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Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
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A Model Selection Approach for Clustering a Multinomial Sequence with Non-Negative Factorization.

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    This study introduces a new model selection criterion for clustering multinomial data, extending existing methods like AIC and BIC to handle sparse observations. The approach ensures consistent estimates for improved data analysis.

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    Area of Science:

    • Statistics
    • Machine Learning
    • Data Mining

    Background:

    • Clustering algorithms are essential for identifying patterns in data.
    • Conventional model selection criteria like AIC and BIC have limitations with sparse multinomial data.
    • Handling varying numbers of trials within clusters complicates analysis.

    Purpose of the Study:

    • To develop a novel model selection criterion for clustering sequences of multinomial observations.
    • To extend existing criteria (AIC, BIC) for applicability to sparse multinomial data with varying trials.
    • To propose a preliminary estimation step using reduced rank projection and non-negative factorization.

    Main Methods:

    • A new penalty term for model selection is proposed.
    • Reduced rank projection combined with non-negative factorization is used for preliminary estimation.
    • Maximum likelihood estimation (MLE) and maximum Lq estimation are considered.
    • Consistency of estimates is demonstrated under simplifying assumptions.

    Main Results:

    • The proposed criterion effectively clusters sparse multinomial observations.
    • The method extends the capabilities of AIC and BIC.
    • Preliminary estimation step yields consistent results.
    • Numerical experiments validate the approach with real and simulated data.

    Conclusions:

    • The developed model selection criterion offers a robust solution for clustering complex multinomial data.
    • The preliminary estimation technique enhances the reliability of clustering results.
    • The approach is validated through empirical studies, showing practical utility.