Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting underlying structures. One of the equivalent definitions of PCA is that it seeks the subspaces that maximize the sum of squared pairwise distances between d...

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...

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...

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

We study the extraction of nonlinear data models in high dimensional spaces with modi ed self organizing maps We present a general algorithm which maps low dimensional lattices into high dimensional data manifolds without violation of topology The approach is based on a new principle exploiting the speci c dynamical properties of the rst order phase tran sition induced by the noise of the data ...

Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations a...

Problem Statement Experimental data to be analyzed is often represented as a number of vectors of fixed dimensionality. A single vector could for example be a set of temperature measurements across Germany. Taking such a vector of measurements at different times results in a number of vectors that altogether constitute the data. Each vector can also be interpreted as a point in a high dimension...

Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA suffers from the fact that each principal component is a linear combination of all the original variables, thus it is often difficult to interpret the results. We introduce a new method called sparse principal component analysis (SPCA) using the lasso (elastic net) to produce modified...

Recently, many l1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed....