Model-Based Clustering for Multivariate Binary Data with Dimension Reduction

• Activity Number: 498
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Michio Yamamoto*+ and Kenichi Hayashi
• Companies: Osaka University and Osaka University Graduate School of Medicine
• Keywords: Clustering ; Dimension reduction ; EM algorithm ; Latent class analysis ; Sparsity

Abstract

It is well-known that reducing dimensionality of data improves the performance of clustering algorithms, especially in high-dimensional data; a lot of methods to perform simultaneously clustering and dimension reduction have been developed. This work presents a new procedure for simultaneously finding the optimal cluster structure of multivariate binary data and a subspace to represent the cluster structure. The method is based on a finite mixture model of multivariate Bernoulli distributions and parameters of each component are assumed to have low-dimensional representations. Our model can be considered as an extension of the traditional latent class analysis model. The proposed method introduces sparsity to the loading vectors, which produce the low-dimensional subspace, for enhanced interpretability and more stable extraction of the subspace. An EM-based algorithm is developed to efficiently solve the proposed optimization problem. The effectiveness of the proposed method is illustrated by application to a simulation study and a real data set.