document: Supervised probabilistic principal component analysis Principal component analysis ( PCA ) has been extensively applied in data mining , pattern recognition and information retrieval for unsupervised dimensionality reduction . When labels of data are available , e.g. , in a classification or regression task , PCA is however not able to use this information . The problem is more interesting if only part of the input data are labeled , i.e. , in a semi-supervised setting . In this paper we propose a supervised PCA model called SPPCA and a semi-supervised PCA model called S2PPCA , both of which are extensions of a probabilistic PCA model . The proposed models are able to incorporate the label information into the projection phase , and can naturally handle multiple outputs ( i.e. , in multi-task learning problems ) . We derive an efficient EM learning algorithm for both models , and also provide theoretical justifications of the model behaviors . SPPCA and S2PPCA are compared with other supervised projection methods on various learning tasks , and show not only promising performance but also good scalability .
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