Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Clustering Method with Graph Maximum Decoding Information

Xinrun Xu, Manying Lv, Zhanbiao Lian, Yurong Wu, Jin Yan, Shan Jiang, Zhiming Ding

TL;DR

This work introduces CMDI, a graph-based clustering framework that maximizes decoding information by combining two-dimensional structural information theory with graph structure extraction and vertex partitioning. It formalizes one- and two-dimensional structural entropies, and defines decoding information as their difference, using a greedy DI-Maximized approximating optimal partition (GDIMAOP) to partition graphs, optionally enhanced by prior knowledge (PK) in CMDI-PK. Empirical results on synthetic and real-world geospatial datasets show CMDI and CMDI-PK achieving higher decoding information ratios (DI-R) and faster convergence than baselines, with maximum-likelihood-based structure extraction and proximity-metric choices guiding graph reconstruction. The approach offers a principled, information-theoretic pathway to robust graph-based clustering, with practical impact in domains requiring reliable discovery of natural data associations and efficient clustering under uncertainty.

Abstract

The clustering method based on graph models has garnered increased attention for its widespread applicability across various knowledge domains. Its adaptability to integrate seamlessly with other relevant applications endows the graph model-based clustering analysis with the ability to robustly extract "natural associations" or "graph structures" within datasets, facilitating the modelling of relationships between data points. Despite its efficacy, the current clustering method utilizing the graph-based model overlooks the uncertainty associated with random walk access between nodes and the embedded structural information in the data. To address this gap, we present a novel Clustering method for Maximizing Decoding Information within graph-based models, named CMDI. CMDI innovatively incorporates two-dimensional structural information theory into the clustering process, consisting of two phases: graph structure extraction and graph vertex partitioning. Within CMDI, graph partitioning is reformulated as an abstract clustering problem, leveraging maximum decoding information to minimize uncertainty associated with random visits to vertices. Empirical evaluations on three real-world datasets demonstrate that CMDI outperforms classical baseline methods, exhibiting a superior decoding information ratio (DI-R). Furthermore, CMDI showcases heightened efficiency, particularly when considering prior knowledge (PK). These findings underscore the effectiveness of CMDI in enhancing decoding information quality and computational efficiency, positioning it as a valuable tool in graph-based clustering analyses.

A Clustering Method with Graph Maximum Decoding Information

TL;DR

This work introduces CMDI, a graph-based clustering framework that maximizes decoding information by combining two-dimensional structural information theory with graph structure extraction and vertex partitioning. It formalizes one- and two-dimensional structural entropies, and defines decoding information as their difference, using a greedy DI-Maximized approximating optimal partition (GDIMAOP) to partition graphs, optionally enhanced by prior knowledge (PK) in CMDI-PK. Empirical results on synthetic and real-world geospatial datasets show CMDI and CMDI-PK achieving higher decoding information ratios (DI-R) and faster convergence than baselines, with maximum-likelihood-based structure extraction and proximity-metric choices guiding graph reconstruction. The approach offers a principled, information-theoretic pathway to robust graph-based clustering, with practical impact in domains requiring reliable discovery of natural data associations and efficient clustering under uncertainty.

Abstract

The clustering method based on graph models has garnered increased attention for its widespread applicability across various knowledge domains. Its adaptability to integrate seamlessly with other relevant applications endows the graph model-based clustering analysis with the ability to robustly extract "natural associations" or "graph structures" within datasets, facilitating the modelling of relationships between data points. Despite its efficacy, the current clustering method utilizing the graph-based model overlooks the uncertainty associated with random walk access between nodes and the embedded structural information in the data. To address this gap, we present a novel Clustering method for Maximizing Decoding Information within graph-based models, named CMDI. CMDI innovatively incorporates two-dimensional structural information theory into the clustering process, consisting of two phases: graph structure extraction and graph vertex partitioning. Within CMDI, graph partitioning is reformulated as an abstract clustering problem, leveraging maximum decoding information to minimize uncertainty associated with random visits to vertices. Empirical evaluations on three real-world datasets demonstrate that CMDI outperforms classical baseline methods, exhibiting a superior decoding information ratio (DI-R). Furthermore, CMDI showcases heightened efficiency, particularly when considering prior knowledge (PK). These findings underscore the effectiveness of CMDI in enhancing decoding information quality and computational efficiency, positioning it as a valuable tool in graph-based clustering analyses.
Paper Structure (16 sections, 2 theorems, 14 equations, 9 figures, 3 tables, 3 algorithms)

This paper contains 16 sections, 2 theorems, 14 equations, 9 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Structural Information And Decoding Information
  3. Essential Definitions
  4. Statements on Decoding Information
  5. Extracting Structure
  6. Extracting Structure Based on Mutual Information
  7. Extracting Structure via Maximum Likelihood Estimation
  8. Extracting Structure Based on Proximity Metrics
  9. CMDI: Clustering Algorithm for Maximum Decoding Information
  10. Experiment Evaluation
  11. Experimental Settings
  12. HIM Distance and DI in the Synthetic Dataset
  13. HIM Distance and DI of the Extracted Graph Based on Different Proximity Metrics
  14. Decoding Information Quantities of GDIMAOP with Different PKs
  15. CMDI Performance on Geo-data (BJ_Busstop and BJ_Parking)
  16. ...and 1 more sections

Key Result

Theorem 1

For node sets $V_i$ and $V_j$ ( $V_i\subset V$, $V_j\subset V$, $V_i\cap V_j=\varnothing$ ), if there is no edge between $V_i$ and $V_j$, $\Delta_{(i, j)}^{p}(G) \geq 0$ is satisfied.

Figures (9)

  • Figure 1: Workflow for partitioning graph based on the greedy DI-Maximized approximating optimal partition (GDIMAOP) with prior knowledge (PK).
  • Figure 2: Illustration of the three different graphs used in the present paper. a. Ring of clique graph with six cliques. b. Grids graph. c. Scale-free graph with Barabasi-Albert model.
  • Figure 3: Workflow for generating synthetic time-series data from a given graph topology. Initially, we select a graph of interest and then build the graph adjacency matrix $A$ whose elements are zeros (based on the ground truth graph, the link of the graph is neglected). Next, the Kinetic Ising model (KIM) is used to simulate the dynamical process of the graph, and then the synthetic time-series data $X$ is generated and the graph reconstruction method is taken to extract the graph structure (the structure reconstruction algorithms: ESMBMI and ESMBMLE). Finally, the graph distance is used to evaluate the similarity between the ground-truth graph and extracted graph.
  • Figure 4: Comparison of HIM-Distances.
  • Figure 5: Comparison of DI.
  • ...and 4 more figures

Theorems & Definitions (7)

  • Definition 1: One-dimensional structural information (ODSI).
  • Definition 2: Two-dimensional structural information (TDSI).
  • Definition 3: Optimal two-dimensional structural information (OTDSI).
  • Definition 4: Decoding information (DI).
  • Theorem 1
  • proof : Proof of Theorem \ref{['th:01']}
  • Theorem 2