Hierarchical Reference Sets for Robust Unsupervised Detection of Scattered and Clustered Outliers
Organizations: School of Computer Science and Technology, Guangdong University of Technology, Guangzhou, China
Abstract
Most real-world IoT data analysis tasks, such as clustering and anomaly event detection, are unsupervised and highly susceptible to the presence of outliers. In addition to sporadic scattered outliers caused by factors such as faulty sensor readings, IoT systems often exhibit clustered outliers. These occur when multiple devices or nodes produce similar anomalous measurements, for instance, owing to localized interference, emerging security threats, or regional false alarms, forming micro-clusters. These clustered outliers can be easily mistaken for normal behavior because of their relatively high local density, thereby obscuring the detection of both scattered and contextual anomalies. To address this, we propose a novel outlier detection paradigm that leverages the natural neighboring relationships using graph structures. This facilitates multi-perspective anomaly evaluation by incorporating reference sets at both local and global scales derived from the graph. Our approach enables the effective recognition of scattered outliers without interference from clustered anomalies, whereas the graph structure simultaneously helps reflect and isolate clustered outlier groups. Extensive experiments, including comparative performance analysis, ablation studies, validation on downstream clustering tasks, and evaluation of hyperparameter sensitivity, demonstrate the efficacy of the proposed method. The source code is available at https://github.com/gordonlok/DROD.
Figures & tables
| Section | Symbol | Definition |
| III | Data sample | |
| Natural neighbor set of | ||
| -nearest neighbors with scope | ||
| Natural Neighborhood Graph | ||
| Edge indicator in between | ||
| IV-A | Local natural density of |
| Case | SAI | LAI | Anomaly Type | Description |
| 1 | High | High | Scatterlier | Clear abnormality with dual evidence |
| 2 | High | Low | Clusterlier | Core member of anomalous micro-cluster |
| 3 | Low | High | Potential noise | Local isolation, global normality |
| 4 | Low | Low | Normal sample | No significant anomaly evidence |
| Real dataset | Samples | Features | Anomaly(%) | Reference |
| PageBlocks | 5393 | 10 | 510 (9.46) | [ 36 ] |
| WPBC | 198 | 33 | 47 (23.74) | [ 37 ] |
| mnist | 7603 | 100 | 700 (9.21) | [ 38 ] |
| musk | 3062 | 166 | 97 (3.17) | [ 39 ] |
| Ionosphere | 351 | 33 | 126 (35.90) | [ 40 ] |
| Waveform | 3443 | 21 | 100 (2.90) | [ 41 ] |
| Dataset | Normal Samples | Scatterliers | Clusterliers |
| D1 | 1000 | 0 | (100,100) |
| D2 | 266 | 0 | (26,26) |
| D3 | 1000 | 50 | (50) |
| D4 | 1000 | 100 | (50,50) |
| D5 | 1000 | 150 | (30,50,70) |
| D6 | 266 | 20 | (20) |
| Datasets | COPOD | ECOD | OCSVM | IFOREST | NN+KFC | LOF+KFC | DGOF+KFC | CBLOF | DROD |
| [ 57 ] ’2020 | [ 58 ] ’2022 | [ 55 ] ’2023 | [ 56 ] ’2023 | [ 53 ] ’2024 | [ 53 ] ’2024 | [ 53 ] ’2024 | [ 54 ] ’2025 | ours | |
| D1 | 0.5070 | 0.4149 | 0.4932 | 0.6759 | 0.1266 | 0.4887 | 0.3562 | 0.2415 | 0.8330 |
| D2 | 0.5227 | 0.3758 | 0.5000 | 0.5454 | 0.8228 | 0.5856 | 0.6076 | 0.0753 | 0.9180 |
| Avg. AUC | 0.5149 | 0.3954 | 0.4966 | 0.6107 | 0.4747 | 0.5732 | 0.4819 | 0.1573 | 0.8755 |
| Datasets | COPOD | ECOD | OCSVM | IFOREST | NN+KFC | LOF+KFC | DGOF+KFC | CBLOF | DROD |
| [ 57 ] ’2020 | [ 58 ] ’2022 | [ 55 ] ’2023 | [ 56 ] ’2023 | [ 53 ] ’2024 | [ 53 ] ’2024 | [ 53 ] ’2024 | [ 54 ] ’2025 | ours | |
| Pageblocks | 0.8754(6) | 0.9139(2) | 0.8903(5) | 0.8977(4) | 0.8061(8) | 0.7512(9) | 0.8413(7) | 0.9083(3) | 0.9154(1) |
| WPBC | 0.5233(4) | 0.4813(7) | 0.4743(8) | 0.4938(5) | 0.5323(2) | 0.4932(6) | 0.5600(1) | 0.4686(9) | 0.5249(3) |
| mnist | 0.7739(8) | 0.7463(9) | 0.8204(3) | 0.8008(5) | 0.8655(1) | 0.8019(4) | 0.7829(7) | 0.7913(6) | 0.8603(2) |
| musk | 0.9463(7) | 0.9559(6) | 0.8094(8) | 0.9996(4) | 1.0000(2) | 0.8014(9) | 1.0000(2) | 1.0000(2) | 0.9888(5) |
| Ionosphere | 0.7895(7) | 0.7284(9) | 0.7395(8) | 0.8503(4) | 0.8300(6) | 0.8889(2) | 0.8379(5) | 0.9013(1) | 0.8598(3) |
| Datasets | COPOD | ECOD | OCSVM | IFOREST | NN+KFC | LOF+KFC | DGOF+KFC | CBLOF | DROD |
| [ 57 ] ’2020 | [ 58 ] ’2022 | [ 55 ] ’2023 | [ 56 ] ’2023 | [ 53 ] ’2024 | [ 53 ] ’2024 | [ 53 ] ’2024 | [ 54 ] ’2025 | ours | |
| Pageblocks | 0.3353(9) | 0.4314(4) | 0.3670(8) | 0.4186(6) | 0.4310(5) | 0.3892(7) | 0.4324(3) | 0.6078(1) | 0.5235(2) |
| WPBC | 0.2128(3) | 0.1277(9) | 0.1702(6.5) | 0.1553(8) | 0.1773(5) | 0.1809(4) | 0.2199(2) | 0.1702(6.5) | 0.2340(1) |
| mnist | 0.2357(8) | 0.1800(9) | 0.3710(3) | 0.2990(6) | 0.4210(2) | 0.2502(7) | 0.3510(4) | 0.3329(5) | 0.5443(1) |
| musk | 0.3608(6) | 0.4948(5) | 0.0223(9) | 0.9495(2) | 0.5052(4) | 0.0464(7) | 0.0395(8) | 1.0000(1) | 0.5361(3) |
| Ionosphere | 0.5873(8) | 0.5317(9) | 0.8479(1) | 0.6706(7) | 0.7315(5) | 0.7659(4) | 0.7262(6) | 0.8254(2) | 0.7698(3) |
| Counterparts | R+ | R- | p-value | null hypothesis ( =0.05) |
| DROD vs NN+KFC | 165 | 45 | 0.0240 | Reject |
| DROD vs LOF+KFC | 201 | 9 | 0.0001 | Reject |
| DROD vs DGOF+KFC | 183 | 27 | 0.0023 | Reject |
| DROD vs IFOREST | 191 | 19 | 0.0006 | Reject |
| DROD vs CBLOF | 180 | 30 | 0.0037 | Reject |
| DROD vs OCSVM | 203 | 7 | 0.0001 | Reject |
| Datasets | NRS (ours) | GB | GNAN | HDIOD |
| Pageblocks | 0.9154 | 0.4562 | 0.5249 | 0.8919 ( =6) |
| WPBC | 0.5249 | 0.4584 | 0.4760 | 0.5942 ( =4) |
| Ionosphere | 0.8598 | 0.7271 | 0.7586 | 0.5867 ( =6) |
| Cardiotocography | 0.7431 | 0.5687 | 0.5107 | 0.7831 ( =7) |
| cardio | 0.9368 | 0.5275 | 0.6151 | 0.9407 ( =8) |
| landsat | 0.6290 | 0.4889 | 0.4849 | 0.6241 ( =3) |
| Datasets | Scales (n d) | Euclidean | Mahalanobis | Chebyshev |
| Pageblocks | 5393 10 | 0.9154 | 0.9129 | 0.9096 |
| WPBC | 198 33 | 0.5249 | 0.4999 | 0.4841 |
| Ionosphere | 351 33 | 0.8598 | 0.8602 | 0.8241 |
| Cardiotocography | 351 33 | 0.7431 | 0.6942 | 0.7829 |
| Cardio | 1831 21 | 0.9368 | 0.9370 | 0.9407 |
| Landsat | 6435 36 | 0.6290 | 0.4499 | 0.6221 |
| Datasets | LOF+KFC | DROD-L | DROD-S | DROD-0 | DROD |
| Pageblocks | 0.7263 | 0.7250 | 0.9020 | 0.9116 | 0.9154 |
| WPBC | 0.4932 | 0.4973 | 0.5545 | 0.5546 | 0.5249 |
| mnist | 0.8019 | 0.4361 | 0.7863 | 0.7599 | 0.8603 |
| musk | 0.8014 | 0.7270 | 0.9604 | 0.9481 | 0.9888 |
| Ionosphere | 0.8889 | 0.7543 | 0.8702 | 0.8504 | 0.8598 |
| Waveform | 0.7826 | 0.3864 | 0.8220 | 0.8182 | 0.8755 |
| Detectors | AUC | DBI ( ) |
| Random | - | 1.9578 (0.0000) |
| NN+KFC | 0.5249 | 1.9132 ( -0.0446 ) |
| LOF+KFC | 0.3921 | 1.9227 ( -0.0351 ) |
| DGOF+KFC | 0.2831 | 1.9117 ( -0.0461 ) |
| IFOREST | 0.7140 | 1.9341 ( -0.0237 ) |
| CBLOF | 0.7547 | 2.0125 ( +0.0547 ) |