No abstract

A least square semi-supervised local clustering algorithm based on the idea of compressed sensing are proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two stage approaches similar to the one in [26]. However, under a weaker assumption and with less computational complexity than the one in [26], the algorithm is shown to be able to find a desired cluster with high probability. Several numerical experiments including the synthetic data and real data such as MNIST, AT&T and YaleB human faces data sets are conducted to demonstrate the performance of our algorithm.

No abstract

In this paper, we propose a Quasi-Orthogonal Matching Pursuit (QOMP) algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials. For the two kinds of sampled data, data with noises and without noises, we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct s-sparse Legendre polynomials, Chebyshev polynomials and trigonometric polynomials in s step iterations. The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials. Finally, numerical experiments will be presented to verify the effectiveness of the QOMP method.