MDAM: A Multidimensional Discriminant Analysis-Based Method for Time Series Modality Testing

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In this paper, we introduce a multidimensional discriminant analysis-based method (MDAM), which is a modality testing method designed to determine whether an unknown input multidimensional time series is unimodal or multimodal. Existing unimodality testing methods face several key limitations: (1) they are primarily designed for unidimensional data and struggle with multidimensional extensions, (2) they rely on probability density function (PDF)-based approaches that fail in the presence of overlapping distributions, skewed data, and noise, and (3) they often misinterpret multimodal structures due to misleading PDF-based marginal analysis. To address these challenges, MDAM leverages a novel function that integrates the between-class mean and variance variables using a discriminant analysis approach. This distribution-independent method effectively detects modality variations across both mean and variance parameters, making it well-suited for high-dimensional and complex datasets. Comparative analysis based on synthetic and real datasets revealed that MDAM consistently outperformed five state-of-the-art techniques such as Folding, Runt, KS, DAT, and Dip, across unidimensional, multidimensional, balanced, unbalanced, unimodal, and multimodal datasets. Notably, MDAM achieved a high average accuracy of 99.8% across all dataset types, with a 20% to 40% accuracy improvement over the next-best algorithms in multimodal and mixed distributions. Its robustness across various evaluation metrics, including precision, recall, and F1 score, further establishes MDAM as a reliable tool for modality testing in time series datasets.

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