Weight-Informed Self-Explaining Clustering for Mixed-Type Tabular Data

Lehao Li; Qiang Huang; Yihao Ang; Bryan Kian Hsiang Low; Anthony K. H. Tung; Xiaokui Xiao

cs.LGApr 7, 2026

Weight-Informed Self-Explaining Clustering for Mixed-Type Tabular Data

Authors: Lehao Li, Qiang Huang, Yihao Ang, Bryan Kian Hsiang Low, Anthony K. H. Tung, Xiaokui Xiao

Organizations: School of Computing, National University of Singapore, Singapore · School of Intelligence Science and Engineering, Harbin Institute of Technology (Shenzhen), China

Abstract

Clustering mixed-type tabular data is fundamental for exploratory analysis, yet remains challenging due to misaligned numerical-categorical representations, uneven and context-dependent feature relevance, and disconnected and post-hoc explanation from the clustering process. We propose WISE, a Weight-Informed Self-Explaining framework that unifies representation, feature weighting, clustering, and interpretation in a fully unsupervised and transparent pipeline. WISE introduces Binary Encoding with Padding (BEP) to align heterogeneous features in a unified sparse space, a Leave-One-Feature-Out (LOFO) strategy to sense multiple high-quality and diverse feature-weighting views, and a two-stage weight-aware clustering procedure to aggregate alternative semantic partitions. To ensure intrinsic interpretability, we further develop Discriminative FreqItems (DFI), which yields feature-level explanations that are consistent from instances to clusters with an additive decomposition guarantee. Extensive experiments on six real-world datasets demonstrate that WISE consistently outperforms classical and neural baselines in clustering quality while remaining efficient, and produces faithful, human-interpretable explanations grounded in the same primitives that drive clustering.

Figures & tables

Figure 1: Overview of WISE . It consists of four modules: Module 1 converts mixed-type tabular data into a unified representation using Binary Encoding with Padding (BEP); Module 2 senses and selects diverse feature-weight vectors via a Leave-One-Feature-Out (LOFO) strategy; Module 3 aggregates multiple weighted views through a two-stage, weight-informed clustering procedure; Finally, Module 4 produces intrinsic and consistent explanations at both the cluster and instance levels using Discriminative FreqItems (DFI).

Figure 2: An illustrative example of the BEP scheme.

Dataset	Method	ARI $\uparrow$	NMI $\uparrow$	Purity $\uparrow$	ACC $\uparrow$	SWC $\uparrow$
Adult	k-Proto	0.259	0.266	0.616	0.475	0.146
	IDC	0.010	0.052	0.446	0.380	-0.042
	TableDC	0.359	0.412	0.682	0.454	0.116
	TELL	0.049	0.109	0.479	0.248	0.094
	SAINT	0.023	0.014	0.422	0.313	-0.002
	WISE	0.663	0.515	0.671	0.633	0.165

Table 1: Clustering quality of all methods. Bold and underlined denote the best and second-best results, respectively.

Method	ARI	NMI	Purity	ACC	SWC
k-Proto	2.67	3.00	2.92	2.67	3.00
IDC	5.67	4.83	5.25	5.00	5.33
TableDC	3.33	3.17	3.25	3.08	1.67
TELL	4.33	4.00	3.58	4.83	4.00
SAINT	4.00	4.67	4.42	4.33	5.33
WISE	1.00	1.33	1.58	1.08	1.67

Table 2: Average rank (

\downarrow

) across datasets. For each dataset and metric, methods are ranked from 1 (best) to 6 (worst); ties are resolved by assigning the average of the tied ranks.

Figure 3: Pairwise ARI comparisons between WISE and each baseline.

Figure 4: Clustering efficiency of all methods on each dataset, measured on the same hardware and software stack. Reported times (seconds; log scale) include the complete clustering pipeline, covering preprocessing, representation learning (if any), and clustering.

Figure 5: Ablation study of WISE evaluating modules 2 and 3.

Figure 6: Runtime breakdown of WISE across its four modules.

Panel of Figure 7 — Figure 7: Case Study on Adult.

Panel of Figure 8 — Figure 8: Case Study on GeoNames.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	# Samples	# Dimensions	# Num. Features	# Cat. Features	Ground-Truth Feature	# Classes
Adult	45,222	14	6	8	Relationship	6
Vermont	129,816	48	8	40	INCWAGE	4
Arizona	203,353	50	8	42	INCWAGE	4
Obesity	2,111	16	8	8	Obesity Level	7
Credit	690	15	6	9	A16-class attribute	2
GeoNames	500,000	11	5	6	Feature Class	10

Appendix

Table 3: The statistics of six real-world mixed-type tabular datasets.

Evaluation Facet	Metric	Computation
External Agreement	ARI ( Hubert and Arabie, 1985 )	Computed on non-noise set
	NMI ( Vinh et al., 2009 )	Computed on non-noise set
	Purity ( Manning et al., 2008 )	Computed on non-noise set
	ACC ( Kuhn, 1955 )	Computed on non-noise set
Intrinsic Structural Quality	SWC ( Rousseeuw, 1987 )	Calculated using unweighted Gower’s distance ( Gower, 1971 )
Computational Efficiency	Time	Total wall-clock time (Seconds)

Appendix

Table 4: Evaluation metrics for clustering quality and efficiency.

Dataset	Candidate grid of $K$
Adult	$\{4,5,6,7,8\}$
Obesity	$\{2,\dots,10,15,20\}$
Credit	$\{1,2,3,4,5,6\}$
Vermont	$\{2,\dots,10,15,20,25,30\}$
Arizona	$\{2,\dots,10,15,20,25,30\}$
GeoNames	$\{5,\dots,15,20,25,30\}$

Appendix

Table 5: Shared candidate grids of

K

used in the controlled cluster-recovery protocol.

Dataset	$B$	$T$	Stage I Clustering: $(k_{0},\alpha_{0},\beta_{0})$	Stage II Clustering: $(K,\alpha)$
Adult	32	30	$k_{0}{=}15,\ \alpha_{0}{=}0.4,\ \beta_{0}{=}0.9$	$K{=}5,\ \alpha{=}0.4$
Vermont	64	30	$k_{0}{=}10,\ \alpha_{0}{=}0.4,\ \beta_{0}{=}0.4$	$K{=}4,\ \alpha{=}0.4$
Arizona	64	30	$k_{0}{=}5,\ \alpha_{0}{=}0.7,\ \beta_{0}{=}0.6$	$K{=}6,\ \alpha{=}0.5$
Obesity	32	30	$k_{0}{=}25,\ \alpha_{0}{=}0.4,\ \beta_{0}{=}0.4$	$K{=}5,\ \alpha{=}0.7$
Credit	32	10	$k_{0}{=}5,\ \alpha_{0}{=}0.2,\ \beta_{0}{=}0.1$	$K{=}2,\ \alpha{=}0.2$
GeoNames	64	30	$k_{0}{=}50,\ \alpha_{0}{=}0.2,\ \beta_{0}{=}0.2$	$K{=}9,\ \alpha{=}0.2$

Appendix

Table 6: Dataset-specific hyperparameter settings for WISE .

B

is the number of bits assigned to each column in BEP. LOFO weight sensing uses

T

trees (shared defaults:

m{=}3

; Q-D balance

\lambda_{\mathrm{QD}}{=}0.5

; max_depth

=20

; min_samples_leaf

=50

; train_sample_frac

=0.1

). Clustering Stage I runs

k

-FreqItems on BEP with

(k_{0},\alpha_{0},\beta_{0})

; Stage II refines in record space with

(K,\alpha)

Dataset	Method	Key Hyperparameters / Settings
Adult	k-Proto	$k{=}5,\ \gamma{=}0.06$ (better than nominal $k{=}6$ )
	IDC	epochs $=800$ ; start_global_gates_training_on_epoch $=400$ ; encoding: TE
	TableDC	AE dim $=64$ ; mode: ER; num_clusters $=6$
	TELL	num_clusters $=6$
	SAINT	$k{=}6$
Vermont	k-Proto	$k{=}4,\ \gamma{=}0.107$

Appendix

Table 7: Key hyperparameters for baselines (others use official defaults). Abbreviations: OH = one-hot encoding; TE = target encoding; AE = auto-encoding; ER = entity-resolution mode.

Panel of Figure 9 — Figure 9: Pairwise comparisons between WISE and each baseline under remaining four metrics.

Feature subset	#Features	Accuracy	Macro-F1
All features	14	0.988	0.986
Top-3 DFI	3	0.984	0.980
Top-5 DFI	5	0.988	0.986
Top-10 DFI	10	0.988	0.986
Random-3	3	0.536	0.300
Random-5	5	0.660	0.494

Appendix

Table 8: Quantitative evaluation of DFI faithfulness.

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