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Clustering and embedding using commute times.

Huaijun John Qiu¹, Edwin R Hancock

¹Queen Mary Vision Laboratory, Department of Computer Science, Queen Mary, University of London, London, UK E1 4NS. John@dcs.qmul.ac.uk

IEEE Transactions on Pattern Analysis and Machine Intelligence

|September 13, 2007

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This study introduces commute time, derived from random walks on graphs, as a robust measure for data proximity. Applications include superior image segmentation and advanced multi-body motion tracking.

Area of Science:

Graph Theory
Computer Vision
Machine Learning

Background:

Commute time, based on random walks and graph Laplacians, offers a robust data proximity measure.
Existing methods like normalized cut can be improved for image segmentation and motion tracking.

Purpose of the Study:

To leverage graph commute time for enhanced data clustering and embedding.
To develop novel applications in image segmentation and multi-body motion tracking.

Main Methods:

Utilizing the lazy random walk and graph Laplacian spectrum to compute commute time via the discrete Green's function.
Developing an image segmentation method using the commute time matrix's smallest eigenvalue eigenvector.
Creating a robust multi-body motion tracking embedding that preserves commute time, similar to kernel PCA and diffusion maps.

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Main Results:

The commute time segmentation method enhances intra-group coherence and reduces inter-group coherence, outperforming normalized cut.
The commute time embedding demonstrates effectiveness in multi-body motion tracking on synthetic and real-world data.
Commute time proves to be a more reliable proximity measure than raw proximity matrices.

Conclusions:

Graph commute time is a powerful tool for data analysis, offering improvements in clustering, embedding, image segmentation, and motion tracking.
This approach provides a robust and effective alternative to existing methods in computer vision and machine learning.