SoF: Soft-Cluster Matrix Factorization for Probabilistic Clustering

We propose SoF (Soft-cluster matrix Factorization), a prob-abilistic clustering algorithm which softly assigns each data point into clusters. Unlike model-based clustering algorithms, SoF does not make assumptions about the data density distri-bution. Instead, we take an axiomatic approach to define 4 properties that the probability of co-clustered pairs of points should satisfy. Based on the properties, SoF utilizes a dis-tance measure between pairs of points to induce the con-ditional co-cluster probabilities. The objective function in our framework establishes an important connection between probabilistic clustering and constrained symmetric Nonneg-ative Matrix Factorization (NMF), hence providing a theo-retical interpretation for NMF-based clustering algorithms. To optimize the objective, we derive a sequential minimiza-tion algorithm using a penalty method. Experimental results on both synthetic and real-world datasets show that SoF sig-nificantly outperforms previous NMF-based algorithms and that it is able to detect non-convex patterns as well as cluster boundaries