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Fast and Probvably Seedings for k-Means

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Kimikazu Kato
Kimikazu Kato

NIPS2016論文読み会の資料です。 Material for NIPS paper reading meetup

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Fast and Provably Good Seedings for k-Means O. Bachem, M. Lucic, S. Hassani, A. Krause Presented by Kimikazu Kato, Silver Egg Technology Co., Ltd.
Algorithm of k-Means clustering Determine initial centroids Update centroids and membership of clusters gradually Improvement of this part Existing results: k-means++: sampling according to some metric Bachem et al. 2016: Performance improvement using MCMC, but has some assumption about the distribution of the data Proposed: Another MCMC based algorithm without assumption of the distribution Outline
Related researches kmeans++ Draw accoding to Intuition: Choose initial centroids from the input data so that they scatter as widely as possible Bachem et al. 2016 Intended to overcome the shortcoming of kmeans++: the marginalization cost Metropolitan Hastings algorithm, which utilizes rejection sampling to emulate the distribution. But have some assumption on the input data. as a centroid C: set of centroids which are already chosen
Proposed Algorithm Update from the preceding result: rejection criterion The convergence is mathematically proved.
Experimental Results 1/3
Experimental Results 2/3
Experimental Results 3/3
Conclusion • Novel algorithm for the initialization of centroids in kmeans • Theoretical guarantee on the convergence and the trade-off of accuracy and speed • Experimentally good result

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Fast and Probvably Seedings for k-Means

  • 1. Fast and Provably Good Seedings for k-Means O. Bachem, M. Lucic, S. Hassani, A. Krause Presented by Kimikazu Kato, Silver Egg Technology Co., Ltd.
  • 2. Algorithm of k-Means clustering Determine initial centroids Update centroids and membership of clusters gradually Improvement of this part Existing results: k-means++: sampling according to some metric Bachem et al. 2016: Performance improvement using MCMC, but has some assumption about the distribution of the data Proposed: Another MCMC based algorithm without assumption of the distribution Outline
  • 3. Related researches kmeans++ Draw accoding to Intuition: Choose initial centroids from the input data so that they scatter as widely as possible Bachem et al. 2016 Intended to overcome the shortcoming of kmeans++: the marginalization cost Metropolitan Hastings algorithm, which utilizes rejection sampling to emulate the distribution. But have some assumption on the input data. as a centroid C: set of centroids which are already chosen
  • 4. Proposed Algorithm Update from the preceding result: rejection criterion The convergence is mathematically proved.
  • 8. Conclusion • Novel algorithm for the initialization of centroids in kmeans • Theoretical guarantee on the convergence and the trade-off of accuracy and speed • Experimentally good result