This paper is concerned with improving the empirical convergence speed of block-coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in-between block updates, referred to as heuristic restarts (HER). HER significantly accelerates most existing dense NTF, in particular challenging computational scenarios, while requiring a neg...

We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious näıve Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative parafac, will always have optimal solutions. The result holds for any choice of norms and, under a mild assumption, even Brègman diverge...

We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious näıve Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative parafac, will always have optimal solutions. The result holds for any choice of norms and, under a mild assumption, even Brègman diverge...

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require matrixinversion; and (ii) they cannot (or at least is very difficult to) handle structured regularizations. We propose a new tensor factorization algorithm that circumven...

In this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums. For matrices these conditions reduce to Menon’s conditions. 2000 Mathematics Subject Classification. 15A39, 15A48, 15A69, 65F35, 65K05.

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogies of component-wise condition numbers for linear systems introduced by Skeel. x

x : Mn-1 ? Rn be an umbilical free hypersurface with non-zero principal curvatures. Then is associated a Laguerre metric g, tensor L, form C, and second fundamental B, which are invariants of under transformation group. In this paper, we will study the parallel nonnegative or non-positive tensor.

Special thanks to my parents and friends for their love and support. 1 3-way PARAFAC model: The tensor is represented as a linear combination of r rank-1 tensors. This will provide a rank-r approximation to the original A plot of the loglikelihood functions (θ) in the case of classification for k = 1 (left, θ true = 0.75) and k = 2 (right, θ true = (0.8, 0.6) 3 A plot of the loglikelihood funct...

Tensor factorizations with nonnegative constraints have found application in analyzing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g., count data), which leads to sparse tensors that can be modeled by sparse factor matrices. In this paper we investigate efficient techniques for computing an app...