We study unsupervised learning in a probabilistic generative model for occlusion. The model uses two types of latent variables: one indicates which objects are present in the image, and the other how they are ordered in depth. This depth order then determines how the positions and appearances of the objects present, specified in the model parameters, combine to form the image. We show that the ...

We study unsupervised learning in a probabilistic generative model for occlusion. The model uses two types of latent variables: one indicates which objects are present in the image, and the other how they are ordered in depth. This depth order then determines how the positions and appearances of the objects present, specified in the model parameters, combine to form the image. We show that the ...

A recurrent linear network can be trained with Oja's constrained Hebbian learning rule. As a result, the network learns to represent the temporal context associated to its input sequence. The operation performed by the network is a generalization of Principal Components Analysis (PCA) to time-series, called Recursive PCA. The representations learned by the network are adapted to the temporal st...

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. Contemporary data sets often have p comparable to, or even much larger than n. Our main assertions, in such settings, are (a) that some initial reduction in dimensionality is desirable before applying any PCA-type search for...

Principal components analysis is an important and well-studied subject in statistics and signal processing. The literature has an abundance of algorithms for solving this problem, where most of these algorithms could be grouped into one of the following three approaches: adaptation based on Hebbian updates and deflation, optimization of a second order statistical criterion (like reconstruction ...

Principal components analysis (PCA) is one of the most widely used techniques in machine learning and data mining. Minor components analysis (MCA) is less well known, but can also play an important role in the presence of constraints on the data distribution. In this paper we present a probabilistic model for “extreme components analysis” (XCA) which at the maximum likelihood solution extracts ...

Derivation of PCA I: For a set of d-dimensional data vectors {x}i=1, the principal axes {e}qj=1 are those orthonormal axes onto which the retained variance under projection is maximal. It can be shown that the vectors ej are given by the q dominant eigenvectors of the sample covariance matrix S, such that Sej = λjej . The q principal components of the observed vector xi are given by the vector ...