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Evolutionary Classifier Chain for Multi-Dimensional Classification
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Proposes ECCO, an evolutionary (two-subpopulation genetic algorithm) method that jointly optimizes classifier-chain order and dimension-specific feature selection for multi-dimensional classification with SVM base classifiers.
Problem
Multi-dimensional classification (MDC) classifier chains rely on greedy or random chain orders that often fit incorrect class dependencies, and they feed all input features to each classifier, so irrelevant features mislead predictions.
Approach
Encode chain order and per-dimension binary feature masks into one individual and evolve them with a two-subpopulation co-evolutionary GA (Pareto dominance plus Tchebycheff decomposition), minimizing feature ratio and (1 - Hamming score) on training data, then selecting the best Pareto solution on test data.
Key results
- ECCO obtains the best Friedman rank on all three metrics (HS 1.679, EM 2.250, SEM 2.286) against 7 MDC baselines.
- ECCO wins on HS in 78.6% of datasets (11 of 14), on EM in 50%, and on SEM in 64.3%.
- ECCO's Hamming Score is significantly better than BR and CP on all datasets by Wilcoxon test at 0.05 level.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ECCO's evolutionary chain-order optimization and dimension-specific feature selection instead of the comparison approaches | MDC models · 14 real datasets | Hamming Score: 78.6% | Mixed |
| Use ECCO's evolutionary chain-order optimization and dimension-specific feature selection instead of the comparison approaches | MDC models · 14 real datasets | Exact Match: 50% | Mixed |
| Use ECCO's evolutionary chain-order optimization and dimension-specific feature selection instead of the comparison approaches | MDC models · 14 real datasets | Sub-Exact Match: 64.3% | Mixed |
| Optimize classifier-chain order and select dimension-specific feature combinations rather than use the compared chain-based methods' chain construction and all original features | MDC models · 14 real datasets | Hamming Score: 1.679 vs 4.500 (ECCO vs ECC); 1.679 vs 5.607 (ECCO vs BCC); 1.679 vs 4.179 (ECCO vs EDCC) | Helped |
Surprising findings
- ECCO does not win on exact match in half of the datasets, indicating gains are concentrated in partial-match metrics.
Limitations
- Evolutionary search over 2^(q*d) feature masks plus chain orders is computationally expensive, and the search uses the training set for fitness.
- Only SVM is used as base classifier, so results with other learners are untested.
- Experiments are limited to 14 tabular MDC datasets; ECCO wins less often on exact match (50% of datasets).
Experimental setup
Datasets: Edm Flare1 Oes97 Jura Oes10 Enb Song WQplants WQanimals WaterQuality BeLaE Voice
Benchmarks: Edm Flare1 Oes97 Jura Oes10 Enb Song WQplants WQanimals WaterQuality BeLaE Voice
Metrics: Hamming Score Exact Match Sub-Exact Match Friedman rank Wilcoxon signed-rank test
Baselines: BR CP ECC BCC EDCC gMML SEEM
Builds on: classifier chain DDFS NSGA-II-style Pareto selection MOEA/D Tchebycheff decomposition
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