Nystr\"om Approximation with Nonnegative Matrix Factorization

TL;DR

This paper introduces a novel approach combining Nyström approximation with Nonnegative Matrix Factorization to improve proximity clustering in networked systems, demonstrating high-quality results on various datasets.

Contribution

It formulates proximity clustering as a Nyström approximation problem and implements it using landmark-based NMF, offering a new method for clustering with partial distance data.

Findings

Achieves nearly optimal clustering quality on synthetic data.

Performs well across different network conditions.

Effectively estimates proximity clusters with partial measurements.

Abstract

Motivated by the needs of estimating the proximity clustering with partial distance measurements from vantage points or landmarks for remote networked systems, we show that the proximity clustering problem can be effectively formulated as the Nystr\"om approximation problem, which solves the kernel K-means clustering problem in the complex space. We implement the Nystr\"om approximation based on a landmark based Nonnegative Matrix Factorization (NMF) process. Evaluation results show that the proposed method finds nearly optimal clustering quality on both synthetic and real-world data sets as we vary the range of parameter choices and network conditions.