Embedding Clustering via Autoencoder and Projection onto Convex Set

Projection onto Convex Set (POCS) is a powerful signal processing tool for various convex optimization problems. For non-intersecting convex sets, the simultaneous POCS method can result in a minimum mean square error solution. This property of POCS has been applied to clustering analysis and the POCS-based clustering algorithm was proposed earlier. In the POCS-based clustering algorithm, each data point is treated as a convex set, and a parallel projection operation from every cluster prototype to its corresponding data members is carried out in order to minimize the objective function and to update the memberships and prototypes. The algorithm works competitively against conventional clustering methods in terms of execution speed and clustering error on general clustering tasks. In this paper, the performance of the POCS-based clustering algorithm on a more complex task, embedding clustering, is investigated in order to further demonstrate its potential in benefiting other high-level tasks. To this end, an off-the-shelf FaceNet model and an autoencoder network are adopted to synthesize two sets of feature embeddings from the Five Celebrity Faces and MNIST datasets, respectively, for experiments and analyses. The empirical evaluations show that the POCS-based clustering algorithm can yield favorable results when compared with other prevailing clustering schemes such as the K-Means and Fuzzy C-Means algorithms in embedding clustering problems.