Describes the state of Apache Mahout with special focus on the upcoming k-nearest neighbor and k-means clustering algorithms.

1. Mahout, New and Improved
Now with Super Fast Clustering
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2. Agenda
 What happened in Mahout 0.7
– less bloat
– simpler structure
– general cleanup
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3. To Cut Out Bloat
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5. Bloat is Leaving in 0.7
 Lots of abandoned code in Mahout
– average code quality is poor
– no users
– no maintainers
– why do we care?
 Examples
– old LDA
– old Naïve Bayes
– genetic algorithms
 If you care, get on the mailing list
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6. Bloat is Leaving in 0.7
 Lots of abandoned code in Mahout
– average code quality is poor
– no users
– no maintainers
– why do we care?
 Examples
– old LDA
– old Naïve Bayes
– genetic algorithms
 If you care, get on the mailing list
– oops, too late since 0.7 is already released
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7. Integration of
Collections
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8. Nobody Cares about Collections
 We need it, math is built on it
 Pull it into math
 Broke the build (battle of the code expanders)
 Fixed now (thanks to Grant)
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9. Pig Vector
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10. What is it?
 Supports access to Mahout functionality from Pig
 So far -- text vectorization
 And classification
 And model saving
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11. What is it?
 Supports Pig access to Mahout functions
 So far text vectorization
 And classification
 And model saving
 Kind of works (see pigML from twitter for better function)
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12. Compile and Install
 Start by compiling and installing mahout in your local repository:
cd ~/Apache
git clone https://github.com/apache/mahout.git
cd mahout
mvn install -DskipTests
 Then do the same with pig-vector
cd ~/Apache
git clone git@github.com:tdunning/pig-vector.git
cd pig-vector
mvn package
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13. Tokenize and Vectorize Text
 Tokenized is done using a text encoder
– the dimension of the resulting vectors (typically 100,000-1,000,000
– a description of the variables to be included in the encoding
– the schema of the tuples that pig will pass together with their data types
 Example:
define EncodeVector
org.apache.mahout.pig.encoders.EncodeVector
('10','x+y+1', 'x:numeric, y:word, z:text');
 You can also add a Lucene 3.1 analyzer in parentheses if you want
something fancier
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14. The Formula
 Not normal arithmetic
 Describes which variables to use, whether offset is included
 Also describes which interactions to use
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15. The Formula
 Not normal arithmetic
 Describes which variables to use, whether offset is included
 Also describes which interactions to use
– but that doesn’t do anything yet!
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16. Load and Encode Data
 Load the data
a = load '/Users/tdunning/Downloads/NNBench.csv' using PigStorage(',')
as (x1:int, x2:int, x3:int);
 And encode it
b = foreach a generate 1 as key, EncodeVector(*) as v;
 Note that the true meaning of * is very subtle
 Now store it
store b into 'vectors.dat' using com.twitter.elephantbird.pig.store.SequenceFileStorage
(
'-c com.twitter.elephantbird.pig.util.IntWritableConverter’, '-c
com.twitter.elephantbird.pig.util.GenericWritableConverter
-t org.apache.mahout.math.VectorWritable’);
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17. Train a Model
 Pass previously encoded data to a sequential model trainer
define train org.apache.mahout.pig.LogisticRegression(
'iterations=5, inMemory=true, features=100000, categories=alt.atheism
comp.sys.mac.hardware rec.motorcycles sci.electronics talk.politics.guns
comp.graphics comp.windows.x rec.sport.baseball sci.med talk.politics.mideast
comp.os.ms-windows.misc misc.forsale rec.sport.hockey sci.space
talk.politics.misc comp.sys.ibm.pc.hardware rec.autos sci.crypt
soc.religion.christian talk.religion.misc');
 Note that the argument is a string with its own syntax
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18. Reservations and Qualms
 Pig-vector isn’t done
 And it is ugly
 And it doesn’t quite work
 And it is hard to build
 But there seems to be promise
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19. Potential
 Add Naïve Bayes Model?
 Somehow simplify the syntax?
 Try a recent version of elephant-bird?
 Switch to pigML?
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20. Large-scale k-Means Clustering
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21. Goals
 Cluster very large data sets
 Facilitate large nearest neighbor search
 Allow very large number of clusters
 Achieve good quality
– low average distance to nearest centroid on held-out data
 Based on Mahout Math
 Runs on Hadoop (really MapR) cluster
 FAST – cluster tens of millions in minutes
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22. Non-goals
 Use map-reduce (but it is there)
 Minimize the number of clusters
 Support metrics other than L2
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23. Anti-goals
 Multiple passes over original data
 Scale as O(k n)
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24. Why?
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25. K-nearest Neighbor with
Super Fast k-means
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26. What’s that?
 Find the k nearest training examples
 Use the average value of the target variable from them
 This is easy … but hard
– easy because it is so conceptually simple and you have few knobs to turn
or models to build
– hard because of the stunning amount of math
– also hard because we need top 50,000 results, not just single nearest
 Initial prototype was massively too slow
– 3K queries x 200K examples takes hours
– needed 20M x 25M in the same time
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27. Modeling with k-nearest Neighbors
a
b c
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28. Subject to Some Limits
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29. Log Transform Improves Things
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30. Neighbors Depend on Good Presentation
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31. How We Did It
 2 week hackathon with 6 developers from MapR customer
 Agile-ish development
 To avoid IP issues
– all code is Apache Licensed (no ownership question)
– all data is synthetic (no question of private data)
– all development done on individual machines, hosting on Github
– open is easier than closed (in this case)
 Goal is new open technology to facilitate new closed solutions
 Ambitious goal of ~ 1,000,000 x speedup
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32. How We Did It
 2 week hackathon with 6 developers from customer bank
 Agile-ish development
 To avoid IP issues
– all code is Apache Licensed (no ownership question)
– all data is synthetic (no question of private data)
– all development done on individual machines, hosting on Github
– open is easier than closed (in this case)
 Goal is new open technology to facilitate new closed solutions
 Ambitious goal of ~ 1,000,000 x speedup
– well, really only 100-1000x after basic hygiene
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33. What We Did
 Mechanism for extending Mahout Vectors
– DelegatingVector, WeightedVector, Centroid
 Shared memory matrix
– FileBasedMatrix uses mmap to share very large dense matrices
 Searcher interface
– Brute, ProjectionSearch, KmeansSearch, LshSearch
 Super-fast clustering
– Kmeans, StreamingKmeans
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34. Projection Search
java.lang.TreeSet!
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35. Projection Search
 Projection onto a line provides a total order on data
 Nearby points stay nearby
 Some other points also wind up close
 Search points just before or just after the query point
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36. How Many Projections?
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37. K-means Search
 Simple Idea
– pre-cluster the data
– to find the nearest points, search the nearest clusters
 Recursive application
– to search a cluster, use a Searcher!
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39. x
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42. x
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43. But This Requires k-means!
 Need a new k-means algorithm to get speed
– Hadoop is very slow at iterative map-reduce
– Maybe Pregel clones like Giraph would be better
– Or maybe not
 Streaming k-means is
– One pass (through the original data)
– Very fast (20 us per data point with threads on one node)
– Very parallelizable
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44. Basic Method
 Use a single pass of k-means with very many clusters
– output is a bad-ish clustering but a good surrogate
 Use weighted centroids from step 1 to do in-memory clustering
– output is a good clustering with fewer clusters
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45. Algorithmic Details
Foreach data point xn
compute distance to nearest centroid, ∂
sample u, if u > ∂/ß add to nearest centroid
else create new centroid
if number of centroids > k log n
recursively cluster centroids
set ß = 1.5 ß if number of centroids did not decrease
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46. How It Works
 Result is large set of centroids
– these provide approximation of original distribution
– we can cluster centroids to get a close approximation of clustering original
– or we can just use the result directly
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47. Parallel Speedup?
200
Non- threaded
✓
100
2
Tim e per point (μs)
Threaded version
3
50
4
40 6
5
8
30
10 14
12
20 Perfect Scaling 16
10
1 2 3 4 5 20
Threads
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48. Warning, Recursive Descent
 Inner loop requires finding nearest centroid
 With lots of centroids, this is slow
 But wait, we have classes to accelerate that!
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49. Warning, Recursive Descent
 Inner loop requires finding nearest centroid
 With lots of centroids, this is slow
 But wait, we have classes to accelerate that!
(Let’s not use k-means searcher, though)
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50. Warning, Recursive Descent
 Inner loop requires finding nearest centroid
 With lots of centroids, this is slow
 But wait, we have classes to accelerate that!
(Let’s not use k-means searcher, though)
 Empirically, projection search beats 64 bit LSH by a bit
– More optimization may change this story
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51. Moving to Ultra Mega Super Scale
 Map-reduce implementation nearly trivial
 Map: rough-cluster input data, output ß, weighted centroids
 Reduce:
– single reducer gets all centroids
– if too many centroids, merge using recursive clustering
– optionally do final clustering in-memory
 Combiner possible, but not important
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52.  Contact:
– tdunning@maprtech.com
– @ted_dunning
 Slides and such:
– http://info.mapr.com/ted-boston-2012-07
Hash tags: #boston-hug #mahout #mapr
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