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  4. Dimension Reduction for Tensor Structure Data
 
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Dimension Reduction for Tensor Structure Data

Date Issued
2014
Date
2014
Author(s)
Niu, Po-Yao
URI
http://ntur.lib.ntu.edu.tw//handle/246246/264033
Abstract
The advances of technologies have created a new era for data collections that the data size and its complexity becomes very challenging to data analysts. Dimension reduction is a key process for statistical inference when facing huge data set. Principal component analysis (PCA) may be the most popular dimension reduction method for vector data. PCA projects the data to a lower space and the features become uncorrelated in the new space, but, in reality, it could be inefficient due to small sample size and large feature dimension. Multilinear principal component analysis (MPCA) has been proposed to reduce the dimension for tensor structure data, including matrix data. MPCA models the space as Kronecker products of vectors to use the parameters in a more efficient way, but it might have correlated scores. In this thesis, we proposed a two-stage dimension reduction method, called structure PCA (SPCA), aiming to combine the advantages of PCA and MPCA. SPCA employs MPCA on the original data in the first step, and then applies PCA on the vectorized core scores in the second step. The statistical efficiency comparisons between PCA and SPCA are made and SPCA has been proved to have better asymptotic efficiency under some conditions. The performance of PCA, MPCA and SPCA are checked for both simulation and real data and SPCA is shown to be a promising method for huge tensor structure data.
Subjects
主成分分析
多線性主成分分析
結構主成分分析
張量
漸進
效度
Type
thesis
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ntu-103-R99221002-1.pdf

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