Consistency Analysis of Spectral Regularization Algorithms

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtai...

Probabilistic Low-Rank Matrix Completion with Adaptive Spectral Regularization Algorithms

We propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an ExpectationMaximization algorithm to obtain a Maximum A Posteriori estimate of the completed l...

Consistency of Spectral Clustering

Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of the popular family of spectral clustering algorithms, which clusters the data with the help of eigenvectors of graph Laplacian matrices. We develop new meth...

Fuzzy Clustering: Consistency of Entropy Regularization

We introduce in this paper a new formulation of the regularized fuzzy C-means (FCM) algorithm which allows us to find automatically the actual number of clusters. The approach is based on the minimization of an objective function which mixes, via a particular parameter, a classical FCM term and a new entropy regularizer. The main contribution of the method is the introduction of a new exponenti...

Consistency of different spectral methods for GW analysis