Concave losses for robust dictionary learning

2017/11/02 by Rafael Will M de Araujo, de Araujo, Rafael Will M, Roberto Hirata +3
Computer Science · Engineering · #Anomaly Detection Techniques and Applications #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1711.00659

openalex publication_date 2017/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Nearly unbiased variable selection under minimax concave penalty
• rm K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

Related

• Dictionary Learning with Almost Sure Error Constraints
• Computational Intractability of Dictionary Learning for Sparse Representation
• Dictionary Learning with Convex Update (ROMD)
• Stable and Interpretable Unrolled Dictionary Learning
• Dictionary learning -- from local towards global and adaptive