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PU classification under Non-SCAR: clustering-assisted logistic model with oversampling enhancement
Konrad Furmańczyk, Kacper Paczutkowski
TL;DR
In PU classification, negative labels are unavailable, and positive labeling may depend on features, violating SCAR. This study evaluates clustering-assisted logistic models with Lasso regularization and SMOTE, reporting performance gains that tend to be larger in non-SCAR settings.
Problem
PU data leave negatives unlabeled, and SCAR’s feature-independent labeling assumption may fail when selection depends on covariates.
Source: §1 · p. 2Method
Results
SMOTE generally improved performance, with some LassoJoint exceptions; gains tended to be larger at small c and in non-SCAR cases.
Source: §4 · pp. 10–11Takeaways & Limitations
The cluster method performed well across SCAR conditions, suggesting applicability when SCAR is not satisfied.
Source: §4 · p. 11The PU setup assumes that negative instances are never labeled positive, while positive-label selection may depend on features.
Source: §1 · p. 2
Abstract
from arXiv · showhide
This study addresses the PU classification problem under violations of the SCAR assumption. We investigate logistic regression-based approaches, namely the cluster method and its extensions with strict and non-strict Lasso regularization. The primary contribution of this work is the integration of the SMOTE technique to alleviate class imbalance and systematically assess its impact on the performance of the considered algorithms. SMOTE is first applied to rebalance the training dataset. Next, cleaning labels are derived via 2-means clustering. Logistic regression is then trained on the cleaned data, where identified positive instances are augmented with additional true positives and the remaining observations are treated as negative. The experimental evaluation is conducted on 13 real benchmark datasets and one synthetic dataset. For comparison, we include the naive approach and the Spy-EM method. The results demonstrate that incorporating SMOTE improves classification performance when the SCAR condition is violated and indicate moderate robustness of the LassoJoint method in this setting.
1 Introduction
PU classification has only labeled positives and unlabeled observations, so the unlabeled group mixes true positives and negatives. This study examines clustering-assisted logistic approaches under SCAR violations and incorporates SMOTE to address class imbalance.
1 Introduction
- PU learning observes labeled positives and unlabeled cases, which may be either truly positive or negative.Medical diagnosis and fraud detection illustrate the ambiguity of unlabeled observations.Source: §1 · pp. 1–2
- SCAR assumes positive labeling is independent of features, whereas SAR allows feature-dependent labeling and makes identification and estimation more challenging.In customer behavior, feedback likelihood may depend on customer characteristics.Source: §1 · p. 2
- The study investigates computationally efficient cluster-based cleaning with logistic regression and strict and non-strict Lasso extensions under SCAR violations.The approach uses clustering to identify reliable negative instances.Source: §1 · p. 2
- SMOTE is incorporated to mitigate PU class imbalance, while the study assesses clustering methods and LassoJoint robustness and benchmarks against naive and Spy-EM methods [20].The evaluation examines SMOTE’s impact on predictive performance and robustness.Source: §1 · pp. 2–3
2 Objectives and Methods
The study evaluates cluster cleaning with SMOTE under SCAR violations and examines LassoJoint robustness under those perturbations. Its methods include pecking-based label cleaning, regularized logistic models, and benchmark approaches.
2 Objectives and Methods
- The study evaluates cluster cleaning with SMOTE under SCAR violations and examines LassoJoint robustness under the same perturbations.Source: §2 · p. 3
- LassoJoint selects predictors with ordinary and thresholded Lasso before jointly estimating coefficients and label frequency; naive logistic regression and Spy-EM serve as comparison methods.Source: §2 · pp. 3–4
2.1 Cluster Cleaning Procedure
- SMOTE is applied during training-data preprocessing to generate synthetic positives, using K=5 and dup_size=0 to automatically balance the minority class toward the majority.Source: §2 · p. 4, §2.1 · p. 5
- Pecking temporarily moves a fraction q% of labeled positives into the unlabeled set, then uses 2-means clustering to form clusters and assign cleaned labels.Source: §2.1 · pp. 4–5
- Across repetitions, logistic regression or strict/non-strict Lasso is fit to cleaned labels, with coefficients averaged across all, universally selected, or any-selected features, respectively.Source: §2.1 · p. 5
3 Numerical Experiments
The experiments evaluate cluster-based PU methods, Lasso variants, and benchmarks on synthetic and real datasets under SCAR and non-SCAR settings, with and without SMOTE. Under non-SCAR, clustering combined with Lasso performs strongly against naive and Spy-EM; SMOTE often improves classification performance, while LassoJoint remains stable.
3.1 Datasets
- The evaluation covered 13 real low-dimensional UCI datasets and one synthetic dataset, with preprocessing to remove quasi-constant and highly correlated features and scale numeric variables.The synthetic dataset used relevant and irrelevant features, with a logistic function generating the binary target.Source: §3.1 · p. 6
3.2 Non-SCAR Scenarios
- Non-SCAR labels were generated using two high-variance features and a linear approximation to control coverage of the true labels near a target c.The experiments set nvars = 2.Source: §3.2 · p. 6
3.3 Calibrations of Parameters and Experiment
- Methods were tested at c = 0.3, 0.5, and 0.8 using 70/30 train-test splits; cluster coefficients were averaged over five repetitions, and each method was evaluated with and without SMOTE.Cluster cleaning used q = 1; LassoJoint tuning used 10-fold cross-validation with λmin and a second-step threshold δ = 0.5·λ.Source: §3.3 · pp. 6–7
3.4 Results
- Across SCAR and non-SCAR simulations, SMOTE improved AUC in 69% of clust and approximately 56% of strict/non-strict Lasso experiments; Accuracy improved in 72%, approximately 67%, and 27%, respectively.Accuracy gains were stronger than AUC gains, especially under SCAR; cluster-method AUC gains were largest at c = 0.8.Source: §3.4 · pp. 7–8
- Under non-SCAR, clustering with strict or non-strict Lasso outperformed naive and Spy-EM; under SCAR, LassoJoint was typically most stable and often best overall.The non-SCAR AUC figure and the methods-with-SMOTE comparison table accompany the reported benchmark comparisons.Source: Figure 1 · p. 7, §3.4 · pp. 9–10, Table 3 · p. 10
4 Conclusions
The study concludes that cluster methods with Lasso regularization work well under the considered SCAR disturbance, while performance varies with labeling frequency. Improvements are strongest at smaller c values and tend to be slightly larger in non-SCAR settings.
4 Conclusions
- In the considered SCAR-disturbance model, clustering methods combined with Lasso were effective, and Lasso regularization generally improved predictions.The authors report exceptions for LassoJoint among methods whose performance improved, especially with SMOTE.Source: §4 · p. 10
- For small c, the methods show their strongest AUC and Accuracy improvements, and the gains tend to be slightly larger in non-SCAR cases.As c approaches 1, the PU task becomes closer to fully labeled classification and the naive method gains an advantage.Source: §4 · p. 11
- Under SCAR, LassoJoint performed nearly optimally, while the cluster method also performed well and was presented as applicable across SCAR assumptions.The authors describe this work as extending prior results to settings where SCAR is not satisfied.Source: §4 · p. 11