Graphlab Ted Dunning Clustering

1©MapR Technologies - Confidential
Large-scale Single-pass k-Means
Clustering at Scale
Ted Dunning

Large-scale Single-pass k-Means
Clustering

Large-scale k-Means Clustering

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

Non-goals
 Use map-reduce (but it is there)
 Minimize the number of clusters
 Support metrics other than L2

Anti-goals
 Multiple passes over original data
 Scale as O(k n)

Why?

K-nearest Neighbor with
Super Fast k-means

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 don’t have knobs to turn
or models to build
– hard because of the stunning amount of math
– also hard because we need top 50,000 results
 Initial prototype was massively too slow
– 3K queries x 200K examples takes hours
– needed 20M x 25M in the same time

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

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

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
– ProjectionSearch, KmeansSearch, LshSearch, Brute
 Super-fast clustering
– Kmeans, StreamingKmeans

Projection Search
java.lang.TreeSet!

How Many Projections?

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!

x

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)
– Very parallelizable

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

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 > 10 log n
recursively cluster centroids
set ß = 1.5 ß if number of centroids did not decrease

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

Parallel Speedup?
1 2 3 4 5 20
10
100
20
30
40
50
200
Threads
Timeperpoint(μs)
2
3
4
5
6
8
10
12
14
16
Threaded version
Non- threaded
Perfect Scaling
✓

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)

(Let’s not use k-means searcher, though)
 Empirically, projection search beats 64 bit LSH by a bit

Moving to 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 essentially never important

 Contact:
– tdunning@maprtech.com
– @ted_dunning
 Slides and such:
– http://info.mapr.com/ted-mlconf
Hash tags: #mlconf #mahout #mapr

Graphlab Ted Dunning Clustering

Recommended

Recommended

More Related Content

What's hot

What's hot (19)

Similar to Graphlab Ted Dunning Clustering

Similar to Graphlab Ted Dunning Clustering (20)

More from MapR Technologies

More from MapR Technologies (20)

Recently uploaded

Recently uploaded (20)

Graphlab Ted Dunning Clustering