Subspace clustering without knowing the number of clusters: A parameter free approach

Abstract

Subspace clustering, the task of clustering high dimensional data when the data points come from a union of subspaces is one of the fundamental tasks in unsupervised machine learning. Most of the existing algorithms for this task involves supplying prior information in form of a parameter, like the number of clusters, to the algorithm. In this work, a parameter free method for subspace clustering is proposed, where the data points are clustered on the basis of the difference in statistical distribution of the angles made by the data points within a subspace and those by points belonging to different subspaces. Given an initial coarse clustering, the proposed algorithm merges the clusters until a true clustering is obtained. This, unlike many existing methods, does not involve the use of an unknown parameter or tuning for one through cross validation. Also, a parameter free method for producing a coarse initial clustering is discussed, which makes the whole process of subspace clustering parameter free. The comparison of algorithm performance with the existing state of the art in synthetic and real data sets, shows the significance of the proposed method.

Generalized Residual Ratio Thresholding

“…However, a recurring problem with BOMP, SOMP etc. (similar to many other signal processing problems like [21], [22]) is the requirement of a priori knowledge of signal sparsity (k 0 or k b ) or ambient noise variance σ 2 . Both sparsity and noise variance are rarely known a priori in practical applications.…”