Hybrid Topic-Semantic Labeling and Graph Embeddings for Unsupervised Legal Document Clustering

Deepak Bastola; Woohyeok Choi

stat.MLAug 31, 2025

Hybrid Topic-Semantic Labeling and Graph Embeddings for Unsupervised Legal Document Clustering

Authors: Deepak Bastola, Woohyeok Choi

Organizations: Department of Mathematical Sciences, Salisbury University · Department of Mathematics and Statistics, Carleton College

Abstract

Legal documents pose substantial challenges for unsupervised knowledge discovery due to specialized domain terminology, multi-scale document lengths, and scarce expert annotations. This paper introduces Topic-Graph Spherical Fusion (TGSF), a dual-manifold representation learning framework for unsupervised legal document clustering that unifies dense topic-semantic discovery and relational graph embeddings on a joint unit hypersphere. Instantiating dense topic discovery via Top2Vec and biased second-order random walks via Node2Vec, TGSF constructs a connected multi-relational document-topic graph combining multi-topic centroid bridges with temperature-sharpened semantic k-Nearest Neighbor (k-NN) document edges, guaranteeing a single connected component. The resulting L2-normalized semantic and graph representations are fused via modality-weighted concatenation onto a joint unit hypersphere prior to KMeans partitioning, decomposing squared chordal distance into a convex combination of semantic and structural cosine similarities. Evaluations across three legal benchmarks (ACORD, CUAD, and LEDGAR) show that TGSF outperforms semantic-only, structural-only, Latent Dirichlet Allocation (LDA), Non-Negative Matrix Factorization (NMF), and TF-IDF baselines. Across 216 factorial grid configurations and 240 Bayesian TPE and Multi-Objective NSGA-II Pareto optimization trials per dataset (720 trials total), TGSF improves Normalized Mutual Information (NMI) from 0.606 to 0.653 on LEDGAR (ARI = 0.425), 0.228 to 0.284 on ACORD (ARI = 0.260), and 0.535 to 0.570 on CUAD (ARI = 0.282). Functional ANOVA and Pareto frontier diagnostics further characterize hyperparameter sensitivity for reproducible legal text mining.

Figures & tables

Figure 1: Architectural overview of the proposed Topic-Graph Spherical Fusion (TGSF) framework (integrating Top2Vec, connected multi-relational graph

G

, second-order Node2Vec, and unit-hypersphere

L_{2}

fusion) alongside lexical (TF-IDF + KMeans), probabilistic/matrix-factorization (LDA, NMF), and unimodal semantic (

\alpha=0

) and structural (

\alpha=1

) baselines across LEDGAR, ACORD, and CUAD.

Figure 2: Topological and spectral comparison between (a) a single-topic bipartite graph (

E_{DT}

only,

M=1

), which decomposes into

T

disconnected star subgraphs (

\dim\ker(\mathcal{L})=T

), and (b) the TGSF multi-relational graph

G=(V_{D}\cup V_{T},E_{DT}\cup E_{DD},W)

, which integrates multi-topic bridges (dashed orange) and cosine-weighted semantic

k

-NN document–document edges (solid blue) to form a connected manifold (

\dim\ker(\mathcal{L})=1

Benchmark	Legal Text Granularity	Documents ( $N$ )	Discovered Topics ( $T$ )	Eval. Clusters ( $K$ )	Source Repository
LEDGAR ( Tuggener et al., 2020 )	Functional Contract Provisions	$4,000$	$73$	$28$	SEC EDGAR / LexGLUE
ACORD ( Wang et al., 2025 )	Retrieval Clauses & Queries	$2,227$	$25$	$7$	Atticus Project
CUAD ( Hendrycks et al., 2021 )	Full Commercial Agreements	$407$	$10$	$20$	SEC EDGAR / Atticus

Table 1: Summary Characteristics of the Three Legal Benchmark Corpora.

Figure 3: Cluster size distributions produced by TGSF across (a) LEDGAR (

N=4,000,K=28

), (b) ACORD (

N=2,227,K=7

), and (c) CUAD (

N=407,K=20

), ordered by cluster rank with dashed horizontal lines indicating the mean cluster size.

Panel of Figure 4 — Figure 4: 3D UMAP manifold projections for baseline (a) NMF and (b) LDA topic models on the ACORD corpus ( $N=2,227,K=10$ ), annotated with cluster centroid markers (T1–T10) and top representative lexical terms.

Panel of Figure 5 — Figure 5: Two- and three-dimensional UMAP manifold projections of the TGSF embeddings across LEDGAR ( $N=4,000,K=28$ ), ACORD ( $N=2,227,K=7$ ), and CUAD ( $N=407,K=20$ ). Centroid labels in the 2D projections mark the median coordinates of each cluster.

Figure 6: 2D UMAP projection of CUAD commercial contract clusters (

N=407,K=20

) generated by TGSF, annotated with the dominant ground-truth SEC contract category for the largest clusters.

Dataset	Model Configuration	Silhouette ( $\uparrow$ )	DBI ( $\downarrow$ )	CHS ( $\uparrow$ )	NMI ( $\uparrow$ )	ARI ( $\uparrow$ )
LEDGAR ( $N=4,000,K=28$ )	TF-IDF + KMeans	0.085	4.564	25.9	0.523	0.213
	LDA ( $K=28$ )	0.594	1.138	601.0	0.567	0.331
	NMF ( $K=28$ )	0.336	1.041	439.4	0.509	0.176
	Top2Vec Only (Semantic, $\alpha=0$ )	0.117	3.063	61.2	0.553	0.324
	Node2Vec Only (Structural $G$ , $\alpha=1$ )	0.271	2.015	110.5	0.593	0.356
	TGSF (Grid Search, MiniLM, $\alpha=0.5$ )	0.203	2.421	88.1	0.606	0.395

Table 2: Multi-Dataset Benchmark Comparison Across LEDGAR (

N=4,000,K=28

), ACORD (

N=2,227,K=7

), and CUAD (

N=407,K=20

) on the Connected Graph

G=(V_{D}\cup V_{T},E_{DT}\cup E_{DD},W)

. Best external validation scores per dataset are highlighted in bold.

Figure 7: Cross-dataset comparison of (a) Normalized Mutual Information (NMI), (b) Adjusted Rand Index (ARI), and (c) Cosine Silhouette Score across TF-IDF + KMeans, Top2Vec Only (Semantic,

\alpha=0

), Node2Vec Only (Structural,

\alpha=1

), TGSF (Grid,

\alpha=0.5

), and TGSF (Bayesian HPO) on LEDGAR, ACORD, and CUAD.

Dataset	Statistic	NMI	ARI	Silhouette	DBI	CHS
LEDGAR ( $N=4,000,K=28$ )	Mean $\pm$ SD	$0.579\pm 0.011$	$0.340\pm 0.016$	$0.191\pm 0.019$	$2.471\pm 0.125$	$78.6\pm 6.7$
	Min – Max	$0.546\text{ -- }0.606$	$0.297\text{ -- }0.395$	$0.156\text{ -- }0.235$	$2.248\text{ -- }2.847$	$66.3\text{ -- }96.6$
	Optimal Config	$k_{\text{NN}}=10,\;M=1,\;d_{\text{graph}}=32,\;R=40,\;L=15$
ACORD ( $N=2,227,K=7$ )	Mean $\pm$ SD	$0.198\pm 0.011$	$0.078\pm 0.015$	$0.151\pm 0.017$	$3.189\pm 0.263$	$99.8\pm 11.4$
	Min – Max	$0.165\text{ -- }0.228$	$0.036\text{ -- }0.115$	$0.114\text{ -- }0.190$	$2.627\text{ -- }4.005$	$75.4\text{ -- }129.5$
	Optimal Config	$k_{\text{NN}}=15,\;M=3,\;d_{\text{graph}}=64,\;R=10,\;L=30$

Table 3: Distributional Stability of TGSF Across the 216-Configuration Hyperparameter Grid Search (

k_{\text{NN}}\in\{2,5,10,15\}

M\in\{1,2,3\}

d_{\text{graph}}\in\{32,64,128\}

R\in\{10,20,40\}

L\in\{15,30\}

Panel of Figure 8 — Figure 8: Hyperparameter sensitivity heatmaps illustrating the interaction between semantic neighborhood size ( $k_{\text{NN}}\in\{2,5,10,15\}$ ) and Node2Vec embedding dimensionality ( $d_{\text{graph}}\in\{32,64,128\}$ ) across (a) LEDGAR, (b) ACORD, and (c) CUAD.

Panel of Figure 9 — Figure 9: Multi-dataset sensitivity analysis of TGSF across cluster counts $K\in\{5,8,10,12,15,20,25,28,30\}$ for (a) LEDGAR, (b) ACORD, and (c) CUAD, with vertical dashed markers indicating the optimal $K^{*}$ for each metric.

Figure 10: Representational saturation analysis showing (a) Davies–Bouldin Index (lower is better) and (b) Cosine Silhouette Score (higher is better) versus number of clusters

K

across corpus subsampling fractions (

50\%\text{--}100\%

). Subsets

\geq 70\%

(solid lines) closely track the full corpus trajectory.

Dataset	HPO Statistic / Optimal Regime	NMI ( $\uparrow$ )	ARI ( $\uparrow$ )	Silhouette ( $\uparrow$ )	DBI ( $\downarrow$ )	CHS ( $\uparrow$ )
LEDGAR ( $N=4,000,K=28$ )	216-Grid Best (MiniLM, $\alpha=0.5$ )	$0.606$	$0.395$	$0.203$	$2.421$	$88.1$
	Bayesian HPO Best (Trial #131)	$\mathbf{0.653}$	$0.422$	$0.316$	$1.916$	$137.2$
	Max-ARI Trial (Trial #50)	$0.649$	$\mathbf{0.425}$	$\mathbf{0.326}$	$\mathbf{1.894}$	$\mathbf{141.5}$
	240-Trial Mean $\pm$ SD	$0.618\pm 0.035$	$0.372\pm 0.052$	$0.293\pm 0.072$	$1.988\pm 0.358$	$139.4\pm 38.9$
	240-Trial Min – Max	$0.493\text{ -- }0.653$	$0.216\text{ -- }0.425$	$0.061\text{ -- }0.472$	$1.327\text{ -- }3.665$	$44.0\text{ -- }433.3$
	Optimal Hyperparameters ( $\boldsymbol{\theta}^{*}$ )	Legal-BERT, $T=15,k_{\text{NN}}=16,M=5,\tau=0.055,\gamma=0.33,\beta=1.45,d_{\text{graph}}=64,L=15,R=45,p=0.65,q=0.74,w=10,\alpha=0.83$

Table 4: Summary of the 720-Trial GPU-Accelerated Bayesian Multivariate TPE and Multi-Objective NSGA-II Pareto Optimization (

240\text{ Trials/Dataset}=180\text{ TPE}+60\text{ NSGA-II}

) for TGSF Across LEDGAR, ACORD, and CUAD.

Panel of Figure 11 — Figure 11: Comprehensive diagnostics of the 720-trial GPU-accelerated Bayesian TPE and Multi-Objective NSGA-II Pareto optimization across (a–c) LEDGAR ( $N=4,000,K=28$ ), ACORD ( $N=2,227,K=7$ ), and CUAD ( $N=407,K=20$ ).

Dataset	Model Configuration	Silhouette ( $\uparrow$ )	CHS ( $\uparrow$ )	DBI ( $\downarrow$ )	NMI ( $\uparrow$ )	ARI ( $\uparrow$ )
LEDGAR ( $N=4,000,K=28$ )	TF-IDF + KMeans (Lexical Baseline)	0.085	25.9	4.564	0.523	0.213
	Top2Vec + KMeans (Semantic-Only, $\alpha=0$ )	0.117	61.2	3.063	0.553	0.324
	Node2Vec + KMeans (Structural-Only, $\alpha=1$ )	0.271	110.5	2.015	0.593	0.356
	TGSF (Balanced Spherical Fusion, $\alpha=0.5$ )	0.203	88.1	2.421	0.606	0.395
	TGSF (Bayesian HPO Spherical Fusion, $\alpha=0.83$ )	0.316	137.2	1.916	0.653	0.422
ACORD ( $N=2,227,K=7$ )	TF-IDF + KMeans (Lexical Baseline)	0.045	26.6	5.084	0.173	0.145

Table 5: Ablation Study Isolating Lexical, Semantic-Only (

\alpha=0

), Structural-Only (

\alpha=1

), Balanced Spherical Fusion (

\alpha=0.5

), and Bayesian HPO Components of TGSF Across LEDGAR, ACORD, and CUAD.

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