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EM in high-dimensional spaces.

Bruce A Draper, Daniel L Elliott, Jeremy Hayes

    IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
    |June 24, 2005
    PubMed
    Summary
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    This study presents a new algorithm for fitting Gaussian mixture models to high-dimensional data, even with fewer samples than features. The method models distributions in the data

    Area of Science:

    • Machine Learning
    • Statistical Modeling
    • Data Analysis

    Background:

    • Fitting Gaussian mixture models to high-dimensional data is challenging, especially when sample size is less than feature dimensionality.
    • Existing methods using Principal Component Analysis (PCA) within Expectation-Maximization (EM) algorithms face limitations in such scenarios.

    Purpose of the Study:

    • To address the limitations of current methods for Gaussian mixture modeling in high-dimensional, low-sample-size settings.
    • To develop a practical and robust algorithm for fitting Gaussian mixture models that overcomes issues with PCA-based dimensionality reduction.

    Main Methods:

    • The proposed algorithm models Gaussian distributions directly within the (N-1)-dimensional space spanned by N data samples.
    • It avoids data compression or explicit low-dimensional model fitting, unlike conventional approaches.

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    Main Results:

    • The developed algorithm demonstrates convergence on datasets where traditional low-dimensional techniques fail.
    • It offers a practical solution for mixture of Gaussians fitting in challenging high-dimensional regimes.

    Conclusions:

    • The novel approach provides a more effective method for Gaussian mixture modeling in high-dimensional, low-sample-size data.
    • This algorithm offers improved performance and convergence properties compared to existing techniques.