Multi-objective Multi-view Spectral Clustering via Pareto Optimization

Traditionally, spectral clustering is limited to a single objective: finding the normalized min-cut of a single graph. However, many real-world datasets, such as scientific data (fMRI scans of different individuals), social data (different types of connections between people), web data (multi-type data), are generated from multiple heterogeneous sources. How to optimally combine knowledge from multiple sources to improve spectral clustering remains a developing area. Previous work on multi-view clustering formulated the problem as a single objective function to optimize, typically by combining the views under a compatibility assumption and requiring the users to decide the importance of each view a priori. In this work, we propose a multi-objective formulation and show how to solve it using Pareto optimization. The Pareto frontier captures all possible good cuts without requiring the users to set the “correct” parameter. The effectiveness of our approach is justified by both theoretical analysis and empirical results. We also demonstrate a novel application of our approach: resting-state fMRI analysis.