A new fast and accurate algorithm for tracking singular values, singular vectors and the dimension of the signal subspace through an overlapping sequence of data matrices is presented. The accuracy of the algorithm approaches that of the Prony-Lanczos (PL) method [1] with speed and accuracy superior to both the PAST and PASTd algorithms [2] for moderate to large size problems. The algorithm is ...

The centroid decomposition, an approximation for the singular value decomposition, had a long history among the statistics/psychometrics community for factor analysis research. We revisit the centroid method first in its original context of factor analysis and then adapt it to other than a covariance matrix. The centroid method can be cast as an O(n)-step ascent method on a hypercube. It is sho...

The centroid decomposition, an approximation for the singular value decomposition (SVD), has a long history among the statistics/psychometrics community for factor analysis research. We revisit the centroid method in its original context of factor analysis and then adapt it to other than a covariance matrix. The centroid method can be cast as an O(n)-step ascent method on a hypercube. It is sho...

The diffusion process on weblogs has attracted great interest since the early days of weblog studies. We propose a ranking technique which extracts topics and innovators by analyzing that process. Our method identifies URLs of topics and the bloggers who trigger topic diffusion. Our assumption is that the strength of propagation of a topic is determined by the influences of topics and bloggers....

Given a weight of sl(n), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module. Moreover, we completely solve the system in a certain space of power series. The polynomial solutions correspond to the singular vectors in the Verma module. The well-known results of Verma, Bernstein-Gel’f...

In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogu...

Recall this theorem from last time. Theorem 1 (Singular Value Decomposition and best rank-k-approximation) An m × n real matrix has t ≤ min {m,n} nonnegative real numbers σ1, σ2, . . . , σt (called singular values) and two sets of unit vectors U = {u1, u2, . . . , ut} which are in <m and V = v1, v2, . . . , vt ∈ <n (all vectors are column vectors) where U, V are orthogonormal sets and ui M = σi...