Dementia, particularly Alzheimer's disease, is a growing global medical and economic problem exacerbated by increasing life expectancy and aging population. This study demonstrates the critical need for efficient data processing methods in biomedical research, focusing on scenarios where the number of observations is smaller than the dimensionality of the data. Based on a dataset of patients with various neurodegenerative diseases including Alzheimer's disease, this paper describes a comprehensive data processing pipeline including dimensionality reduction and clustering. The methodology is based on the combined use of principal component analysis (PCA) and uniform manifold approximation and projection (UMAP) for dimensionality reduction, followed by clustering with optimized parameters. The study demonstrates how these methods can mitigate problems such as data sparsity and the curse of dimensionality, providing a pipeline to gain insights into potential biomarkers for early diagnosis of neurodegenerative diseases. Although this study does not directly interpret clustering results, it lays the groundwork for experts in the field to explore new hypotheses and improve diagnostic tools.