- 著者
- Akisato Kimura Masashi Sugiyama Hitoshi Sakano Hirokazu Kameoka
- 雑誌
- 情報処理学会論文誌数理モデル化と応用(TOM) (ISSN:18827780)
- 巻号頁・発行日
- vol.6, no.1, pp.136-145, 2013-03-12
It is well known that dimensionality reduction based on multivariate analysis methods and their kernelized extensions can be formulated as generalized eigenvalue problems of scatter matrices, Gram matrices or their augmented matrices. This paper provides a generic and theoretical framework of multivariate analysis introducing a new expression for scatter matrices and Gram matrices, called Generalized Pairwise Expression (GPE). This expression is quite compact but highly powerful. The framework includes not only (1) the traditional multivariate analysis methods but also (2) several regularization techniques, (3) localization techniques, (4) clustering methods based on generalized eigenvalue problems, and (5) their semi-supervised extensions. This paper also presents a methodology for designing a desired multivariate analysis method from the proposed framework. The methodology is quite simple: adopting the above mentioned special cases as templates, and generating a new method by combining these templates appropriately. Through this methodology, we can freely design various tailor-made methods for specific purposes or domains.
- 著者
- Akisato Kimura Masashi Sugiyama Takuho Nakano Hirokazu Kameoka Hitoshi Sakano Eisaku Maeda Katsuhiko Ishiguro
- 雑誌
- 情報処理学会論文誌数理モデル化と応用(TOM) (ISSN:18827780)
- 巻号頁・発行日
- vol.6, no.1, pp.128-135, 2013-03-12
Canonical correlation analysis (CCA) is a powerful tool for analyzing multi-dimensional paired data. However, CCA tends to perform poorly when the number of paired samples is limited, which is often the case in practice. To cope with this problem, we propose a semi-supervised variant of CCA named SemiCCA that allows us to incorporate additional unpaired samples for mitigating overfitting. Advantages of the proposed method over previously proposed methods are its computational efficiency and intuitive operationality: it smoothly bridges the generalized eigenvalue problems of CCA and principal component analysis (PCA), and thus its solution can be computed efficiently just by solving a single eigenvalue problem as the original CCA.