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Exclusive Sparsity Norm Minimization With Random Groups via Cone Projection.

Yijun Huang, Ji Liu

IEEE Transactions on Neural Networks and Learning Systems

|July 12, 2018

Summary

This study introduces efficient algorithms for exclusive sparsity norm optimization, achieving optimal convergence rates. A novel random grouping scheme is proposed for scenarios lacking predefined group information, enhancing feature selection effectiveness.

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Area of Science:

Machine Learning
Optimization
Data Science

Background:

Many applications require sparse solutions for feature selection, favoring non-zeros distributed across groups.
The exclusive sparsity norm is used for this purpose, but lacks systematic optimization studies.

Purpose of the Study:

To develop efficient algorithms for exclusive sparsity norm minimization with smooth and nonsmooth losses.
To propose and validate a random grouping scheme for exclusive sparsity when group information is unavailable.

Main Methods:

Development of several efficient algorithms to solve exclusive sparsity norm minimization problems.
Theoretical analysis to guarantee optimal convergence rates for the proposed algorithms.
Introduction and analysis of a random grouping scheme for constructing groups in feature selection.

Main Results:

Algorithms achieve optimal convergence rates for exclusive sparsity norm minimization, a first for general cases.
The random grouping scheme effectively groups true features with high probability when group information is absent.
Empirical studies confirm the efficiency of the algorithms and the effectiveness of the random grouping scheme.

Conclusions:

The proposed algorithms offer efficient and theoretically sound solutions for exclusive sparsity norm optimization.
The random grouping strategy provides a robust alternative for feature selection in the absence of prior group knowledge.
This work advances the optimization of exclusive sparsity norms, with practical implications for various data analysis tasks.