In many settings, we have multiple data sets (also called views) that capture different and overlapping aspects of the same phenomenon. We are often interested in finding patterns that are unique to one or to a subset of the views. For example, we might have one set of molecular observations and one set of physiological observations on the same group of individuals, and we want to quantify mole...

Aiming at quantifying the dependency of pairs of functional data (X,Y ), we develop the concept of functional singular value decomposition for covariance and functional singular component analysis, building on the concept of “canonical expansion” of compact operators in functional analysis. We demonstrate the estimation of the resulting singular values, functions and components for the practica...

Abstract: Given a set of M signal mixtures (x1, x2, . . . , xM ) (e.g. microphone outputs), each of which is a different mixture of a set of M statistically independent source signals (s1, s2, . . . , sM ) (e.g. voices), independent component analysis (ICA) recovers the source signals (voices) from the signal mixtures. ICA is based on the assumptions that source signals are statistically indepe...

Conventional blind signal separation algorithms do not adopt any asymmetric information of the input sources, thus the convergence point of a single output is always unpredictable. However, in most of the applications, we are usually interested in only one or two of the source signals and prior information is almost always available. In this paper, a principal independent component analysis (PI...

This article presents a unified theory for analysis of components in discrete data, and compares the methods with techniques such as independent component analysis, non-negative matrix factorisation and latent Dirichlet allocation. The main families of algorithms discussed are a variational approximation, Gibbs sampling, and Rao-Blackwellised Gibbs sampling. Applications are presented for votin...

The transformation of a data set using a second-order polynomial mapping to find statistically independent components is considered (quadratic independent component analysis or ICA). Based on overdetermined linear ICA, an algorithm together with separability conditions are given via linearization reduction. The linearization is achieved using a higher dimensional embedding defined by the linear...

where each column is a data sample. Analyzing—and hopefully understanding— the result of an experiment often consists in uncovering regularity or structure in the data matrix. Unfortunately, measured data is often “messy” in the sense that it is too high-dimensional for us to detect structure by direct inspection and in the sense that noise and/or redundancy often impairs data visualization. Pr...

Editorial Source separation is not a new problem. We, human beings, as well as many other species, do it unconsciously at every instant of our lives. Our organisms receive a multitude of signals mixed together from the environment, and we are constantly uncovering the relevant ones in order to derive vital information to continue our lives. Other than the biological signals that are occurring a...

This paper presents an automated and compositional procedure to solve the substitutability problem in the context of evolving software systems. Our solution contributes two techniques for checking correctness of software upgrades: 1) a technique based on simultaneous use of over and under approximations obtained via existential and universal abstractions; 2) a dynamic assumeguarantee reasoning ...

Dictionary learning and component analysis models are fundamental in learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by means of specific structure, such as sparsity, low-rankness, or nonnegativity. Unfortunately, approaches like K-SVD that learn dictionaries for sparse coding via...