Geometric Disentanglement by Random Convex Polytopes

2020/09/29 by Michael Joswig, Joswig, Michael, Marek Kaluba +3
Computer Science · Mathematics · #Biometric Identification and Security #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2009.13987

openalex publication_date 2020/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of random convex polytopes. We demonstrate the use of our technique by qualitatively comparing the behavior of classic and regularized autoencoders. This reveals that applying regularization to autoencoder networks may decrease the out-of-distribution detection performance in latent space. While our technique is similar in spirit to k-means clustering, we achieve significantly better false positive/negative balance in clustering tasks on autoencoded datasets.

Citations

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Related

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• Representation Learning on a Random Lattice
• Geometric Autoencoders -- What You See is What You Decode
• Improving k-Means Clustering Performance with Disentangled Internal\n Representations
• Disentangling Learning Representations with Density Estimation