Abstract
Subspace clustering (SC) exploits the potential capacity of self-expressive modeling of unsupervised learning frameworks, representing each data point as a linear combination of the other related data points. Advanced self-expressive approaches construct an affinity matrix from the representation coefficients by imposing an additional regularization, reflecting the prior data distribution. An affine constraint is widely used for regularization in subspace clustering studies according on the grounds that, in real-world applications, data points usually lie in a union of multiple affine subspaces rather than linear subspaces. However, a strict affine constraint is not flexible enough to handle the real-world cases, as the observed data points are always corrupted by noise and outliers. To address this issue, we introduce the concept of scalable affine constraint to the SC formulation. Specifically, each coefficient vector is constrained to sum up to a soft scalar s rather than 1. The proposed method can estimate the most appropriate value of scalar s in the optimization stage, adaptively enhancing the clustering performance. Besides, as clustering benefits from multiple representations, we extend the scalable affine constraint to a multi-view clustering framework designed to achieve collaboration among the different representations adopted. An efficient optimization approach based on ADMM is developed to minimize the proposed objective functions. The experimental results on several datasets demonstrate the effectiveness of the proposed clustering approach constrained by scalable affine regularisation, with superior performance compared to the state-of-the-art.