based on the compressed sensing theory, if a signal is sparse in a suitable space, by using the optimization methods, signal could be accurately reconstructed from measurements that are significantly less than the theoretical shannon requirements. the sparse representation may exist for the signal and it is not available for the noise; this could be used to distinguish these two. on the other h...

For most of vibration signals of civil infrastructures have sparse characteristic, namely, only a few modes contribute to the vibration of the structures. Additionally, the measured vibration data by the sensors placed on different locations of structure almost has same sparse structure in the frequency domain. Based on this group sparsity of the vibration data of structure, the group sparse op...

In this paper, we propose to apply sparse canonical correlation analysis (sparse CCA) to an important genome-wide association study problem, eQTL mapping. Existing sparse CCA models do not incorporate structural information among variables such as pathways of genes. This work extends the sparse CCA so that it could exploit either the pre-given or unknown group structure via the structured-spars...

We study stochastic optimization problems when the data is sparse, which is in a sense dual to current perspectives on high-dimensional statistical learning and optimization. We highlight both the difficulties—in terms of increased sample complexity that sparse data necessitates—and the potential benefits, in terms of allowing parallelism and asynchrony in the design of algorithms. Concretely, ...

Reverse-convex programming (RCP) concerns global optimization of a specific class of non-convex optimization problems. We show that a recently proposed model for sparse non-negative matrix factorization (NMF) belongs to this class. Based on this result, we design two algorithms for sparse NMF that solve sequences of convex secondorder cone programs (SOCP). We work out some well-defined modifica...

Many clustering methods highly depend on extracted features. In this paper, we propose a joint optimization framework in terms of both feature extraction and discriminative clustering. We utilize graph regularized sparse codes as the features, and formulate sparse coding as the constraint for clustering. Two cost functions are developed based on entropy-minimization and maximum-margin clusterin...