Principal component analysis (PCA) is a popular dimension reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-b...

Principal Components Analysis (PCA) consists in nding the orthogonal directions of highest variance in a distribution of vectors. In this paper, we propose to extract the principal components of a random vector that partially results from a previous PCA. We demonstrate that this contextual PCA pro vides an optimal linear encoding of temporal con text. A recurrent neural netw ork based on this p...

We introduce an efficient statistical modeling technique called Mixture of Principal Components (MPC). This model is a linear extension to the traditional Principal Component Analysis (PCA) and uses a mixture of eigenspaces to capture data variations. We use the model to capture face appearance variations due to pose and lighting changes. We show that this more efficient modeling leads to impro...

Traditional tensor decompositions such as the CANDECOMP / PARAFAC (CP) and Tucker decompositions yield higher-order principal components that have been used to understand tensor data in areas such as neuroimaging, microscopy, chemometrics, and remote sensing. Sparsity in high-dimensional matrix factorizations and principal components has been well-studied exhibiting many benefits; less attentio...