Parametric Models for Mutual Kernel Matrix Completion

Rachelle RIVERO  Tsuyoshi KATO  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E101-D   No.12   pp.2976-2983
Publication Date: 2018/12/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.2018EDP7139
Type of Manuscript: PAPER
Category: Fundamentals of Information Systems
Keyword: 
multiview learning,  incomplete-data problem,  probabilistic PCA,  factor analysis,  kernel matrix completion,  

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Summary: 
Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the flexibility of the model by parameterizing the model matrix. By imposing restrictions on the model covariance, overfitting of the data is avoided. A limitation of kernel matrix estimations done via optimization of an objective function is that the positive definiteness of the result is not guaranteed. In view of this limitation, our proposed methods employ the LogDet divergence, which ensures the positive definiteness of the resulting inferred kernel matrix. We empirically show that our proposed restricted covariance models, employed with LogDet divergence, yield significant improvements in the generalization performance of previous completion methods.