Recently, sparse coding has been widely used in many applications ranging from image recovery to pattern recognition. The low mutual coherence of a dictionary is an important property that ensures the optimality of the sparse code generated from this dictionary. Indeed, most existing dictionary learning methods for sparse coding either implicitly or explicitly tried to learn an incoherent dicti...

A recent work introduced the concept of deep dictionary learning. The first level is a dictionary learning stage where the inputs are the training data and the outputs are the dictionary and learned coefficients. In subsequent levels of deep dictionary learning, the learned coefficients from the previous level acts as inputs. This is an unsupervised representation learning technique. In this wo...

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...