A proposal for PU classification under Non-SCAR using clustering and logistic model

arXiv stat.ML / 4/21/2026

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Key Points

The paper proposes a PU (Positive-Unlabeled) classification approach for cases where the SCAR assumption does not hold, using a simple cluster-cleaning method.
It first generates “cleaning labels” via 2-means clustering, then fits logistic regression on the cleaned data by treating clustered positives as positives with extra true-positive observations.
Remaining samples are labeled as negative, enabling the classifier to learn from the cleaned PU structure.
The method is evaluated on 11 real machine-learning datasets plus a synthetic dataset, showing that the clustering step can still be effective under SCAR violations.
The study also assesses robustness, finding that the LassoJoint method exhibits moderate robustness to perturbations of the SCAR condition.

Abstract

The present study aims to investigate a cluster cleaning algorithm that is both computationally simple and capable of solving the PU classification when the SCAR condition is unsatisfied. A secondary objective of this study is to determine the robustness of the LassoJoint method to perturbations of the SCAR condition. In the first step of our algorithm, we obtain cleaning labels from 2-means clustering. Subsequently, we perform logistic regression on the cleaned data, assigning positive labels from the cleaning algorithm with additional true positive observations. The remaining observations are assigned the negative label. The proposed algorithm is evaluated by comparing 11 real data sets from machine learning repositories and a synthetic set. The findings obtained from this study demonstrate the efficacy of the clustering algorithm in scenarios where the SCAR condition is violated and further underscore the moderate robustness of the LassoJoint algorithm in this context.