Dual-center RAPID-LSSVM: Radius-adaptive, probability and imbalance driven weighting for Alzheimer's diagnosis

Alzheimer's disease (AD) is a leading neurodegenerative disorder and the primary cause of dementia, where early, reliable diagnosis remains challenging. Although many machine learning methods have been developed for early AD detection, their performance often degrades under label noise, outliers, and class imbalance. To counter these issues, we propose RAPID, a Radius-Adaptive, Probability and Imbalance Driven flexible weighting mechanism, and integrate it into least-squares SVM to obtain two models: RAPID-LSSVM-I (mean-center) and RAPID-LSSVM-II (median-center). RAPID combines three complementary components. First, a radius-adaptive proximity weight that plateaus for samples near the class center and decays smoothly beyond a threshold, preserving the influence of boundary samples while improving robustness to central noise. Second, a local class-probability term that down-weights potentially mislabeled or ambiguous instances, and third, an imbalance-ratio term that compensates for class prior skew. The dual-center design enables either conventional mean centering or a median-based center that is resilient to outliers and asymmetric distributions. To validate the effectiveness of the proposed RAPID-LSSVM models, experiments are conducted on benchmark KEEL and UCI datasets under both clean and label-noise settings. Additionally, we tested the models on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset for AD diagnosis. Empirical findings demonstrate the superiority of the RAPID-LSSVM models over baseline models, highlighting their potential in improving AD diagnosis and handling noisy data.