Embedded clustering via robust orthogonal least square discriminant analysis

In this paper, a novel embedded clustering (EC) method is derived from the perspective of extending the supervised orthogonal least square discriminant analysis (OLSDA) method to the unsupervised case, which proves to be closely related to k-means. To achieve more statistical and structural properties, the robust learning of unsupervised OLSDA is investigated to further derive the unsupervised robust OLSDA (ROLSDA) problem. For the convenience of solving the proposed ROLSDA problem, re-weighted counterpart of ROLSDA is utilized with self-adaptive weight, such that the smaller weight would be assigned to the term with larger outliers automatically. Consequently, aforementioned EC method is proposed with not only the robust outliers but also the optimal weighted cluster centroids. Comparative experiments are presented to show the effectiveness of the EC method under the proposed ROLSDA problem.