演講公告

東海大學統計學系學術演講20170516

公告時間:2017-05-10 11:42:20
公告單位:統計學系

 

 

東海大學統計學系學術演講

間:1060516日(星期二下午14:10~15:00

點:管理學院新大樓M367

主講人:杜憶萍   研究員   (中研院統計科學研究所)

題:Rank Selection for Multilinear Principal Component Analysis

Abstract

   Multilinear Principal Component Analysis (MPCA) has been a popular method to reduce the dimension of tensor data. One key challenge for further statistical applications of MPCA is to choose a proper tensor rank. Both Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) need the likelihood function of the observation data that a more strong model assumption than the original model is required. We propose a rank selection criterion for MPCA based on the minimum risk criterion and employ Stein's unbiased risk estimate (SURE). We present SURE for the MPCA model in a neat formula composed of a residual sum for model fitting and a penalty on the model complexity expressed as the generalized degrees of freedom (GDF). We are able to match each term of the GDF to either the number of parameters used in the model or the complexity in separating the signal from the noise. Furthermore, SURE for the Principal Component Analysis model becomes a special case in our criterion. Even for the data generated according to the assumptions of AIC and BIC, the selection method based on SURE reaches higher selection accuracies with much less computation loading, when the matrix size is large and the sample size is moderate.

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