Given a hypergraph H with m hyperedges and a set Q of m pinning subspaces, i.e. globally fixed subspaces in Euclidean space R, a pinned subspace-incidence system is the pair (H,Q), with the constraint that each pinning subspace in Q is contained in the subspace spanned by the point realizations in R of vertices of the corresponding hyperedge of H . This paper provides a combinatorial characteri...

Most of the research on dictionary learning has focused on developing algorithms under the assumption that data is available at a centralized location. But often the data is not available at a centralized location due to practical constraints like data aggregation costs, privacy concerns, etc. Using centralized dictionary learning algorithms may not be the optimal choice in such settings. This ...

In recent years, sparse representation and dictionary-learning-based methods have emerged as powerful tools for efficiently processing data in nontraditional ways. A particular area of promise for these theories is face recognition. In this paper, we review the role of sparse representation and dictionary learning for efficient face identification and verification. Recent face recognition algor...

Traditional Compressive Sensing (CS) recovery techniques resorts a dictionary matrix to recover a signal. The success of recovery heavily relies on finding a dictionary matrix in which the signal representation is sparse. Achieving a sparse representation does not only depend on the dictionary matrix, but also depends on the data. It is a challenging issue to find an optimal dictionary to recov...

A new dictionary learning method for exact sparse representation is presented in this paper. As the dictionary learning methods often iteratively update the sparse coefficients and dictionary, when the approximation error is small or zero, algorithm convergence will be slow or non-existent. The proposed framework can be used in such a setting by gradually increasing the fidelity of the approxim...

Abstract. Dictionary learning is a challenge topic in many image processing areas. The basic goal is to learn a sparse representation from an overcomplete basis set. Due to combining the advantages of generic multiscale representations with learning based adaptivity, multiscale dictionary representation approaches have the power in capturing structural characteristics of natural images. However...

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using dictionary learning. We then perform an SVD on the dictionary and use the first few left singular vectors as the rows of the measurement matrix to obtain th...

In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies, we propose efficient dictionary learning schemes to solve several practical formulations of this problem to stationary points. Unlike many existing algorith...

Dictionary learning plays an important role in machine learning, where data vectors are modeled as a sparse linear combinations of basis factors (i.e., dictionary). However, how to conduct dictionary learning in noisy environment has not been well studied. Moreover, in practice, the dictionary (i.e., the lower rank approximation of the data matrix) and the sparse representations are required to...

the study aimed at investigating whether the retention of vocabulary acquired incidentally is dependent upon the amount of task-induced involvement. immediate and delayed retention of twenty unfamiliar words was examined in three learning tasks( listening comprehension + group discussion, listening comprehension + dictionary checking + summary writing in l1, and listening comprehension + dictio...