Latent Dimensionality Estimation for Probabilistic Canonical Correlation Analysis Using Normalized Maximum Likelihood Code-Length
Tomohiko Nakmaura, Tomoharu Iwata, Kenji Yamanishi · 2017
Discovering hidden common factors from multiple different but related datasets is an important task in data mining. Probabilistic canonical correlation analysis (PCCA) is successfully used for this task, where private factors, which represent independent factors that have influence on a dataset, are modeled as well as common factors. We propose a method for estimating the latent dimensionality of PCCA, which represents the numbers of common and private factors. The dimensionality estimation is indispensable for both generalization ability and interpretability. The proposed method applies the minimum description length criterion using normalized maximum likelihood coding to PCCA in a theoretically justified manner, where PCCA is transformed to a regular model by latent variable completion. We demonstrate that the proposed method surpasses conventional methods in terms of dimensionality estimation performance.