Multi-Task Clustering using Constrained Symmetric Non-Negative Matrix Factorization

Researchers have attempted to improve the quality of clustering solutions through various mechanisms. A promising new approach to improve clustering quality is to combine data from multiple related datasets (tasks) and apply multi-task clustering. In this paper, we present a novel framework that can simultaneously cluster multiple tasks through balanced Intra-Task (within-task) and Inter-Task (between-task) knowledge sharing. We propose an effective and flexible geometric affine transformation (contraction or expansion) of the distances between Inter-Task and Intra-Task instances. This transformation allows for an improved Intra-Task clustering without overwhelming the individual tasks with the bias accumulated from other tasks. A constrained low-rank decomposition of this multi-task transformation will allow us to maintain the class distribution of the clusters within each individual task. We impose an Intra-Task soft orthogonality constraint to a Symmetric Non-Negative Matrix Factorization (NMF) based formulation to generate basis vectors that are near orthogonal within each task. Inducing orthogonal basis vectors within each task imposes the prior knowledge that a task should have orthogonal (independent) clusters. Using several real-world experiments, we demonstrate that the proposed framework produces improves clustering quality compared to the state-of-the-art methods proposed in literature.