Computing absolute maximum correlation

Zhang, Leihong; Chu, Moody T.

doi:10.1093/imanum/drq029

Cited by 11 publications

(12 citation statements)

References 18 publications

(34 reference statements)

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“…If x is a global maximizer of the MCP (1.2), then the first inequality in (4.10) is already proved by Zhang and Chu [19]. Note that A ii is symmetric, the second inequality in (4.10) follows from (4.9) due to…”

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confidence: 81%

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Sensitivity analysis for the multivariate eigenvalue problem

Liu¹,

Wang²,

Xu³

2013

ELA

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Abstract. This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the first-order perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate eigenvector are presented. The explicit expressions of condition numbers, perturbation upper bounds and backward errors for multivariate eigenpairs are derived.

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confidence: 81%

“…The convergence of the P-SOR method has been established in [14]. Recently, several results on the global maximizer of the maximal correlation problem are presented by [5,18,19,20,21].…”

Section: St X ∈ Smentioning

confidence: 99%

Sensitivity analysis for the multivariate eigenvalue problem

Liu¹,

Wang²,

Xu³

2013

ELA

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“…In Section 3.1, we established a connection among the NMC optimization (3), the Maximum Correlation Problem (MCP) and the Multivariate Eigenvalue Problem (MEP) (see e.g., [38], [39], [40], [41]). After showing that the NMC optimization can be reformulated as the MCP, we use existing techniques from the literature to solve it.…”

Section: An Ace Approach To Compute Nmcmentioning

confidence: 99%

“…In Section 2, for finite discrete random variables, we characterize the solution of the NMC optimization using a natural basis expansion. For finite discrete random variables, we show that the NMC optimization is an instance of the Maximum Correlation Problem (MCP), which is NP-hard [38], [39], [40], [41].…”

Section: Introductionmentioning

confidence: 99%

Network Maximal Correlation

Feizi

Makhdoumi

Duffy

et al. 2017

IEEE Trans. Netw. Sci. Eng.

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Abstract-We introduce Network Maximal Correlation (NMC) as a multivariate measure of nonlinear association among random variables. NMC is defined via an optimization that infers transformations of variables by maximizing aggregate inner products between transformed variables. For finite discrete and jointly Gaussian random variables, we characterize a solution of the NMC optimization using basis expansion of functions over appropriate basis functions. For finite discrete variables, we propose an algorithm based on alternating conditional expectation to determine NMC. Moreover we propose a distributed algorithm to compute an approximation of NMC for large and dense graphs using graph partitioning. For finite discrete variables, we show that the probability of discrepancy greater than any given level between NMC and NMC computed using empirical distributions decays exponentially fast as the sample size grows. For jointly Gaussian variables, we show that under some conditions the NMC optimization is an instance of the Max-Cut problem. We then illustrate an application of NMC in inference of graphical model for bijective functions of jointly Gaussian variables. Finally, we show NMC's utility in a data application of learning nonlinear dependencies among genes in a cancer dataset.

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“…Some distinctive traits of MEP were discussed in [14]. Currently, some algorithms have been developed for solving the MEP mentioned above, including Horst method, Power method and Gauss-Seidel method, et al Since Gauss-Seidel method takes good convergence performance, it was adopted for solving the MEP with Eq.9.…”

Section: Multivariate Eigenvalue Problemmentioning

confidence: 99%

Orthogonal graph-regularized matrix factorization and its application for recommendation

Zhu

Xin

Wei

et al. 2013

2013 IEEE International Conference on Multimedia and Expo (ICME)

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As one of the most successful approaches for recommendation, matrix factorization based Collaborative Filtering (CF) technique has received considerable attentions over the past years. In this paper, we propose an orthogonal matrix factorization model with graph regularization to preserve the consistency of the local structure both in user and item spaces, respectively. Instead of traditional alternating optimization method, a greedy sequential one is introduced to optimize a pair of coupled factor vector and its corresponding loading vector simultaneously each time, thus the original optimization problem is converted into the well-studied Multivariate Eigen Problem (MEP). Furthermore, multiple pairs of coupled eigen-vectors can be obtained in sequence. To guarantee nonrecurring of repetition of solutions, a novel dualdeflation technique is developed to incorporate into the sequential optimization. Experimental results on MovieLens and Each Movie data sets demonstrate that the proposed method is much more competitive compared with the state of the art matrix factorization based collaborative filtering methods.

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Computing absolute maximum correlation

Cited by 11 publications

References 18 publications

Sensitivity analysis for the multivariate eigenvalue problem

Sensitivity analysis for the multivariate eigenvalue problem

Network Maximal Correlation

Orthogonal graph-regularized matrix factorization and its application for recommendation

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