Multi-Objective Optimisation for the Selection of Clusterings across Time †
Abstract
:1. Introduction
2. Related Work
3. Framework
3.1. Weighting Procedure
- Weights with should match the endpoints of ;
- Every element from should be selectable by an appropriate weight (surjectivity);
- Two different weights should not map to the same element on (injectivity).
3.2. Transition-Based Temporal Quality Metric
4. Experiments
4.1. Datasets and Frameworks for Comparison
4.2. Instantiations of Clustering Algorithms
- Cluster all time series at time t with all combinations of and .
- Let each framework select a clustering from the set of resulting clusterings.
- Move to the next time point, .
4.3. Framework Parameter Settings and Clustering Evaluation Metric
4.4. Results
5. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
MOSCAT | Multi-objective optimisation for selection of clusterings across time (method) |
DBSCAN | Density-Based Spatial Clustering of Applications with Noise (method) |
TOPSIS | Technique for Order Preference by Similarity to Ideal Solution (method) |
COVID-19 | Coronavirus disease 2019 (infectious disease) |
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Term | Description |
---|---|
Maximum snapshot quality | |
Maximum temporal quality | |
Snapshot quality of given solution at time t | |
Temporal quality of given solution at time t | |
w | weight with |
Dataset | No. Features | No. Time Series | No. Classes | Time Series Length |
---|---|---|---|---|
ERing | 4 | 300 | 6 | 65 |
Motions | 6 | 80 | 4 | 100 |
Dataset | Baseline | Evol. Clustering | MOSCAT |
---|---|---|---|
ERing | 0.191 ± 0.058 | 0.178 ± 0.005 | 0.180 ± 0.004 |
Motions | 0.288 ± 0.057 | 0.284 ± 0.049 | 0.477 ± 0.057 |
Purity | Weight | ||||
---|---|---|---|---|---|
Dataset | k | Baseline | Evol. Clustering | MOSCAT | MOSCAT |
Motions | 2 | 0.371 ± 0.016 | 0.280 ± 0.016 | 0.280 ± 0.016 | 0.8 |
3 | 0.388 ± 0.048 | 0.421 ± 0.044 | 0.397 ± 0.037 | 0.9 | |
4 | 0.450 ± 0.046 | 0.485 ± 0.039 | 0.469 ± 0.042 | 0.8 | |
5 | 0.451 ± 0.045 | 0.479 ± 0.038 | 0.465 ± 0.051 | 0.8 | |
6 | 0.476 ± 0.035 | 0.497 ± 0.030 | 0.504 ± 0.047 | 0.8 | |
7 | 0.459 ± 0.048 | 0.499 ± 0.026 | 0.547 ± 0.047 | 0.8 | |
8 | 0.485 ± 0.042 | 0.503 ± 0.026 | 0.507 ± 0.043 | 0.7 | |
9 | 0.484 ± 0.040 | 0.500 ± 0.024 | 0.510 ± 0.048 | 0.7 | |
10 | 0.461 ± 0.047 | 0.501 ± 0.026 | 0.510 ± 0.059 | 0.7 | |
ERing | 2 | 0.325 ± 0.013 | 0.324 ± 0.013 | 0.325 ± 0.013 | 0.0 |
3 | 0.448 ± 0.039 | 0.445 ± 0.045 | 0.448 ± 0.039 | 0.0 | |
4 | 0.535 ± 0.063 | 0.530 ± 0.069 | 0.536 ± 0.061 | 0.8 | |
5 | 0.524 ± 0.069 | 0.537 ± 0.069 | 0.526 ± 0.066 | 0.8 | |
6 | 0.569 ± 0.071 | 0.573 ± 0.077 | 0.567 ± 0.074 | 0.8 | |
7 | 0.586 ± 0.086 | 0.587 ± 0.088 | 0.589 ± 0.085 | 0.8 | |
8 | 0.598 ± 0.076 | 0.582 ± 0.077 | 0.600 ± 0.079 | 0.7 | |
9 | 0.602 ± 0.078 | 0.592 ± 0.079 | 0.604 ± 0.082 | 0.7 | |
10 | 0.611 ± 0.074 | 0.602 ± 0.076 | 0.612 ± 0.078 | 0.8 |
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Korlakov, S.; Klassen, G.; Bauer, L.T.; Conrad, S. Multi-Objective Optimisation for the Selection of Clusterings across Time. Eng. Proc. 2024, 68, 48. https://doi.org/10.3390/engproc2024068048
Korlakov S, Klassen G, Bauer LT, Conrad S. Multi-Objective Optimisation for the Selection of Clusterings across Time. Engineering Proceedings. 2024; 68(1):48. https://doi.org/10.3390/engproc2024068048
Chicago/Turabian StyleKorlakov, Sergej, Gerhard Klassen, Luca T. Bauer, and Stefan Conrad. 2024. "Multi-Objective Optimisation for the Selection of Clusterings across Time" Engineering Proceedings 68, no. 1: 48. https://doi.org/10.3390/engproc2024068048