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Neighborhood-Adaptive Generalized Linear Graph Embedding with Latent Pattern Mining

S. Peng, L. Hu, W. Zhang, B. Jie, Y. Luo

TL;DR

This work tackles fixed neighborhood size and reliance on a single latent pattern in graph embedding by proposing Neighborhood-Adaptive Generalized Linear Graph Embedding (NGLGE). NGLGE jointly learns an adaptive graph, a low-rank global representation, and a column-sparse projection via a $\ell_{2,0}$ constraint, solved efficiently with an ADMM-based algorithm. The method demonstrates superior performance across six diverse datasets, highlighting its ability to capture both local and global data structure and to perform effective feature selection. The approach offers practical impact for scalable, interpretable graph embeddings in varied domains such as vision and bioinformatics.

Abstract

Graph embedding has been widely applied in areas such as network analysis, social network mining, recommendation systems, and bioinformatics. However, current graph construction methods often require the prior definition of neighborhood size, limiting the effective revelation of potential structural correlations in the data. Additionally, graph embedding methods using linear projection heavily rely on a singular pattern mining approach, resulting in relative weaknesses in adapting to different scenarios. To address these challenges, we propose a novel model, Neighborhood-Adaptive Generalized Linear Graph Embedding (NGLGE), grounded in latent pattern mining. This model introduces an adaptive graph learning method tailored to the neighborhood, effectively revealing intrinsic data correlations. Simultaneously, leveraging a reconstructed low-rank representation and imposing $\ell_{2,0}$ norm constraint on the projection matrix allows for flexible exploration of additional pattern information. Besides, an efficient iterative solving algorithm is derived for the proposed model. Comparative evaluations on datasets from diverse scenarios demonstrate the superior performance of our model compared to state-of-the-art methods.

Neighborhood-Adaptive Generalized Linear Graph Embedding with Latent Pattern Mining

TL;DR

This work tackles fixed neighborhood size and reliance on a single latent pattern in graph embedding by proposing Neighborhood-Adaptive Generalized Linear Graph Embedding (NGLGE). NGLGE jointly learns an adaptive graph, a low-rank global representation, and a column-sparse projection via a constraint, solved efficiently with an ADMM-based algorithm. The method demonstrates superior performance across six diverse datasets, highlighting its ability to capture both local and global data structure and to perform effective feature selection. The approach offers practical impact for scalable, interpretable graph embeddings in varied domains such as vision and bioinformatics.

Abstract

Graph embedding has been widely applied in areas such as network analysis, social network mining, recommendation systems, and bioinformatics. However, current graph construction methods often require the prior definition of neighborhood size, limiting the effective revelation of potential structural correlations in the data. Additionally, graph embedding methods using linear projection heavily rely on a singular pattern mining approach, resulting in relative weaknesses in adapting to different scenarios. To address these challenges, we propose a novel model, Neighborhood-Adaptive Generalized Linear Graph Embedding (NGLGE), grounded in latent pattern mining. This model introduces an adaptive graph learning method tailored to the neighborhood, effectively revealing intrinsic data correlations. Simultaneously, leveraging a reconstructed low-rank representation and imposing norm constraint on the projection matrix allows for flexible exploration of additional pattern information. Besides, an efficient iterative solving algorithm is derived for the proposed model. Comparative evaluations on datasets from diverse scenarios demonstrate the superior performance of our model compared to state-of-the-art methods.

Paper Structure

This paper contains 18 sections, 2 theorems, 38 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Notations and definitions
  4. Adaptive neighbors learning
  5. Efficient sparse feature selection
  6. Methodology
  7. Proposed method
  8. Optimization
  9. Optimization algorithm for updating $S$
  10. Complexity analyses
  11. Experiments
  12. Databases
  13. Experimental setup
  14. Experiment result and analysis
  15. Parameters sensitivity study
  16. ...and 3 more sections

Key Result

Lemma 1

The sequence $c^t,~t=0,1,\dots$, is nonincreasing.

Figures (4)

  • Figure 1: Recognition rate versus the parameters $\lambda_1$ and $\lambda_2$ on six databases with training samples of 10, 10, 10, 20, 20 and 20 per category respectively.
  • Figure 2: Classification performance (%) versus hyper-paramater $\lambda_3$ on six different databases with 10, 10, 10, 20, 20 and 20 training samples per class, respectively.
  • Figure 3: Recognition rate versus the reduced dimension on six databases with training samples of 10, 10, 10, 20, 20 and 20 per category respectively.
  • Figure 4: Convergence curves of our method on six databases with training samples of 10, 10, 10, 20, 20 and 20 per category respectively.

Theorems & Definitions (2)

  • Lemma 1
  • Theorem 1