Open House, ISM in Tachikawa, 2017.6.16統計数理研究所オープンハウス（立川）、H29.6.16ポスター発

Andrade Silva Daniel Georg

Daniel Georg Andrade Silva

English

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所 学術研究リポジトリ

Variable Clustering With the Gaussian Graphical ModelAndrade Daniel 総合研究大学院大学 統計科学専攻 ５年一貫制博士課程４年2017年6月16日 統計数理研究所 オープンハウスGoal:• Cluster objects according to their pair-wise correlations. Mean is not useful for distinguishing group of objects.• Model-based clustering including principled methods for selection of number of clusters.Applications: • Detecting independent groups of stocks, sensors, genes, costumers, politicians,…Assumptions:• Data is generated iid from Normal distribution with mean 0 and block-diagonal precision matrix X.• Number of blocks m is unknown.Proposed Approach:ppPrecision matrix X𝑞 ∈ 1, 2Express constraintusing (unnormalized) Laplacian LConvex relaxation of rank constraintS is the sample covariance matrixq = 1: Problem is equivalent to Graphical Lasso (GL)q = 2: Squared (SQR) penalty on partial correlations. Solvable via a new efficient fix-point iteration algorithm. Model Selection:where 𝐿(𝑋)	; 	𝑆, 𝐶.,/	) is the unpenalized log-likelihood, and 𝐶.,/ is the partition of the variables (found by spectral clustering)(3)(1)(2)(4)Experiments:SummaryDPCV = Dirichlet Process Variable Clustering proposed in [Palla et al. 2012]SLC = Single Linkage Clustering including model selection proposed in [Tan et al. 2015]ALC =  Average Linkage Clustering including model selection proposed in [Tan et al. 2015]SQR-Spectral-BIC = Use of proposed Algorithm 1 with q = 2.GL-Spectral-BIC = Use of proposed Algorithm 1 with q = 1.ID-Spectral-BIC = Use of proposed Algorithm 1 with 𝑋∗	 = 𝑆 + 𝜆𝐼 67Evaluation of clustering results for "ideal" and "noise-corrupted" synthetic data with 4 clusters,p = 400, and n in {100, 200, 400, 800, 1600}. Shows the adjusted normalized mutual information (ANMI) and the number of clusters (Clusters).Conclusions:- Combination of Spectral clustering and BIC for clustering selection is useful, even when model assumptions are violated (“noise-corrupted”).- Performance of SQR-Spectral-BIC is comparable or better than GL-Spectral-BIC,while being almost 10 times faster.  - SQR-Spectral-BIC and GL-Spectral-BIC can perform considerably better than previously proposed methods (also on real data, results omitted here).Average runtime in minutes of algorithms for "ideal" synthetic data with p = 400, n = 1600:

Variable Clustering With the Gaussian Graphical Model

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Variable Clustering With the Gaussian Graphical Model

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RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所学術研究リポジトリ

Variable Clustering With the Gaussian Graphical Model

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RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所 学術研究リポジトリ

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所学術研究リポジトリ