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Sharp analysis of low-rank kernel matrix approximations
Sharp analysis low-rank kernel matrix approximations
2012/9/18
We consider supervised learning problems within the positive-definite kernel framework,such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading t...
Let (V,A) be a weighted graph with a finite vertex set V,with a symmetric matrix of nonnegative weightsAand with Laplacian ∆. LetS∗: V ×V 7→ R be a symmetric kernel defined on the vertex s...
Condition Numbers of Indefinite Rank 2 Ghost Wishart Matrices
Condition Numbers Indefinite Rank 2 Ghost Wishart Matrices
2012/9/19
We define an indefinite Wishart matrix as a matrix of the formA=WTWΣ, where Σis an indefinite diagonal matrix andWis a matrix of independent standard normals. We focus on the case whereWis L×2which ha...
Non-Convex Rank Minimization via an Empirical Bayesian Approach
Non-Convex Rank Minimization via Empirical Bayesian Approach
2012/9/19
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem.Consequently, the convex nuclear ...
A Subspace Estimator for Fixed Rank Perturbations of Large Random Matrices
Large Random Matrix Theory MUSIC Algorithm Extreme Eigenvalues
2011/7/6
This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series...
Functional principal components analysis via penalized rank one approximation
Functional data analysis penalization regularization singular value decomposition
2009/9/16
Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in ...