Sparse multi-way DMDC for longitudinal classification in high dimension low sample size data

Recent advances in data registration techniques have enabled researchers to analyze high-dimensional, low sample size (HDLSS) data, which poses challenges for traditional statistical and machine learning methods-especially in fields like neurodevelopmental disorder classification. Among various proposed solutions, the Data Maximum Dispersion Classifier (DMDC) has demonstrated superior performance. This study introduces two extensions: Sparse DMDC (SDMDC) and Longitudinal Sparse DMDC (LSDMDC), with the latter leveraging multi-way data frameworks. Simulated HDLSS datasets were generated from multivariate normal distributions with sparse structures. Evaluation of SDMDC involved varying class imbalance, predictor count, and correlation structures. Performance was measured via average F-measure and signal-to-noise ratio (SNR). Results showed that SDMDC outperformed other sparse models. Moreover, promising improvement was observed in model classification performance and the selection of effective predictors when the correlation between predictor variables was increased. In longitudinal simulations, LSDMDC maintained performance even as the number of predictors increased along the first dimension, effectively handling rank-1 and rank-2 data. Notably, LSDMDC achieved the best results under autoregressive correlation. In conclusion, SDMDC demonstrated clear advantages over other sparse classifiers, while LSDMDC proved highly effective for complex longitudinal structures.