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Large Graph Clustering With Simultaneous Spectral Embedding and Discretization.

Zhen Wang, Zhaoqing Li, Rong Wang

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |August 6, 2020
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    Summary
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    This study introduces a novel spectral clustering method for graphs, simultaneously optimizing embedding and rotation. The new approach enhances accuracy and significantly reduces computation time for complex graph data.

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    Area of Science:

    • Computer Science
    • Data Science
    • Machine Learning

    Background:

    • Spectral clustering methods are widely used but face challenges with global optimality and high computational complexity, especially for graph data represented by similarity matrices.
    • Existing methods often address these issues in separate stages (spectral embedding and spectral rotation), potentially compromising overall performance.
    • Complexity reduction techniques have been developed for data vectors but not extensively for graph similarity matrices.

    Purpose of the Study:

    • To address the limitations of traditional spectral clustering methods in graph analysis.
    • To develop a unified framework that performs spectral embedding and spectral rotation concurrently.
    • To improve both the accuracy and computational efficiency of spectral clustering algorithms for graph data.

    Main Methods:

    • A novel objective function integrating both embedding and rotation terms was designed.
    • An improved spectral rotation technique was employed for mathematical rigor in optimization.
    • Label propagation was utilized to derive a low-dimensional graph representation, enabling reconstruction of a double-stochastic and positive semidefinite similarity matrix.

    Main Results:

    • The proposed method successfully integrates spectral embedding and rotation into a single optimization framework.
    • Experimental results show significant improvements in both time cost and clustering accuracy compared to existing methods.
    • The derived low-dimensional representation aids in reconstructing an effective similarity matrix for accelerated processing.

    Conclusions:

    • The new spectral clustering method offers a more efficient and accurate solution for graph clustering problems.
    • Simultaneous optimization of embedding and rotation is a viable strategy to overcome limitations of sequential approaches.
    • The use of label propagation for matrix reconstruction presents a promising direction for accelerating spectral graph algorithms.