An Effective Flow-based Method for Positive-Unlabeled Learning: 2-HNC

TL;DR

This paper introduces 2-HNC, a flow-based method for positive-unlabeled learning that ranks unlabeled samples by their likelihood of being negative using nested partitions derived from Hochbaum's Normalized Cut, improving classification accuracy.

Contribution

The paper presents a novel flow-based approach, 2-HNC, which leverages nested partitions from Hochbaum's Normalized Cut to effectively rank and classify unlabeled data in PU learning scenarios.

Findings

2-HNC outperforms existing methods on synthetic datasets.

The method achieves competitive results on real-world datasets.

It provides a reliable ranking of unlabeled samples by negative likelihood.

Abstract

In many scenarios of binary classification, only positive instances are provided in the training data, leaving the rest of the data unlabeled. This setup, known as positive-unlabeled (PU) learning, is addressed here with a network flow-based method which utilizes pairwise similarities between samples. The method we propose here, 2-HNC, leverages Hochbaum's Normalized Cut (HNC) and the set of solutions it provides by solving a parametric minimum cut problem. The set of solutions, that are nested partitions of the samples into two sets, correspond to varying tradeoff values between the two goals: high intra-similarity inside the sets and low inter-similarity between the two sets. This nested sequence is utilized here to deliver a ranking of unlabeled samples by their likelihood of being negative. Building on this insight, our method, 2-HNC, proceeds in two stages. The first stage generates this ranking without assuming any negative labels, using a problem formulation that is constrained only on positive labeled samples. The second stage augments the positive set with likely-negative samples and recomputes the classification. The final label prediction selects among all generated partitions in both stages, the one that delivers a positive class proportion, closest to a prior estimate of this quantity, which is assumed to be given. Extensive experiments across synthetic and real datasets show that 2-HNC yields strong performance and often surpasses existing state-of-the-art algorithms.