Graph Construction for Learning with Unbalanced Data

TL;DR

This paper introduces a novel graph construction method that uses global statistical information to improve learning with unbalanced data, addressing failures of traditional graphs like k-NN.

Contribution

The paper proposes a rank-modulated degree scheme that encodes density information into graph construction, enhancing performance on unbalanced datasets.

Findings

Significantly improves graph-based learning on unbalanced data

Theoretical justification via limit cut analysis

Demonstrated effectiveness on synthetic and real datasets

Abstract

Unbalanced data arises in many learning tasks such as clustering of multi-class data, hierarchical divisive clustering and semisupervised learning. Graph-based approaches are popular tools for these problems. Graph construction is an important aspect of graph-based learning. We show that graph-based algorithms can fail for unbalanced data for many popular graphs such as k-NN, \epsilon-neighborhood and full-RBF graphs. We propose a novel graph construction technique that encodes global statistical information into node degrees through a ranking scheme. The rank of a data sample is an estimate of its p-value and is proportional to the total number of data samples with smaller density. This ranking scheme serves as a surrogate for density; can be reliably estimated; and indicates whether a data sample is close to valleys/modes. This rank-modulated degree(RMD) scheme is able to significantly sparsify the graph near valleys and provides an adaptive way to cope with unbalanced data. We then theoretically justify our method through limit cut analysis. Unsupervised and semi-supervised experiments on synthetic and real data sets demonstrate the superiority of our method.