Adaptive self-optimal softmax clustering

Discriminative clustering approaches assign data points to different groups by identifying sparse regions, without explicitly modeling the dataset and categories. Such methods are flexible and powerful in practice since they make few assumptions. In particular, the probabilistic-based Softmax model makes only one assumption, which is that data points are linearly separable. Therefore, it is potentially suitable in clustering data processed by feature transformation techniques. The principle of cluster assumption states that decision boundaries of clusters should lie in low-density regions. In previous works on discriminative clustering, this principle has been compromised by the cluster balance consideration, which is incorporated to avoid degenerate clustering solutions. However, datasets are rarely balanced with respect to attributes of interest. Furthermore, large clusters from imbalanced datasets might also contain sparse regions, where decision boundaries should not be positioned. In this thesis, we present self-optimality, a novel criterion for Softmax discriminative clustering, which is faithful to the cluster assumption principle and is free of cluster balance considerations. We also propose an adaptive algorithm aimed at finding self-optimal solutions, which can accurately recognize clusters from linearly separable imbalanced datasets with multiple degrees of sparseness.