Parallelizing a Co-Clustering Application with a Reduction

Based Framework on Multi-Core Clusters

Venkatram Ramanathan

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OutlineMotivation

Evolution of Multi-Core Machines and the challenges

Background: MapReduce and FREERIDE

Co-clustering on FREERIDE Experimental EvaluationConclusion

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Motivation - Evolution Of Multi-Core Machines

Performance Increase: Increased number of cores with lower

clock frequencies Cost Effective Scalability of performance

HPC Environments – Cluster of Multi-Cores

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Challenges

Multi-Level Parallelism Within Cores in a node – Shared

Memory Parallelism - Pthreads, OpenMP Within Nodes – Distributed Memory

Parallelism - MPI Achieving Programmability and Performance – Major Challenge

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Challenges

Possible solutionUse higher-level/restricted APIsReduction based APIs

Map-ReduceHigher-level APIProgram Cluster of Multi-Cores with 1 APIExpressive Power Considered Limited

Expressing computations using reduction-based APIs

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Background

MapReduceMap (in_key,in_value) ->

list(out_key,intermediate_value)Reduce(out_key,list(intermediate_value) -> list(out_value)

FREERIDEUsers explicitly declare Reduction Object

and update itMap and Reduce steps combined Each data element – processed and reduced

before next element is processed6

MapReduce and FREERIDE: Comparison

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Co-clustering

Involves simultaneous clustering of rows to row clusters and columns to column clusters

Maximizes Mutual Information Uses Kullback-Leibler Divergence

x

xqxpxpqpKL ))()(log()(),(

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Overview of Co-clustering Algorithm – Preprocessing

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Overview of Co-clustering Algorithm – Iterative Procedure

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Parallelizing Co-clustering on FREERIDE

Input matrix and its transpose pre-computed Input matrix and transpose

Divided into files Distributed among nodes Each node - same amount of row and column data

rowCL and colCL – replicated on all nodes Initial clustering

Round robin fashion - consistency across nodes

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Parallelizing Preprocess Step

In Preprocessing, pX and pY – normalized by total sum

Wait till all nodes process to normalize Each node calculates pX and pY with local data Reduction object updated partial sum, pX and pY

values Accumulated partial sums - total sum pX and pY normalized

xnorm and ynorm calculated in second iteration as they need total sum

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Parallelizing Preprocess Step

Compressed Matrix of size #rowclusters x #colclusters, calculated with local data Sum of values of values of each row cluster

across each column cluster Final compressed matrix -sum of local

compressed matrices Local compressed matrices – updated in

reduction object Produces final compressed matrix on

accumulation Cluster Centroids calculated

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Parallelizing Iterative Procedure

Reassign clusteringDetermined by Kullback-Leibler divergence Reduction object updated

Compute compressed matrix Update reduction object

Column Clustering – similar Objective function – finalize Next iteration

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Parallelizing Co-clustering on FREERIDE

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Parallelizing Iterative Procedure

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Experimental Results

Algorithm - same for shared memory, distributed memory and hybrid parallelization

Experiments conducted 2 clusters env1

Intel Xeon E5345 Quad Core Clock Frequency 2.33 GHz Main Memory 6 GB 8 nodes

env2 AMD Opteron 8350 CPU 8 Cores Main Memory 16 GB 4 Nodes

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Experimental Results

2 Datasets 1 GB Dataset

Matrix Dimensions 16k x 16k 4 GB Dataset

Matrix Dimensions 32k x 32k Datasets and transpose

Split into 32 files each (row partitioning) Distributed among nodes

Number of row and column clusters: 4

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Experimental Results

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Experimental Results

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Experimental Results

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Experimental Results

Preprocessing stage – bottleneck for smaller dataset – not compute intensive

Speedup with Preprocessing : 12.17 Speedup without Preprocessing: 18.75 Preprocessing stage scales well for Larger

dataset – more computation Speedup is the same with and without

preprocessing. Speedup for larger dataset : 20.7

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Conclusion

FREERIDE Offers the Following Advantages: No need for loading data in custom file-systems C/C++ based frameworkMuch better performance (comparison for other

algorithms) Co-clusterings can be viewed as

generalized reduction Implementing them on FREERIDE

Speedup of 21 on 32 cores.

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