Topographic Independent Component Analysis

Abstract

A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Well-known linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis ICA , in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA.

On Recovering Missing Ground Penetrating Radar Traces by Statistical Interpolation Methods

“…Estimation of the ICAMM parameters, however, was a complex process because of the high dimensionality of signals and the high correlation between radargram patches. In the end, we opted for an ICAMM with a single class, whose parameters were found using topographic independent component analysis (TICA [22]). TICA is an ICA algorithm that is commonly used to model natural images, and it employs the same data alignment as that shown in Figure 1.…”

Blind Signal Separation of Unknown Source Number under the Constraint Based on Uniform Linear Array

“…Previous blind signal separation algorithms can be divided into two categories, one needs to know the source signal number in advance, and the other does not. A main representative of the former is principal component analysis (PCA) [3] [4]. With these methods, the covariance matrix is calculated first, and then the eigenvector corresponding to the eigenvalue with the same number as source signals is found, and finally, the principal component vector obtained by transforming Karhunen-Loeveb, which is also known as the separated source signal [5][6] [7].…”

Adaptive Image Fusion Using Ica Bases

“…The estimation of these basis vectors is performed using a population of training image patches I w (t) and a criterion (cost function) that selects the basis vectors. We can train analysis bases using Independent Component Analysis (ICA) and topographic ICA [4], as explained in [3]. The training procedure needs to be completed only once, as the estimated transform can be used for fusing similar content images.…”

“…It is always possible to keep the complete set of bases. Then, we iterate the ICA update rule in [5] or the topographical ICA rule in [4] for a chosen L × L neighbourhood until convergence. Each iteration, we orthogonalise the bases using a symmetric decorrelation scheme [5].…”