Robust physiological mappings: from non-invasive to invasive

The goal of this paper is to highlight the challenges on the three methods of data analysis, namely: robust, component, and dynamical analysis with respect to the epilepsey. A forward and inverse mapping model for the human brain is presented. Research directions for obtaining robust inverse mapping, and conducting dynamical analysis of the epileptic brain are discussed.Проаналізовано проблеми, пов’язані з трьома методами аналізу даних щодо епілепсії головного мозку: робастним, покомпонентним і динамічним. Запропоновано пряму і обернену моделі відображення головного мозку. Також обговорюються напрями досліджень для отримання робастних обернених відображень і проведення динамічного аналізу епілептичного мозк

A bilinear algorithm for sparse representations

We consider the following sparse representation problem: represent a given matrix X∈ℝ m×N as a multiplication X=AS of two matrices A∈ℝ m×n (m≤n<N) and S∈ℝ n×N , under requirements that all m×m submatrices of A are nonsingular, and S is sparse in sense that each column of S has at least n−m+1 zero elements. It is known that under some mild additional assumptions, such representation is unique, up to scaling and permutation of the rows of S. We show that finding A (which is the most difficult part of such representation) can be reduced to a hyperplane clustering problem. We present a bilinear algorithm for such clustering, which is robust to outliers. A computer simulation example is presented showing the robustness of our algorithm

A Bilinear Algorithm for Sparse Representations

We consider the following sparse representation problem: represent a given matrix X as a multiplication X = AS of two matrices (m # n N) and S , under requirements that all mm submatrices of A are nonsingular, and S is sparse in sense that each column of S has at least n m + 1 zero elements. It is known that under some mild additional assumptions, such representation is unique, up to scaling and permutation of the rows of S. We show that finding A (which is the most di#cult part of such representation) can be reduced to a hyperplanes clustering problem. We present a bilinear algorithm for such clustering, which is robust to outliers. A computer simulation example is presented showing the robustness of our algorithm