Exploring label correlations using decision templates for ensemble of classifier chains

Victor F. Rocha; Alexandre L. Rodrigues; Thiago Oliveira-Santos; Flávio M. Varejão

cs.LGMar 13, 2026

Exploring label correlations using decision templates for ensemble of classifier chains

Authors: Victor F. Rocha, Alexandre L. Rodrigues, Thiago Oliveira-Santos, Flávio M. Varejão

Organizations: Department of Statistics, Federal University of Espírito Santo, Vitória, Espírito Santo, 29075-910, Brazil

Abstract

The use of ensemble-based multi-label methods has been shown to be effective in improving multi-label classification results. One of the most widely used ensemble-based multi-label classifiers is Ensemble of Classifier Chains. Decision templates for Ensemble of Classifier Chains (DTECC) is a fusion scheme based on Decision Templates that combines the predictions of Ensemble of Classifier Chains using information from the decision profile for each label, without considering information about other labels that might contribute to the classified result. Based on DTECC, this work proposes the Unconditionally Dependent Decision Templates for Ensemble of Classifier Chains (UDDTECC) method, a classifier fusion method that seeks to exploit correlations between labels in the fusion process. In this way, the classification of each label in the problem takes into account the label values that are considered conditionally dependent and that can lead to an improvement in the classification performance. The proposed method is experimentally compared with two traditional classifier fusion strategies and with a stacking-based strategy. Empirical evidence shows that using the proposed Decision Templates adaptation can improve the performance compared to the traditionally used fusion schemes on most of the evaluated metrics.

Figures & tables

$\mathcal{L}$ =	{	Desert	Mountains	Sea	Sunset	Trees	}
${\boldsymbol{y}}_{1}$	(	1	0	0	1	1	)
${\boldsymbol{y}}_{2}$	(	1	1	0	1	0	)
${\boldsymbol{y}}_{3}$	(	0	0	0	1	0	)
${\boldsymbol{y}}_{4}$	(	1	0	0	1	0	)
${\boldsymbol{y}}_{5}$	(	0	1	0	1	1	)
${\boldsymbol{W}}$	(	3	2	0	5	2	)

Table 1: Example of Majority Vote fusion function for classifying an instance of the Image data set with an ensemble consisting of 5 multi-label classifiers. Each instance of the data set represents an image that can be classified according to five possible labels: Desert, Mountains, Sea, Sunset and Trees. If the average of the binary decisions for each label is larger than the threshold, the label is chosen. In this example, a user defined value of threshold

\emph{t}=0.5

defines the labels present in the final classification result. The label set ultimately assigned to the image is Desert + Sunset.

$\mathcal{H}$ =	{	Desert	Mountains	Sea	Sunset	Trees	}
$\boldsymbol{\hat{h}}_{1}$	(	0.8	0.3	0.1	0.6	0.7	)
$\boldsymbol{\hat{h}}_{2}$	(	0.7	0.8	0.1	0.8	0.3	)
$\boldsymbol{\hat{h}}_{3}$	(	0.2	0.4	0.2	0.8	0.2	)
$\boldsymbol{\hat{h}}_{4}$	(	0.9	0.2	0.1	0.9	0.4	)
$\boldsymbol{\hat{h}}_{5}$	(	0.3	0.8	0.2	0.8	0.8	)
${\boldsymbol{W}}$	(	2.9	2.5	0.7	3.9	2.4	)

Table 2: Example of MeanEnsemble fusion function for classifying an instance of the Image data set with an ensemble consisting of 5 multi-label classifiers.

Panel of Figure 1 — Figure 1: The Stacking Classifier Ensemble training diagram.

Panel of Figure 2 — Figure 2: Schematic representation of the Stacking Classifier Ensemble’s classification process for an unseen instance.

	$\ell_{b}$	$\neg\ell_{b}$
$\ell_{a}$	A	B
$\neg\ell_{a}$	C	D

Table 3: Contingency table for labels

\ell_{a}

and

\ell_{b}

Figure 3: Matrix of the $\phi$ coefficients absolute values of the Scene dataset labels.

Panel of Figure 4 — Figure 4: Example of classifier fusion using the UDDTECC method on an instance of the Scene data set for the label Mountain.

Panel of Figure 5 — Figure 5: UDDTECC training workflow.

Name	Features	Diversity	Instances	Labels
3sources_guardian1000	1000	0.219	302	6
3sources_inter3000	3000	0.172	169	6
CAL500	68	1.000	502	174
Emotions	72	0.422	593	6
Enron	1001	0.442	1702	53
Genbase	1186	0.048	662	27

Table 4: Characteristics of the multi-label benchmark datasets: showing the number of features, label diversity, instances, and labels)

Panel of Figure 6 — Figure 6: Fold division used in the experiments.

	DTECC	MEECC	MVECC	STACKECC	UDDTECC
Dataset
3sources_bbc1000	0.1497(4.5)	0.1526(3.0)	0.1547(2.0)	0.2852(1.0)	0.1497(4.5)
3sources_guardian1000	0.0778(3.5)	0.0790(2.0)	0.0773(5.0)	0.2243(1.0)	0.0778(3.5)
3sources_inter3000	0.0059(4.0)	0.0088(2.0)	0.0059(4.0)	0.1538(1.0)	0.0059(4.0)
CAL500	0.2186(3.0)	0.2210(2.0)	0.2212(1.0)	0.1991(5.0)	0.2175(4.0)
Emotions	0.5329(1.0)	0.5322(2.0)	0.5301(4.0)	0.5141(5.0)	0.5307(3.0)

Table 5: Results for Accuracy for the ECC using all the fusion schemes and data sets.

	DTECC	MEECC	MVECC	STACKECC	UDDTECC
Dataset
3sources_bbc1000	0.1640(4.5)	0.1669(3.0)	0.1699(2.0)	0.3618(1.0)	0.1640(4.5)
3sources_guardian1000	0.0859(3.5)	0.0866(2.0)	0.0854(5.0)	0.3053(1.0)	0.0859(3.5)
3sources_inter3000	0.0078(4.0)	0.0098(2.0)	0.0078(4.0)	0.2238(1.0)	0.0078(4.0)
CAL500	0.3447(3.0)	0.3477(2.0)	0.3483(1.0)	0.3217(5.0)	0.3428(4.0)
Emotions	0.6295(1.0)	0.6278(3.0)	0.6270(4.0)	0.6175(5.0)	0.6279(2.0)

Table 6: Results for F-Measure for the ECC using all the fusion schemes and data sets.

	DTECC	MEECC	MVECC	STACKECC	UDDTECC
Dataset
3sources_bbc1000	0.1133(4.0)	0.1162(2.5)	0.1162(2.5)	0.0996(5.0)	0.1786(1.0)
3sources_guardian1000	0.0562(3.5)	0.0596(2.0)	0.0562(3.5)	0.0528(5.0)	0.1423(1.0)
3sources_inter3000	0.0000(4.5)	0.0059(2.5)	0.0000(4.5)	0.0059(2.5)	0.0180(1.0)
CAL500	0.0000(3.0)	0.0000(3.0)	0.0000(3.0)	0.0000(3.0)	0.0000(3.0)
Emotions	0.2327(2.0)	0.2361(1.0)	0.2310(4.0)	0.1940(5.0)	0.2326(3.0)

Table 7: Results for Subset Accuracy for the ECC using all the fusion schemes and data sets.

	DTECC	MEECC	MVECC	STACKECC	UDDTECC
Dataset
3sources_bbc1000	0.2174(2.5)	0.2155(1.0)	0.2179(4.0)	0.3433(5.0)	0.2174(2.5)
3sources_guardian1000	0.2037(2.0)	0.2037(2.0)	0.2059(4.0)	0.4411(5.0)	0.2037(2.0)
3sources_inter3000	0.2011(3.0)	0.2001(1.0)	0.2011(3.0)	0.4643(5.0)	0.2011(3.0)
CAL500	0.2909(4.0)	0.2855(1.0)	0.2892(2.0)	0.3737(5.0)	0.2899(3.0)
Emotions	0.2459(2.0)	0.2454(1.0)	0.2468(3.5)	0.2684(5.0)	0.2468(3.5)

Table 8: Results for Hamming Loss for the ECC using all the fusion schemes and data sets.

	Accuracy	F-measure	Hamming	Subset
Learner			Loss	Accuracy
DTECC	3.250000	3.187500	3.500000	2.781250
UDDTECC	1.952381	2.125000	2.343750	2.500000
MEECC	2.860000	3.125000	2.437500	2.406250
MVECC	2.600000	2.687500	2.781250	3.156250
STACKECC	3.565217	3.875000	3.937500	4.156250

Table 9: Average rank of the ECC methods using the evaluated fusion schemes for all datasets.

Panel of Figure 7 — Figure 7: Critical difference (CD) diagram comparing all methods across evaluation metrics.

	Accuracy	F-measure	Hamming	Subset
Learner			Loss	Accuracy
DTECC	3.250000	2.958333	2.500000	3.333333
UDDTECC	1.952381	1.750000	2.041667	2.083333
MEECC	2.860000	3.250000	2.625000	2.583333
MVECC	2.600000	3.125000	3.625000	3.083333
STACKECC	3.565217	3.916667	4.208333	3.916667

Table 10: Average rank of the ECC methods using the evaluated fusion schemes for higher diversity datasets.

Panel of Figure 8 — Figure 8: Critical difference (CD) diagrams for comparing the average of the methods evaluated in the 12 data sets with the highest diversity. The diagram shows average ranks (left axis) with connecting lines indicating groups of methods not significantly different at $\alpha=0.1$ (Bonferroni-Dunn test). Lower ranks indicate better performance. The critical difference threshold (right axis) determines the minimum rank difference required for statistical significance.

Metric	EBR	UDDTEBR
F-measure	1.85	1.15
Accuracy	1.75	1.25
Subset Accuracy	1.65	1.35
Hamming Loss	1.65	1.35

Table 11: Performance comparison between EBR and UDDTEBR

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