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We propose a constrained EM algorithm for principal component analysis (PCA) using a coupled probability model derived from single-standard factor analysis models with isotropic noise structure. The single probabilistic PCA, especially for the case where there is no noise, can find only a vector set that is a linear superposition of principal components and… (More)

A common derivation of principal component analysis (PCA) is based on the minimization of the squared-error between centered data and linear model, corresponding to the reconstruction error. In fact, minimizing the squared-error leads to principal subspace analysis where scaled and rotated principal axes of a set of observed data, are estimated. In this… (More)

We present a generalization of the nonnegative matrix factorization (NMF), where a multilayer generative network with nonnegative weights is used to approximate the observed nonnegative data. The multilayer generative network with nonnegativity constraints, is learned by a multiplicative uppropagation algorithm, where the weights in each layer are updated… (More)

Minimization of reconstruction error (squared-error) leads to principal subspace analysis (PSA) which estimates scaled and rotated principal axes of a set of observed data. In this paper we introduce a new alternative error, so called, integrated-squared-error, the minimization of which determines the exact principal axes (without rotational ambiguity) of a… (More)

In this paper we introduce a new error measure, integrated reconstruction error (IRE) and show that the minimization of IRE leads to principal eigenvectors (without rotational ambiguity) of the data covariance matrix. Then we present iterative algorithms for the IRE minimization, where we use the projection approximation. The proposed algorithm is referred… (More)

Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that… (More)