Synchronization-Inspired Partitioning and Hierarchical Clustering

Abstract

Synchronization is a powerful and inherently hierarchical concept regulating a large variety of complex processes ranging from the metabolism in a cell to opinion formation in a group of individuals. Synchronization phenomena in nature have been widely investigated and models concisely describing the dynamical synchronization process have been proposed, e.g., the well-known Extensive Kuramoto Model. We explore the potential of the Extensive Kuramoto Model for data clustering. We regard each data object as a phase oscillator and simulate the dynamical behavior of the objects over time. By interaction with similar objects, the phase of an object gradually aligns with its neighborhood, resulting in a nonlinear object movement naturally driven by the local cluster structure. We demonstrate that our framework has several attractive benefits: 1) It is suitable to detect clusters of arbitrary number, shape, and data distribution, even in difficult settings with noise points and outliers. 2) Combined with the Minimum Description Length (MDL) principle, it allows partitioning and hierarchical clustering without requiring any input parameters which are difficult to estimate. 3) Synchronization faithfully captures the natural hierarchical cluster structure of the data and MDL suggests meaningful levels of abstraction. Extensive experiments demonstrate the effectiveness and efficiency of our approach.