A Clustering Validity Criteria-Guided Unsupervised Sparse Subset Selection Algorithm

The newly proposed sparse subset selection (DS3) algorithm can effectively perform the clustering of data and the selection of representatives for each cluster (i.e. a subset of the entire data set) simultaneously. It can be formulated as a row-sparsity of membership matrix and minimizing coding loss problem. However, the regularization parameter in DS3 has a great impact on the performance of the algorithm. Different regularization parameter values will lead the algorithm to select a different number of representatives or clusters. However, for a given data set, which can have a definite number of classes, the DS3 algorithm can not automatically select the optimal regularization parameter. In view of this problem that DS3 has, noting that clustering validity criteria can be used to determine the number of clusters and the close relationship between the number of clusters and the value of the regularization parameter, we propose to use the clustering validity criteria to determine the optimal regularization parameter and thus propose an unsupervised DS3 (UDS3) algorithm that can automatically determine the regularization parameter. Compared with the original DS3 algorithm, the proposed UDS3 algorithm will give more constructive clustering results when the number of classes of the data set to be clustered is not given. Video summarization experiments on several Youtube data sets show the effectiveness of the proposed UDS3 algorithm.