Riordan matrices are infinite lower triangular determined by a pair of formal power series over the real or complex field. These have been mainly studied as combinatorial objects with an emphasis placed on algebraic structure. The present paper contributes to linear discussion analysis means interaction properties algebra. Specifically, it is shown that if matrix A n×n pseudo-involution then si...

Spectral methods use selected eigenvectors of a data affinity matrix to obtain a data representation that can be trivially clustered or embedded in a low-dimensional space. We present a theorem that explains, for broad classes of affinity matrices and eigenbases, why this works: For successively smaller eigenbases (i.e., using fewer and fewer of the affinity matrix’s dominant eigenvalues and ei...

Department of Electrical and Computer Engineering Ben-Gurion University of the Negev Beer-Sheva 84105, Israel Abstract Feature extraction has been always mutually studied for exploratory data projection and for classification. Feature extraction for exploratory data projection aims for data visualization by a projection of a high-dimensional space onto two or three-dimensional space, while feat...