Learning a Self-Expressive Network for Subspace Clustering

Abstract

State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. However, such methods are designed for a finite sample dataset and lack the ability to generalize to out-of-sample data. Moreover, since the number of self-expressive coefficients grows quadratically with the number of data points, their ability to handle large-scale datasets is often limited. In this paper, we propose a novel framework for subspace clustering, termed Self-Expressive Network (SENet), which employs a properly designed neural network to learn a self-expressive representation of the data. We show that our SENet can not only learn the self-expressive coefficients with desired properties on the training data, but also handle out-of-sample data. Besides, we show that SENet can also be leveraged to perform subspace clustering on large-scale datasets. Extensive experiments conducted on synthetic data and real world benchmark data validate the effectiveness of the proposed method. In particular, SENet yields highly competitive performance on MNIST, Fashion MNIST and Extended MNIST and state-of-the-art performance on CIFAR-10. The code is available at https://github.com/zhangsz1998/Self-Expressive-Network.

arXiv comment15 pages, 11 figures, 6 tables. The paper is the complete version of the CVPR2021's paper with a set of extra experimental results and a link to download the code

References in corpus (12)

• A geometric analysis of subspace clustering with outliers
• Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework
• Sketched Subspace Clustering
• Scalable and Robust Sparse Subspace Clustering Using Randomized Clustering and Multilayer Graphs
• On Geometric Analysis of Affine Sparse Subspace Clustering
• Deep Sparse Subspace Clustering
• Analysis and Design of Convolutional Networks via Hierarchical Tensor Decompositions
• Neural Collaborative Subspace Clustering
• Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms
• Basis Pursuit and Orthogonal Matching Pursuit for Subspace-preserving Recovery: Theoretical Analysis
• Residual Encoder-Decoder Network for Deep Subspace Clustering
• Learning Self-Expression Metrics for Scalable and Inductive Subspace Clustering