Locally Regularized Sparse Graph by Fast Proximal Gradient Descent

TL;DR

This paper introduces SRSG, a novel sparse graph construction method that incorporates local geometric information for improved data clustering, solved efficiently with a fast proximal gradient descent algorithm.

Contribution

The paper proposes SRSG, a support regularized sparse graph method that aligns with local data geometry, and develops a fast optimization algorithm with optimal convergence.

Findings

SRSG outperforms existing clustering methods on real datasets.

The proposed algorithm converges at Nesterov's optimal rate.

Extensive experiments validate the effectiveness of SRSG.

Abstract

Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by performing sparse representation for each datum separately. In order to obtain a sparse graph aligned with the local geometric structure of data, we propose a novel Support Regularized Sparse Graph, abbreviated as SRSG, for data clustering. SRSG encourages local smoothness on the neighborhoods of nearby data points by a well-defined support regularization term. We propose a fast proximal gradient descent method to solve the non-convex optimization problem of SRSG with the convergence matching the Nesterov's optimal convergence rate of first-order methods on smooth and convex objective function with Lipschitz continuous gradient. Extensive experimental results on various real data sets demonstrate the superiority of SRSG over other competing clustering methods.