Hierarchical Clustering of Knowledge Graphs

• The paper introduces hierarchical clustering methods that structure knowledge graphs, capturing multi-granular semantics and overlapping relationships.
• It employs advanced methodologies like formal concept analysis and neural architectures to improve scalability, precision, and zero-shot learning in graph analysis.
• These techniques enable ontology induction, semantic search, and explainable recommendations, addressing practical challenges such as noise handling and computation.

Hierarchical clusterings of knowledge graphs are methodologies and algorithmic frameworks for extracting, structuring, and analyzing multi-level groupings of entities, facts, or subgraphs within knowledge graphs, often to reflect taxonomic, semantic, relational, or data-driven hierarchies. These techniques serve foundational roles in organizing knowledge, supporting reasoning, and enabling downstream applications such as entity typing, link prediction, relational inference, and large-scale search and recommendation. Hierarchical clusterings differ from flat clustering by explicitly modeling relationships between clusters—such as subset, superset, or partial overlap—often accommodating both strict trees and more general partial orders or lattices. Below, recent research advances are synthesized across theoretical innovations, algorithmic constructions, evaluation strategies, applications, and open challenges, with reference to representative work across the field.

1. Foundational Principles and Motivations

Hierarchical clustering in the context of knowledge graphs seeks to organize entities, types, or relational patterns into nested or overlapping structures that capture both granularity and generalization. Unlike flat clustering—where each item belongs to a single group—hierarchical methods represent multi-level groupings, typically using trees, directed acyclic graphs, or lattices, with nodes corresponding to clusters and edges representing inclusion or inheritance. This provides several key advantages:

• Multi-granular representation: Enables both coarse and fine semantic distinctions, as in ontology induction or multi-label taxonomies (Yoneda et al., 2018, Mohamed, 2019, Pietrasik et al., 2021).
• Discovery of latent structure: Identifies not just clusters but the inter-relationships among clusters, which is vital for semantic search, navigation, and reasoning (Sarrafzadeh et al., 2020, Chen et al., 2021).
• Faithfulness to real-world semantics: Many real-world domains, especially those modeled as knowledge graphs (e.g., biology, linguistics, academic research), have inherently hierarchical or multi-relational organization (Zheng et al., 2022, Li et al., 7 Feb 2024).

Traditional approaches include agglomerative and divisive hierarchical clustering, formal concept analysis, taxonomy induction, and blockmodels; recent advances incorporate neural architectures, hyperbolic geometries, and probabilistic generative models for scalability and expressiveness.

2. Algorithmic Frameworks and Methodologies

Hierarchical clusterings in knowledge graphs are realized through a diverse array of methods, with several representative approaches outlined below:

a. Formal Concept Analysis (FCA):

The method in (Yoneda et al., 2018) converts multivariate numerical data into binary nearest-neighbor transactions before applying FCA to extract a concept lattice. Each node is a cluster defined by closure over data points and shared attributes, and directed edges encode subset–superset (covering) relations. The resulting structure forms a directed acyclic graph or Hasse diagram, accommodating rich overlapping clusters uncommon in classical binary trees.

b. Unsupervised Grouping by Overlap:

In (Mohamed, 2019), entities are first grouped by shared predicate-object relations (“LiveIn_Europe” as a group), then hierarchical relationships between groups are inferred by measuring set containment using similarity metrics such as the hub promoted index (HPI). Groups are connected hierarchically if one is (nearly) entirely contained within another, with robust handling of noise and high parallelizability.

c. Path-based Taxonomy Induction:

(Pietrasik et al., 2021) extends earlier taxonomy induction with a path-based, tag similarity-driven methodology. Triples are transformed into subject–tag pairs, co-occurrence statistics inform the construction of a tag hierarchy (with explicit decay factors for ancestor influence), and a Jaccard coefficient-based assignment maps subjects to the hierarchy. This process can be parallelized and tuned for various notions of semantic generality.

d. Neural and Deep Generative Approaches:

Layered neural architectures, such as deep belief networks (DBNs) with stacked restricted Boltzmann machines (Murphy, 2019), decompose the entity–attribute structure of a knowledge graph into hierarchical layers, each modeling a branching or bifurcation. Each layer captures statistical dependencies at its level, and the entire model reproduces the (approximate) equilibrium distribution of the original relational data.

e. Probabilistic Blockmodels:

Stochastic blockmodels, particularly their nonparametric hierarchical variants incorporating Nested Chinese Restaurant and Stick-Breaking processes (Pietrasik et al., 28 Aug 2024), allow the induction of cluster hierarchies without explicit constraints on their number or arrangement. Gibbs sampling or similar inference schemes are used for parameter learning and posterior estimation.

f. Graph Neural Networks with Hierarchical Signals:

Hierarchical or multiscale GCNs (Lipov et al., 2020) use a clustering pre-step (e.g., Girvan–Newman) to segment the graph at multiple granularities. Each hierarchical segment informs a separate GCN branch, and concatenated latent representations across scales are fed to prediction or classification heads, capturing both local and global structure.

g. Integration with LLMs and Knowledge-Augmented Prompts:

Emergent techniques (Zang et al., 8 May 2025, Sharma et al., 11 Apr 2024) combine retrieval-augmented generation with explicit graph-based prompts. Subgraphs—extracted based on similarity to the input and hierarchical consistency—are formatted in a structured prompt (e.g., with “A → B” relationships) and provided to LLMs, improving zero-shot classification or clustering across hierarchical taxonomies.

3. Structural Properties: Overlap, Partial Orders, and Multi-Scale Representation

Hierarchical clusterings in knowledge graphs are not restricted to strict tree structures; they often support richer relationships:

• Overlap: FCA-based methods (Yoneda et al., 2018) and grouping-by-overlap (Mohamed, 2019) explicitly permit clusters to share elements, forming lattices and DAGs rather than trees.
• Partial Orders: Clusters are related via subset or superset relations, and the hierarchical structure may include cycles or multiple parentage (as in DAG taxonomies).
• Multi-scale Representation: The output may encode the clustering at several levels of granularity, with dendrograms (as in Girvan–Newman (Lipov et al., 2020)) or multiple abstraction levels (entity–triplet–context in HiRe (Wu et al., 2022)), supporting both low- and high-resolution analysis.
• Semantic Hierarchies in Embeddings: Methods leveraging hyperbolic geometry (Zheng et al., 2022, Sohn et al., 2022) encode levels by radial distance from the origin, allowing continuous and scalable modeling of tree-like semantic hierarchies.

Hierarchical structures can be visualized using Hasse diagrams, central-concept minimaps, or tree overlays on graph networks to support both exploration and computational reasoning (Sarrafzadeh et al., 2020).

4. Empirical Evaluation and Comparative Results

Evaluation of hierarchical clusterings is conducted with both internal consistency metrics and task-oriented measures:

• Dendrogram Purity: As in (Yoneda et al., 2018), the dendrogram purity metric assesses the correspondence between the lowest common ancestor clusters and known ground-truth classes, favoring methods that create pure, meaningful splits.
• Assignment Scores: Path-based clustering methods (Pietrasik et al., 2021) compute Hie-F₁ (hierarchy accuracy), Sub-F₁ (subject assignment), and Tag-F₁ (tag/cluster purity), showing that the method captures both structural and associational accuracy.
• Robustness and Noise Handling: Group overlap (Mohamed, 2019) and multiscale neural methods (Lipov et al., 2020) demonstrate that hierarchical methods are robust to noise, sparse data, and parameter settings—provided thresholds or parameters like group size, similarity cutoff, or decay factors are tuned.
• Scalability: Efficient parallelization and design (e.g., parallel group assignment (Mohamed, 2019), shot-based and cyclical generation (Sharma et al., 11 Apr 2024)) make these approaches amenable to large KGs, with coverage increases (up to 99% in domain hierarchies (Sharma et al., 11 Apr 2024)) and sublinear runtime for certain metrics (Kapralov et al., 2022).
• Task Performance: Integration into LLMs boosts zero-shot classification accuracy, especially at deeper hierarchy levels (Zang et al., 8 May 2025), and hierarchical clustering improves performance in event extraction (Huang et al., 2020), recommendation systems (Sharma et al., 11 Apr 2024), and few-shot learning (Wu et al., 2022).

5. Practical Applications in Knowledge Graphs

Hierarchical clusterings underpin a variety of real-world and research-critical tasks:

• Schema and Ontology Induction: Leveraged for discovering type hierarchies, semantic classes, and relational abstractions in open-world KGs (Mohamed, 2019, Pietrasik et al., 2021).
• Exploratory Search and Recommendation: HKGs (Sarrafzadeh et al., 2020, Li et al., 7 Feb 2024) offer combined overview/detail navigation and explainable recommendation paths, particularly in academic survey, enterprise, and content platforms.
• Zero-shot and Few-shot Learning: Integration with LLMs via KG-HTC (Zang et al., 8 May 2025) and hierarchical meta-representation models (HiRe (Wu et al., 2022)) enables effective classification and completion with very limited supervision, especially important in long-tailed or rapidly evolving domains.
• Semantic Search and Disambiguation: Overlapping and multi-scale structures improve entity disambiguation, retrieval, question answering, and detection of semantic anomalies (Sarrafzadeh et al., 2020, Huang et al., 2020, Chen et al., 2021).
• Multimodal Narrative Understanding: Hierarchical KGs, combined with semantic normalization and embedding-based clustering, enable robust reasoning in image–text narratives as evidenced in Manga109 evaluations (Chen, 20 Aug 2025).

6. Limitations, Open Questions, and Future Directions

While hierarchical clustering frameworks exhibit considerable utility, several challenges persist:

• Parameter Sensitivity and Scalability: Setting parameters such as similarity thresholds, group size, neighbor count (k), decay factors (α), and clustering depth remains crucial, often requiring dataset-specific tuning (Yoneda et al., 2018, Pietrasik et al., 2021, Mohamed, 2019).
• Explosion of Clusters: Methods generating overlapping clusters or operating in the lattice setting can yield massive numbers of clusters, necessitating robust pruning and summarization schemes.
• Computation and Storage: Enumerating closed itemsets or sampling from nonparametric models can be computationally intensive; future work is needed for large-scale, efficient inference and approximation (Yoneda et al., 2018, Pietrasik et al., 28 Aug 2024).
• Quality Evaluation: Internal and extrinsic evaluation strategies sometimes yield conflicting signals (e.g., high assignment F₁ but lower hierarchy match (Pietrasik et al., 2021)); benchmarking on downstream tasks is necessary for holistic assessment.
• Integration with Neural Models: While neural and hybrid approaches (GCNs, transformers, message-passing networks) show promise, their full potential for interpretability and hierarchy alignment remains under active investigation (Sharma et al., 11 Apr 2024, Sohn et al., 2022).
• Dynamic, Temporal, and Mixed-Curvature Hierarchies: Time-sensitive models and dynamic curvature settings (e.g., HyperVC (Sohn et al., 2022)) are needed for evolving KGs, while mixed-mode embeddings offer flexibility for heterogeneous graphs.

Ongoing research explores scalable inference schemes for probabilistic blockmodels (Pietrasik et al., 28 Aug 2024), context-sensitive hierarchical meta-learning (Wu et al., 2022), and advanced semantic normalization for robust multimodal graph reasoning (Chen, 20 Aug 2025).

7. Significance and Synthesis

Hierarchical clusterings of knowledge graphs are central in facilitating high-fidelity, interpretable, and scalable organization of relational data. They underlie advances in automatic ontology construction, semantic enrichment for LLM-driven systems, explainable search and recommendation, few-shot relational inference, event and narrative understanding, and efficient evaluation of large graph structures. The diversity in mathematical frameworks—lattices, trees, DAGs, hyperbolic spaces, blockmodels, neural and probabilistic models—reflects the field’s attention to both theoretical rigor and real-world adaptability. Future directions will likely deepen the integration of structured and neural representations, further automate cluster quality assessment, and extend hierarchical modeling to dynamic, heterogeneous, and multimodal knowledge sources.