Subspace Clustering on Incomplete Data with Self-Supervised Contrastive Learning

TL;DR

This work tackles subspace clustering under incomplete observations by introducing Contrastive Subspace Clustering (CSC), a self-supervised framework that learns invariant embeddings from masked views of partially observed data using a SimCLR-style NT-Xent objective with temperature $\tau$. The learned backbone $f_\theta$ produces embeddings for original incomplete samples, which are then clustered via Sparse Subspace Clustering (SSC). Empirical results across six image and hyperspectral datasets show that CSC outperforms classical HRMC-based approaches and modern deep baselines, particularly at high missing rates, while remaining scalable on large datasets. The authors propose future directions including streaming and multi-view extensions, along with theoretical analyses for contrastive objectives under missing data.

Abstract

Subspace clustering aims to group data points that lie in a union of low-dimensional subspaces and finds wide application in computer vision, hyperspectral imaging, and recommendation systems. However, most existing methods assume fully observed data, limiting their effectiveness in real-world scenarios with missing entries. In this paper, we propose a contrastive self-supervised framework, Contrastive Subspace Clustering (CSC), designed for clustering incomplete data. CSC generates masked views of partially observed inputs and trains a deep neural network using a SimCLR-style contrastive loss to learn invariant embeddings. These embeddings are then clustered using sparse subspace clustering. Experiments on six benchmark datasets show that CSC consistently outperforms both classical and deep learning baselines, demonstrating strong robustness to missing data and scalability to large datasets.

Figures (4)

• Figure 1: Overview of our Contrastive Subspace Clustering (CSC) pipeline. Two disjoint random masks generate augmented views of each incomplete sample, which are passed through a shared deep network and trained with a SimCLR‐style loss to pull same‐sample embeddings together and push different‐sample embeddings apart. At inference, the original incomplete data is embedded and fed to a subspace‐clustering algorithm.
• Figure 2: (a) Clustering error vs. sampling rate $\rho$ for models of depth with $N = 5000$. (b) Clustering error vs. sampling rate $\rho$ for $N=5000$ under noise ($\sigma=0.3$).
• Figure 3: Clustering error as a function of dataset size $N$ and sampling rate $\rho$ for the three residual‐connection configurations: (a) Full residual, (b) Block Residual, and (c) No Residual.
• Figure 4: Clustering error versus sampling rate $\rho$ for CSC and MAE under (a,b) low‐noise $\sigma=0.1$ and (c,d) high‐noise $\sigma=0.3$. CSC consistently outperforms MAE across all $\rho$ and noise levels.