Data Dimensionality

Data dimensionality, the number of features or variables describing a dataset, significantly impacts the performance and efficiency of machine learning and data analysis techniques. Current research focuses on mitigating the "curse of dimensionality"—the exponential increase in computational cost and data requirements with increasing dimensionality—through methods like dimensionality reduction (PCA, t-SNE, UMAP), the development of algorithms specifically designed for high-dimensional spaces (e.g., modified nearest neighbor classifiers, Separable DeepONets), and exploiting inherent data structures such as low-dimensional manifolds or compositional functions. Addressing dimensionality challenges is crucial for advancing various fields, including machine learning, signal processing, and scientific computing, enabling the analysis of complex, high-dimensional data in applications ranging from medical imaging to climate modeling.