Classification Probabilistic PCA with Application in Domain Adaptation

Conventional dimensionality reduction algorithms such as principle component analysis (PCA) and non-negative matrix factorization (NMF) are unsupervised. Supervised probabilistic PCA (SPPCA) can utilize label information. However, this information is usually treated as regression targets rather than discrete nominal labels. We propose a classification probabilistic PCA (CPPCA) which is an extension of probabilistic PCA. Unlike SPPCA, the label class information is turned into a class probabilistic function by using a sigmoidal function. As the posterior distribution of latent variables are non-Gaussian, we use Laplace approximation with Expectation Maximization (EM) to obtain the solution. The formulation is applied to a domain adaptation classification problem where the labeled training data and unlabeled test data come from different but related domains. Experimental results show that the proposed model has accuracy over conventional probabilistic PCA, SPPCA and its semi-supervised version. It has similar performance when compared with popular dedicated algorithms for domain adaptation, the structural correspondence learning (SCL) and its variants.