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LSCP: Locally Selective Combination in Parallel Outlier Ensembles
Yue Zhao, Zain Nasrullah, Maciej K. Hryniewicki, Zheng Li
TL;DR
Unsupervised outlier ensembles lack ground truth and reliable detector selection, making combination difficult. LSCP addresses this by selecting locally competent detectors around each test instance and combining them. Across 20 real-world datasets, LSCP outperforms baseline parallel methods, with LSCP AOM achieving the strongest reported coverage.
Problem
Parallel outlier ensembles lack a reliable way to select competent base detectors without ground truth, while global combination can ignore data locality.
Method
LSCP defines a local region from nearest-neighbor consensus in randomly selected feature subspaces, evaluates detector competence against a pseudo ground truth, and selectively combines detectors.
Results
LSCP outperforms baseline algorithms on 20 real-world datasets; LSCP AOM achieves the highest detection score on 13/20 datasets by ROC-AUC and 14/20 by mAP.
Takeaways & Limitations
LSCP demonstrates the promise of local detector selection for parallel unsupervised outlier ensembles and supports further work on heterogeneous detectors and improved pseudo ground truths.
Takeaways & Limitations
The study uses simple pseudo ground-truth generation methods, and LSCP’s local-region definition can be costly or degrade with many irrelevant high-dimensional features.
Abstract
from arXiv · showhide
In unsupervised outlier ensembles, the absence of ground truth makes the combination of base outlier detectors a challenging task. Specifically, existing parallel outlier ensembles lack a reliable way of selecting competent base detectors, affecting accuracy and stability, during model combination. In this paper, we propose a framework---called Locally Selective Combination in Parallel Outlier Ensembles (LSCP)---which addresses the issue by defining a local region around a test instance using the consensus of its nearest neighbors in randomly selected feature subspaces. The top-performing base detectors in this local region are selected and combined as the model's final output. Four variants of the LSCP framework are compared with seven widely used parallel frameworks. Experimental results demonstrate that one of these variants, LSCP_AOM, consistently outperforms baselines on the majority of twenty real-world datasets.
1 Introduction
The paper introduces LSCP, an unsupervised framework that selects and combines locally competent outlier detectors to address limitations in parallel ensembles. It reports broad empirical validation and emphasizes interpretability and reproducibility.
- Motivation: Existing parallel ensembles often combine all detectors without selection, allowing poor detectors to neutralize good ones and neglecting data locality.These limitations can produce sub-optimal model combinations because detector competence may vary across local regions.
- Method: LSCP defines a test instance’s local region from nearest-neighbor consensus in randomly selected feature subspaces, then selects competent base detectors using a pseudo ground truth.The framework adapts the local-competency idea of Dynamic Classifier Selection to fully unsupervised outlier detection.
- Contribution: LSCP is presented as the first published adaptation of Dynamic Classifier Selection to unsupervised parallel outlier ensembles.The contribution transfers dynamic selection from supervised classification to outlier detection without requiring ground-truth labels.
- Evaluation: Experiments on 20 real-world datasets show that LSCP consistently performs better than existing parallel combination methods.The paper evaluates LSCP against established parallel combination approaches.
- Scope: LSCP is formulated to support different base-detector types and is demonstrated using a homogeneous pool of Local Outlier Factor detectors.This positions LSCP as a general combination framework rather than a method restricted to one detector family.
- Analysis and Reproducibility: The authors provide theoretical analysis, visualizations, statistical tests, shared implementation materials, and a PyOD implementation to improve interpretation and reproduction.Source code, experiment results, and figures are shared, and the framework includes a unified API with documentation.
2 Related Works
Related work covers dynamic selection, locality in outlier detection, and established parallel and sequential ensemble strategies. The paper positions LSCP as a parallel, locally selective alternative to global combination methods that may retain poor detectors.
- Dynamic Selection: Dynamic Classifier Selection chooses locally accurate classifiers, while Dynamic Ensemble Selection selects multiple competent classifiers for second-phase combination.LSCP adapts these local-selection ideas from supervised classification to unsupervised outlier detection.
- Dynamic Selection: LSCP refines an earlier dynamic detector-combination framework by improving local-region definition for a more stable combination mechanism.The cited prior work identifies LSCP as an extension of DCSO.
- Locality: Outlier detection methods may be global or local, and their applicability depends on the structure of the data.Global methods consider all objects, whereas local methods use a selected neighborhood of objects.
- Outlier Ensembles: Parallel ensembles include Feature Bagging and Isolation Forest, while sequential approaches include CARE, SELECT, and Boost-Select, with hybrid methods such as BORE and XGBOD.The paper focuses on parallel detector selection rather than sequential selection models.
- Combination Baselines: The global baselines include averaging, maximization, weighted averaging, threshold sum, average-of-maximum, maximum-of-average, and Feature Bagging.These methods combine detector scores globally without the local selection mechanism emphasized by LSCP.
- Combination Baselines: Global combination methods ignore data locality and may allow poor detectors to hurt ensemble performance, motivating their use as LSCP baselines.The paper links this limitation to the characteristics of outliers and the absence of a selection process.
3 Algorithm Design
LSCP locally selects and combines competent detectors for each test instance using a pseudo ground truth and a locality-based competency measure. Its variants define local regions, evaluate detector similarity, and aggregate selected predictions while reusing precomputed scores where possible.
- Base detector generation: LSCP begins with diversified base detectors, trains them on Xtrain, and forms a normalized training outlier-score matrix for subsequent selection.The framework can use homogeneous detectors with varied hyperparameters or heterogeneous detector types.
- Pseudo ground truth generation: Pseudo ground truth is generated by aggregating all training detector scores with either an average or maximum operation.These alternatives define LSCP A and LSCP M targets used solely for detector selection.
- Local region definition: For each test instance, LSCP defines a local region from consensus nearest neighbors across randomly selected feature subspaces, with region size determined by the selection criterion.The method balances locality against instability and computational cost through the local-region factor k.
- Computational considerations: Local regions are recomputed for each test instance, while local scores and targets are retrieved from precomputed values; defining a region can add O(nd + nlog(n)) time with suitable implementation.Here n denotes the number of training objects considered for a test instance and d its dimensionality.
- Local competency evaluation: Detector competency is measured by Pearson correlation between each detector’s local scores and the local pseudo target rather than by binary-label accuracy.This avoids relying on unavailable labels and avoids choosing an uncertain threshold for converting pseudo scores into binary labels.
- Model selection and combination: LSCP selects the most locally similar detector or a competent subset, then returns either its score or an ensemble aggregation such as maximum-of-average or average-of-maximum.A group size of one recovers the original single-detector variants, whereas selecting all detectors produces a fully global algorithm.
4 Numerical Experiments
Experiments compare four LSCP variants with seven parallel combination methods across 20 real-world datasets. LSCP generally improves performance, with LSCP AOM strongest overall, while results depend on the combination strategy and local-region suitability.
- 20 public datasets were evaluated using 30 independent trials, ROC-AUC, and mAP, with 60% training data and 40% validation data.
- LSCP achieved the highest ROC-AUC on 15 datasets and highest mAP on 18 datasets, while statistical tests found significant differences among the 11 algorithms.Friedman tests reported χ2 = 43.34, p = 4.3160 × 10^-6 for ROC-AUC and χ2 = 43.49, p = 4.0632 × 10^-6 for mAP.
- LSCP A and LSCP M performed weakly relative to their GG counterparts because heuristic pseudo-ground-truth generation can impair local competency evaluation.Selecting only one detector may reduce variance reduction enough that it cannot offset bias from pseudo-ground-truth generation.
- LSCP AOM ranked highest on 13 datasets by ROC-AUC and 14 datasets by mAP, outperforming all models on those datasets.Its improvement over GG methods was especially considerable on Breastw, Cardio, Satimage-2, and Thyroid.
- LSCP MOA did not outperform LSCP A or GG MOA because second-phase combination cannot recover information lost during initial averaging.
- LSCP performs better when outliers form local clusters, but dispersed or interleaved outliers can reduce its advantage; a smaller local region may suit datasets with few outliers.Vowels and Letter contain only 3.43% and 6.25% outliers, respectively, which may be insufficient to form clusters in a 10% local region.
- Euclidean nearest-neighbor regions can be computationally expensive and degrade with many irrelevant high-dimensional features, while heterogeneous detectors remain unverified.The study also explores only simple averaging and maximization for pseudo-ground-truth generation.
5 Conclusions
LSCP is an unsupervised outlier-detection framework that selects top-performing base detectors for each test instance using its local region. Across 20 real-world datasets, LSCP_AOM achieves the strongest reported results among the evaluated ensemble variants, while future work targets heterogeneous detectors and improved pseudo ground truth.
- LSCP proposes four variants of an unsupervised framework that identify top-performing base detectors relative to each test instance’s local region.
- 20 real-world datasets were used to assess LSCP against baseline algorithms.
- 13/20 datasets achieved the highest ROC-AUC with LSCP_AOM, compared with 14/20 datasets for the highest mAP.
- Future work includes heterogeneous base detectors and more reliable pseudo ground truth generation methods.