Concave losses for robust dictionary learning

TL;DR

This paper introduces a robust dictionary learning framework using concave loss functions, improving outlier detection and dictionary quality over traditional quadratic loss methods.

Contribution

It develops a generic approach for robust dictionary learning with concave losses, including super-gradient computation and an initialization heuristic for outlier detection.

Findings

Better outlier detection compared to existing methods

Produces higher quality dictionaries in experiments

Outperforms state-of-the-art algorithms like K-SVD and LC-KSVD

Abstract

Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results on composition of concave functions, notably regarding super-gradient computations, that are key for developing generic dictionary learning algorithms applicable to smooth and non-smooth losses. In order to improve identification of outliers, we introduce an initialization heuristic based on undercomplete dictionary learning. Experimental results using synthetic and real data demonstrate that our method is able to better detect outliers, is capable of generating better dictionaries, outperforming state-of-the-art methods such as K-SVD and LC-KSVD.