Large-Scale Subspace Clustering for Computer Vision

Given data that lies in a union of low-dimensional subspaces, the problem of subspace clustering aims to learn - in an unsupervised manner - the membership of the data to their respective subspaces. State-of-the-art subspace clustering methods typically adopt a two-step procedure, by (a) constructing an affinity measure among data points is constructed, and (b) applying spectral clustering to find the membership of the data to their respective subspaces. However, such methods difficulty scale up to large-scale datasets.

In this work, we propose a divide-and-conquer framework for large-scale subspace clustering, allowing SSC techniques to scale up to datasets of more than 100,000 points. We highlighted the performance of our approach on synthetic large-scale datasets with 1,000,000 data points, as well as on the MNIST database, which contains 70,000 images of handwritten digits.