Many applications in data analysis rely on the decomposition of a data matrix into a low-rank and a sparse component. Existing methods that tackle this task use the nuclear norm and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\ell _1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math> </EquationSource> </InlineEquation>-cost functions as convex relaxations of the rank constraint and the sparsity measure,...</equationsource></equationsource></inlineequation>

A cluster-based method for constructing sparse principal components is proposed. The method initially forms clusters of variables, using a new clustering approach called the semi-partition, in two steps. First, the variables are ordered sequentially according to a criterion involving the...

The article begins with a review of the main approaches for interpretation the results from principal component analysis (PCA) during the last 50–60 years. The simple structure approach is compared to the modern approach of sparse PCA where interpretable solutions are directly obtained. It is...

The independent exploratory factor analysis method is introduced for recovering independent latent sources from their observed mixtures. The new model is viewed as a method of factor rotation in exploratory factor analysis (EFA). First, estimates for all EFA model parameters are obtained...