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Application of Multi-Dimensional Principal Component Analysis to Medical Data

Year: 2012 Volume: 6 Issue: 3 315 - 321 Pages

• Authors:
• Naoki Yamamoto
• Jun Murakami
• Chiharu Okuma
• Yutaro Shigeto
• Satoko Saito
• Takashi Izumi
• Nozomi Hayashida

Abstract: Multi-dimensional principal component analysis (PCA) is the extension of the PCA, which is used widely as the dimensionality reduction technique in multivariate data analysis, to handle multi-dimensional data. To calculate the PCA the singular value decomposition (SVD) is commonly employed by the reason of its numerical stability. The multi-dimensional PCA can be calculated by using the higher-order SVD (HOSVD), which is proposed by Lathauwer et al., similarly with the case of ordinary PCA. In this paper, we apply the multi-dimensional PCA to the multi-dimensional medical data including the functional independence measure (FIM) score, and describe the results of experimental analysis.

• Keywords:
• multi-dimensional principal component analysis
• higher-order SVD (HOSVD)
• functional independence measure (FIM)
• medical data
• tensor decomposition

Comparison between Higher-Order SVD and Third-order Orthogonal Tensor Product Expansion

Year: 2009 Volume: 3 Issue: 3 539 - 545 Pages

• Authors:
• Chiharu Okuma
• Jun Murakami
• Naoki Yamamoto

Abstract: In digital signal processing it is important to approximate multi-dimensional data by the method called rank reduction, in which we reduce the rank of multi-dimensional data from higher to lower. For 2-dimennsional data, singular value decomposition (SVD) is one of the most known rank reduction techniques. Additional, outer product expansion expanded from SVD was proposed and implemented for multi-dimensional data, which has been widely applied to image processing and pattern recognition. However, the multi-dimensional outer product expansion has behavior of great computation complex and has not orthogonally between the expansion terms. Therefore we have proposed an alterative method, Third-order Orthogonal Tensor Product Expansion short for 3-OTPE. 3-OTPE uses the power method instead of nonlinear optimization method for decreasing at computing time. At the same time the group of B. D. Lathauwer proposed Higher-Order SVD (HOSVD) that is also developed with SVD extensions for multi-dimensional data. 3-OTPE and HOSVD are similarly on the rank reduction of multi-dimensional data. Using these two methods we can obtain computation results respectively, some ones are the same while some ones are slight different. In this paper, we compare 3-OTPE to HOSVD in accuracy of calculation and computing time of resolution, and clarify the difference between these two methods.

• Keywords:
• Singular value decomposition (SVD)
• higher-order SVD (HOSVD)
• higher-order tensor
• outer product expansion
• power method.