Subspace Clustering Without Knowing the Number of Clusters: A Parameter Free Approach

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 require prior knowledge of the number of clusters along with few additional parameters which need to be set or tuned apriori according to the type of data to be clustered. 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 the statistical distributions of the angles subtended by the data points within a subspace and those by points belonging to different subspaces. Given an initial fine clustering, the proposed algorithm merges the clusters until a final clustering is obtained. This, unlike many existing methods, does not require the number of clusters apriori. Also, the proposed algorithm does not involve the use of an unknown parameter or tuning for one. A parameter free method for producing a fine initial clustering is also discussed, making the whole process of subspace clustering parameter free. The comparison of the proposed algorithm's performance with that of the existing state-of-the-art techniques in synthetic and real data sets shows the significance of the proposed method.