[jira] [Commented] (SPARK-14174) Accelerate KMeans via Mini-Batch EM

["zhengruifeng (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/SPARK-14174?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15643101#comment-15643101 ] 

zhengruifeng commented on SPARK-14174:
--------------------------------------

In addition, MiniBatch EM can also be used in MixtureModels. see {{6 EM variants}} in  http://www.cs.ubc.ca/%7Emurphyk/Teaching/CS340-Fall06/reading/mixtureModels.pdf 
  

> Accelerate KMeans via Mini-Batch EM
> -----------------------------------
>
>                 Key: SPARK-14174
>                 URL: https://issues.apache.org/jira/browse/SPARK-14174
>             Project: Spark
>          Issue Type: Improvement
>          Components: MLlib
>            Reporter: zhengruifeng
>            Priority: Minor
>
> The MiniBatchKMeans is a variant of the KMeans algorithm which uses mini-batches to reduce the computation time, while still attempting to optimise the same objective function. Mini-batches are subsets of the input data, randomly sampled in each training iteration. These mini-batches drastically reduce the amount of computation required to converge to a local solution. In contrast to other algorithms that reduce the convergence time of k-means, mini-batch k-means produces results that are generally only slightly worse than the standard algorithm.
> I have implemented mini-batch kmeans in Mllib, and the acceleration is realy significant.
> The MiniBatch KMeans is named XMeans in following lines.
> {code}
> val path = "/tmp/mnist8m.scale"
> val data = MLUtils.loadLibSVMFile(sc, path)
> val vecs = data.map(_.features).persist()
> val km = KMeans.train(data=vecs, k=10, maxIterations=10, runs=1, initializationMode="k-means||", seed=123l)
> km.computeCost(vecs)
> res0: Double = 3.317029898599564E8
> val xm = XMeans.train(data=vecs, k=10, maxIterations=10, runs=1, initializationMode="k-means||", miniBatchFraction=0.1, seed=123l)
> xm.computeCost(vecs)
> res1: Double = 3.3169865959604424E8
> val xm2 = XMeans.train(data=vecs, k=10, maxIterations=10, runs=1, initializationMode="k-means||", miniBatchFraction=0.01, seed=123l)
> xm2.computeCost(vecs)
> res2: Double = 3.317195831216454E8
> {code}
> The above three training all reached the max number of iterations 10.
> We can see that the WSSSEs are almost the same. While their speed perfermence have significant difference:
> {code}
> KMeans                                                    2876sec
> MiniBatch KMeans (fraction=0.1)             263sec
> MiniBatch KMeans (fraction=0.01)           90sec
> {code}
> With appropriate fraction, the bigger the dataset is, the higher speedup is.
> The data used above have 8,100,000 samples, 784 features. It can be downloaded here (https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/multiclass/mnist8m.scale.bz2)
> Comparison of the K-Means and MiniBatchKMeans on sklearn : http://scikit-learn.org/stable/auto_examples/cluster/plot_mini_batch_kmeans.html#example-cluster-plot-mini-batch-kmeans-py



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