clustering

Mahout Math Summary
 Matrices, Vectors
– views
– in-place assignment
– aggregations
– iterations
 Functions
– lots built-in
– cooperate with sparse vector optimizations
 Sampling
– abstract samplers
– samplers as functions
 Other stuff … clustering, SVD

Recommenders

Recommendations
 Often known as collaborative filtering
 Actors interact with items
– observe successful interaction
 We want to suggest additional successful interactions
 Observations inherently very sparse

The Big Ideas
 Cooccurrence is the core operation (and it is pretty simple)
 Cooccurrence can be extended to handle important new
capabilities
 Recommendation systems can be deployed ideally using search
technology

Examples of Recommendations
 Customers buying books (Linden et al)
 Web visitors rating music (Shardanand and Maes) or movies (Riedl,
et al), (Netflix)
 Internet radio listeners not skipping songs (Musicmatch)
 Internet video watchers watching >30 s (Veoh)
 Visibility in a map UI (new Google maps)

A simple recommendation architecture
 Look at the history of interactions
 Find significant item cooccurrence in user histories
 Use these cooccurring items as “indicators”
 For all indicators in user history, accumulate scores for related
items

Recommendation Basics
 History:
User Thing
1 3
2 4
3 4
2 3
3 2
1 1
2 1

 History as matrix:
 (t1, t3) cooccur 2 times,
 (t1, t4) once,
 (t2, t4) once,
 (t3, t4) once
t1 t2 t3 t4
u1 1 0 1 0
u2 1 0 1 1
u3 0 1 0 1

A Quick Simplification
 Users who do h
 Also do r
Ah
AT
Ah( )
AT
A( )h
User-centric recommendations
Item-centric recommendations

 Coocurrence
t1 t2 t3 t4
t1 2 0 2 1
t2 0 1 0 1
t3 2 0 1 1
t4 1 1 1 2

Problems with Raw Cooccurrence
 Very popular items co-occur with everything
– Welcome document
– Elevator music
 That isn’t interesting
– We want anomalous cooccurrence

 Coocurrence
t1 t2 t3 t4
t1 2 0 2 1
t2 0 1 0 1
t3 2 0 1 1
t4 1 1 1 2
t3 not t3
t1 2 1
not t1 1 1

Spot the Anomaly
 Root LLR is roughly like standard deviations
A not A
B 13 1000
not B 1000 100,000
A not A
B 1 0
not B 0 2
A not A
B 1 0
not B 0 10,000
A not A
B 10 0
not B 0 100,000
0.44 0.98
2.26 7.15

Threshold by Score
 Coocurrence
t1 t2 t3 t4
t1 2 0 2 1
t2 0 1 0 1
t3 2 0 1 1
t4 1 1 1 2

Threshold by Score
 Significant cooccurrence => Indicators
t1 t2 t3 t4
t1 1 0 0 1
t2 0 1 0 1
t3 0 0 1 1
t4 1 0 0 1

So Far, So Good
 Classic recommendation systems based on these approaches
– Musicmatch (ca 2000)
– Veoh Networks (ca 2005)
 Currently available in Mahout
– See RowSimilarityJob
 Very simple to deploy
– Compute indicators
– Store in search engine
– Works very well with enough data

What’s right
about this?

Virtues of Current State of the Art
 Lots of well publicized history
– Musicmatch, Veoh, Netflix, Amazon, Overstock
 Lots of support
– Mahout, commercial offerings like Myrrix
 Lots of existing code
– Mahout, commercial codes
 Proven track record
 Well socialized solution

What’s wrong
about this?

Problems for Recommenders
 Cold start
 Disjoint populations
 Long tail
 Multiple kinds of evidence (multi-modal recommendations)
– unstructured add-on data
– other transaction streams
– textual descriptions

What is this multi-modal stuff?
 But people don’t just do one thing
 One kind of behavior is useful for predicting other kinds
 Having a complete picture is important for accuracy
 What has the user said, viewed, clicked, closed, bought lately?

Example Multi-modal Inputs
 Overlap in restaurant visits is useful
 Big spender cues
 Cuisine as an indicator
 Review text as an indicator

Too Limited
 People do more than one kind of thing
 Different kinds of behaviors give different quality, quantity and
kind of information
 We don’t have to do co-occurrence
 We can do cross-occurrence
 Result is cross-recommendation

Heh?

For example
 Users enter queries (A)
– (actor = user, item=query)
 Users view videos (B)
– (actor = user, item=video)
 ATA gives query recommendation
– “did you mean to ask for”
 BTB gives video recommendation
– “you might like these videos”

The punch-line
 BTA recommends videos in response to a query
– (isn’t that a search engine?)
– (not quite, it doesn’t look at content or meta-data)

Real-life example
 Query: “Paco de Lucia”
 Conventional meta-data search results:
– “hombres del paco” times 400
– not much else
 Recommendation based search:
– Flamenco guitar and dancers
– Spanish and classical guitar
– Van Halen doing a classical/flamenco riff

Real-life example

Hypothetical Example
 Want a navigational ontology?
 Just put labels on a web page with traffic
– This gives A = users x label clicks
 Remember viewing history
– This gives B = users x items
 Cross recommend
– B’A = label to item mapping
 After several users click, results are whatever users think they
should be

Nice. But we
can do better?

Ausers
things

A1 A2
é
ë
ù
û
users
thing
type 1
thing
type 2

A1 A2
é
ë
ù
û
T
A1 A2
é
ë
ù
û=
A1
T
A2
T
é
ë
ê
ê
ù
û
ú
ú
A1 A2
é
ë
ù
û
=
A1
T
A1 A1
T
A2
AT
2A1 AT
2A2
é
ë
ê
ê
ù
û
ú
ú
r1
r2
é
ë
ê
ê
ù
û
ú
ú
=
A1
T
A1 A1
T
A2
AT
2A1 AT
2A2
é
ë
ê
ê
ù
û
ú
ú
h1
h2
é
ë
ê
ê
ù
û
ú
ú
r1 = A1
T
A1 A1
T
A2
é
ëê
ù
ûú
h1
h2
é
ë
ê
ê
ù
û
ú
ú

Summary
 Input: Multiple kinds of behavior on one set of things
 Output: Recommendations for one kind of behavior with a
different set of things
 Cross recommendation is a special case

Now again, without
the scary math

Input Data
 User transactions
– user id, merchant id
– SIC code, amount
– Descriptions, cuisine, …
 Offer transactions
– user id, offer id
– vendor id, merchant id’s,
– offers, views, accepts

Input Data
 User transactions
– user id, merchant id
– SIC code, amount
– Descriptions, cuisine, …
 Offer transactions
– user id, offer id
– vendor id, merchant id’s,
– offers, views, accepts
 Derived user data
– merchant id’s
– anomalous descriptor terms
– offer & vendor id’s
 Derived merchant data
– local top40
– SIC code
– vendor code
– amount distribution

Cross-recommendation
 Per merchant indicators
– merchant id’s
– chain id’s
– SIC codes
– indicator terms from text
– offer vendor id’s
 Computed by finding anomalous (indicator => merchant) rates

How can we deploy
this?

Search-based Recommendations
 Sample document
– Merchant Id
– Field for text description
– Phone
– Address
– Location

 Sample document
– Merchant Id
– Phone
– Address
– Location
– Indicator merchant id’s
– Indicator industry (SIC) id’s
– Indicator offers
– Indicator text
– Local top40

 Sample document
– Merchant Id
– Phone
– Address
– Location
– Indicator text
– Local top40
 Sample query
– Current location
– Recent merchant descriptions
– Recent merchant id’s
– Recent SIC codes
– Recent accepted offers
– Local top40

 Sample document
– Merchant Id
– Phone
– Address
– Location
– Indicator text
– Local top40
 Sample query
– Current location
– Recent merchant descriptions
– Recent merchant id’s
– Recent SIC codes
– Recent accepted offers
– Local top40
Original data
and meta-data
Derived from cooccurrence
and cross-occurrence
analysis
Recommendation
query

SolR
Indexer
SolR
Indexer
Solr
indexing
Cooccurrence
(Mahout)
Item meta-
data
Index
shards
Complete
history
Analyze with Map-Reduce

SolR
Indexer
SolR
Indexer
Solr
search
Web tier
Item meta-
data
Index
shards
User
history
Deploy with Conventional Search System

Objective Results
 At a very large credit card company
 History is all transactions
 Development time to minimal viable product about 4 months
 General release 2-3 months later
 Search-based recs at or equal in quality to other techniques

 Contact:
– tdunning@maprtech.com
– @ted_dunning
– @apachemahout
– @user-subscribe@mahout.apache.org
 Slides and such
http://www.slideshare.net/tdunning
 Hash tags: #mapr #apachemahout #recommendations

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