We study the task of constructing sports news report automatically from live commentary and focus on content selection. Rather than receiving every piece of text of a sports match before news construction, as in previous related work, we novelly verify the feasibility of a more challenging setting to generate news report on the fly by treating live text input as a stream. We design scoring func...

It is known that a higher order tensor does not necessarily have an optimal low rank approximation, and that a tensor might not be orthogonally decomposable (i.e., admit a tensor SVD). We provide several sufficient conditions which lead to the failure of the tensor SVD, and characterize the existence of the tensor SVD with respect to the Higher Order SVD (HOSVD). In face of these difficulties t...

A problem for many kernel-based methods is that the amount of computation required to find the solution scales as O(n), where n is the number of training examples. We develop and analyze an algorithm to compute an easily-interpretable low-rank approximation to an n × n Gram matrix G such that computations of interest may be performed more rapidly. The approximation is of the form G̃k = CW + k C ...

We present some observations on the block triangular form (btf) of structurally symmetric, square, sparse matrices. If the matrix is structurally rank deficient, its canonical btf has at least one underdetermined and one overdetermined block. We prove that these blocks are transposes of each other. We further prove that the square block of the canonical btf, if present, has a special fine struc...

The current study is built upon prior research and is an attempt to explore the roles of affective variables in user technology adoption. Two different affective variables, computer playfulness and perceived enjoyment, were examined and their relationships with each other and with cognitive and behavioral variables were hypothesized. An empirical study using survey method was conducted. Analyse...

Stanley conjectured in 1977 that the h-vector of a matroid simplicial complex is a pure O-sequence. We give simple constructive proofs that the conjecture is true for matroids of rank less than or equal to 3, and corank 2. We used computers to verify that Stanley’s conjecture holds for all matroids on at most nine elements.

— In this paper, we present a Rank Revealing Randomized Singular Value Decomposition (R 3 SVD) algorithm to incrementally construct a low-rank approximation of a potentially large matrix while adaptively estimating the appropriate rank that can capture most of the actions of the matrix. Starting from a low-rank approximation with an initial guessed rank, R 3 SVD adopts an orthogonal Gaussian sa...

Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be solved in O (̃α2n) operations, where n is the matrix size, α is its displacement rank, and O ̃ denotes the omission of logarithmic factors. We show that for such matrices, this cost can be reduced to O (̃αω−1n), where ω is a feasible exponent for matrix multiplication over the base field. The best known estimate...

I n this paper we introduce min-plus low rank matrix approximation. By using min and plus rather than plus and times as the basic operations in the matrix multiplication; min-plus low rank matrix approximation is able to detect characteristically different structures than classical low rank approximation techniques such as Principal Component Analysis (PCA). We also show howminplus matrix algeb...

This paper presents a novel algorithm for recovering missing data of phasor measurement units (PMUs). Due to the low-rank property of PMU data, missing measurement recovery can be formulated as a low-rank matrix-completion problem. Based on maximum-margin matrix factorization, we propose an efficient algorithm based on alternating direction method of multipliers (ADMM) for solving the matrix co...