Scalable Deep Subspace Clustering Network

2025-12-24

AI Summary

Subspace clustering suffers from cubic time complexity $O(n^3)$ due to the need to construct a full $n imes n$ affinity matrix and perform spectral decomposition, severely limiting scalability to large-scale data. This paper proposes the first deep subspace clustering framework with linear time complexity $O(n)$. Our method overcomes this bottleneck via three key innovations: (1) landmark-based sparse affinity approximation; (2) joint optimization of convolutional autoencoder-driven reconstruction and self-expression, regularized by subspace-preserving constraints; and (3) spectral clustering performed directly in the low-rank factor space, eliminating explicit affinity matrix construction and decomposition. Extensive experiments on multiple benchmark datasets demonstrate that our approach achieves state-of-the-art clustering accuracy while incurring only linear computational cost—marking a significant advance in practicality and scalability for large-scale subspace clustering.

Technology Category

• Machine Learning: Clustering
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Subspace clustering methods face inherent scalability limits due to the $O(n^3)$ cost (with $n$ denoting the number of data samples) of constructing full $n imes n$ affinities and performing spectral decomposition. While deep learning-based approaches improve feature extraction, they maintain this computational bottleneck through exhaustive pairwise similarity computations. We propose SDSNet (Scalable Deep Subspace Network), a deep subspace clustering framework that achieves $mathcal{O}(n)$ complexity through (1) landmark-based approximation, avoiding full affinity matrices, (2) joint optimization of auto-encoder reconstruction with self-expression objectives, and (3) direct spectral clustering on factorized representations. The framework combines convolutional auto-encoders with subspace-preserving constraints. Experimental results demonstrate that SDSNet achieves comparable clustering quality to state-of-the-art methods with significantly improved computational efficiency.

Problem

• Addresses scalability limits in subspace clustering from O(n^3) complexity.
• Avoids exhaustive pairwise similarity computations in deep learning approaches.
• Reduces computational cost while maintaining clustering quality and efficiency.

Innovation

• Landmark-based approximation avoids full affinity matrices.
• Joint optimization of auto-encoder and self-expression objectives.
• Direct spectral clustering on factorized representations.