Examinando por Materia "Third and fourth moments"

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    On a Combination of Skewness and Kurtosis Matrices for Pro jection Pursuit Exploratory Cluster Analysis
    (Universidad EAFIT, 2025) Jaramillo Osorio, Esteban; Ortiz Arias, Santiago
    Skewness and kurtosis are statistical measures critical for understanding distribu- tion characteristics, particularly in normality testing, clustering, and outlier detec- tion. While kurtosis has been widely explored in the literature, skewness remains un- derutilized despite its potential for identifying asymmetrical patterns in data. Com- bining these measures could create a robust tool for exploratory data analysis (EDA). This research proposes a novel approach by developing a convex combination of skew- ness and kurtosis matrices. Using iterative procedures to maximize or minimize this combination, we aim to construct a matrix serving as a projection index for a projec- tion pursuit algorithm. This matrix can identify clusters and outliers more effectively than either measure alone. To validate the methodology, experiments on artificial datasets and real-world data demonstrate the benefits of this combined approach in detecting non-normal features, evaluating clustering performance, and enhancing outlier detection.