Diffusion in sparse networks: linear to semilinear crossover

Percolation, sliding, localization and relaxation in topologically closed circuits

Considering a random walk in a random environment in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization" of eigenstates of non-hermitian Hamiltonians has been addressed by Hatano, Nelson, and followers. But we show that for a conservative stochastic process the implied spectral properties are dramatically different. In particular we determine the threshold for under-damped relaxation, and observe "complexity saturation" as the bias is increased.

Dissimilarity sparsity-preserving projections in feature extraction for visual recognition

This paper investigates the use of feature dimensionality reduction approaches for high-dimensional data analysis. Most of the existing preserving projection methods are based on similarity, such as the well-known locality-preserving projections, neighborhood-preserving embedding, and sparsity-preserving projections. Here, we propose a simple yet very efficient preserving projection method based on sparsity and dissimilarity for feature extraction, named dissimilarity sparsity-preserving projections, which is an extended version of sparsity-preserving projections. Both projection coefficients and reconstructive residuals are considered in our proposed framework. We give an idea of a "dissimilarity metric" as the measurement of the relationship among the object data. If the value of the dissimilarity metric of two samples is large, the possibility of them belonging to the same class is small. The proposed methods do not have to preset the number of neighbors and heat kernel width, which is one of the important differences from other projection methods. In practical applications, an approximately direct and complete solution is obtained for the proposed algorithm. Experimental results on three widely used face datasets demonstrate that the proposed framework could achieve competitive performance in terms of accuracy and efficiency.