Topological Regularization for Representation Learning via Persistent Homology

• Published in: Mathematics (Basel) Vol. 11; no. 4; p. 1008
• Main Authors: Chen, Muyi, Wang, Daling, Feng, Shi, Zhang, Yifei
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.02.2023
• Subjects: Algebra; Artificial neural networks; Control methods; Data analysis; deep neural network; Feature extraction; Homology; Homology theory (Mathematics); Image classification; Machine learning; Mathematical research; Neural networks; Optimization; persistent homology; push-forward probability measure; Regularization; Regularization methods; representation space; Representations; Sample size; Topology; Weighting functions; United States

Generalization is challenging in small-sample-size regimes with over-parameterized deep neural networks, and a better representation is generally beneficial for generalization. In this paper, we present a novel method for controlling the internal representation of deep neural networks from a topolog...