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The characteristics of data like distribution and heterogeneity, become morecomplex and counterintuitive as the dimensionality increases. This phenomenonis known as curse of dimensionality, where common patterns and relationships(e.g., internal and boundary pattern) that hold in low-dimensional space may beinvalid in higher-dimensional space. It leads to a decreasing performance forthe regression, classification or clustering models or algorithms. Curse ofdimensionality can be attributed to many causes. In this paper, we firstsummarize five challenges associated with manipulating high-dimensional data,and explains the potential causes for the failure of regression, classificationor clustering tasks. Subsequently, we delve into two major causes of the curseof dimensionality, distance concentration and manifold effect, by performingtheoretical and empirical analyses. The results demonstrate that nearestneighbor search (NNS) using three typical distance measurements, Minkowskidistance, Chebyshev distance, and cosine distance, becomes meaningless as thedimensionality increases. Meanwhile, the data incorporates more redundantfeatures, and the variance contribution of principal component analysis (PCA)is skewed towards a few dimensions. By interpreting the causes of the curse ofdimensionality, we can better understand the limitations of current models andalgorithms, and drive to improve the performance of data analysis and machinelearning tasks in high-dimensional space.

Interpreting the Curse of Dimensionality from Distance Concentration and Manifold Effect