large-scale single-pass k-means clustering at scale
DESCRIPTION
Large-scale Single-pass k-Means Clustering at Scale. 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 - PowerPoint PPT PresentationTRANSCRIPT
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Large-scale Single-pass k-Means Clustering at Scale
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Large-scale Single-pass k-Means Clustering
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Large-scale k-Means Clustering
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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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Non-goals
Use map-reduce (but it is there) Minimize the number of clusters Support metrics other than L2
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Anti-goals
Multiple passes over original data Scale as O(k n)
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Why?
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K-nearest Neighbor withSuper Fast k-means
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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
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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
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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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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
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Projection Search
java.lang.TreeSet!
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How Many Projections?
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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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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
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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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Algorithmic Details
Foreach data point xn
compute distance to nearest centroid, ∂sample u, if u > ∂/ß add to nearest centroidelse create new centroid
if number of centroids > 10 log nrecursively cluster centroidsset ß = 1.5 ß if number of centroids did not decrease
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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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Parallel Speedup?
✓
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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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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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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
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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
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Contact:– [email protected]– @ted_dunning
Slides and such:– http://info.mapr.com/ted-mlconf.html
Hash tags: #mlconf #mahout #mapr