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    Statistical analysis reveals Nonnegative Matrix Factorization (NMF) and k-means clustering perform similarly on gene expression data, outperforming spectral clustering. Gaussian Mixture Models (GMM) show superior performance, suggesting data follows Gaussian distributions.

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    Area of Science:

    • Bioinformatics
    • Computational Biology
    • Machine Learning

    Background:

    • Clustering algorithms like Nonnegative Matrix Factorization (NMF), spectral clustering, k-means, and Gaussian Mixture Models (GMM) are widely used for analyzing microarray gene expression data.
    • Limited statistical analysis exists to rigorously compare the performance differences between these unsupervised learning methods in this domain.

    Purpose of the Study:

    • To conduct a statistical analysis comparing the performance of NMF, spectral clustering, GMM, and k-means algorithms.
    • To evaluate these algorithms on eleven publicly available microarray gene expression datasets.
    • To determine the significance of performance differences across various cluster numbers (2-10).

    Main Methods:

    • Implementation and evaluation of ten NMF variations, six spectral clustering algorithms, four GMM approaches, and standard k-means.
    • Clustering of eleven diverse microarray gene expression datasets.
    • Statistical analysis to assess performance differences and multidimensional scaling for visual inspection of data structures.

    Main Results:

    • Nonnegative Matrix Factorization (NMF) and k-means demonstrated statistically similar performance, outperforming spectral clustering.
    • Visual inspection via multidimensional scaling plots suggested a lack of manifold structures in the datasets.
    • Gaussian Mixture Models (GMM) exhibited superior performance, indicating that the gene expression datasets likely follow Gaussian distributions, evidenced by elliptical cluster boundaries.

    Conclusions:

    • NMF and k-means are robust choices for gene expression clustering, while spectral clustering may be less suitable due to the absence of manifold structures.
    • The superior performance of GMM suggests that gene expression data often adheres to Gaussian distributions.
    • Further research could explore tailored algorithms for non-Gaussian or complex data structures in transcriptomics.