C Elementary and special functions (search also class L5 ) C1 Integer-valued functions (e.g., factorial, binomial coefficient, permutations, combinations, floor, ceiling) C06GXFP Factorizes a positive integer n as n = n1 × n2. This routine may be used in conjunction with C06MCFP D Linear Algebra D1 Elementary vector and matrix operations D1a Elementary vector operations D1a1 Set to constant D1a...

For linear least squares problems minx kAx ? bk2, where A is sparse except for a few dense rows, a straightforward application of Cholesky or QR factorization will lead to a catastrophic ll in the factor R. We consider handling such problems by a matrix stretching technique, where the dense rows are split into several more sparse rows. We develop both a recursive binary splitting algorithm and ...

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

Operations on Sparse Matrices are the key computational kernels in many scientific and engineering applications. They are characterized with poor substantiated performance. It is not uncommon for microprocessors to gain only 10-20% of their peak floating-point performance when doing sparse matrix computations even when special vector processors have been added as coprocessor facilities. In this...

We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In particular, our formulation introduces an explicit trade-off between size and sparsity of the decomposition of rectangular matrices. Using a large set of synth...

In a large-scale and distributed matrix multiplication problem C = AB, where C ∈ Rr×t, the coded computation plays an important role to effectively deal with “stragglers” (distributed computations that may get delayed due to few slow or faulty processors). However, existing coded schemes could destroy the significant sparsity that exists in large-scale machine learning problems, and could resul...

Matrix-variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with structured information. In this paper, we propose a novel sparse matrix graphical model for this type of statistical problems. By penalizing respectively two precision matrices corresponding to the rows and columns, our method yields a sparse ma...

We investigate the problem of factoring a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and also values of hidden units. We prove that under certain assumptions on a sparse li...

Many kinds of data can be viewed as consisting of a set of vectors, each of which is a noisy combination of a small number of noisy prototype vectors. Physically, these prototype vectors may correspond to different hidden variables that play a role in determining the measured data. For example, a gene’s expression is influenced by the presence of transcription factor proteins, and two genes may...

Abstract: Gender recognition and age detection are important problems in telephone speech processing to investigate the identity of an individual using voice characteristics. In this paper a new gender and age recognition system is introduced based on generative incoherent models learned using sparse non-negative matrix factorization and atom correction post-processing method. Similar to genera...