Computational geometry algorithms for high-dimensional clustering analysis

In the field of scientific and engineering applications, as well as biomedical and artificial intelligence applications, high-dimensional clustering analysis is very important in order to extract meaningful patterns from the complex data sets.Clustering methods, such as the traditional ones, have the problem of curse of dimensionality, resulting in low clustering accuracy and low computational efficiency.In this study we propose a geometric distance measure-based framework for high dimensional clustering analysis, that combines geometric distance measure, partitioning strategies for the space, optimization of the nearest neighbor computation and efficient indexing techniques.The proposed mathematical model is based on the geometric transformation and multidimensional search algorithm, which helps to enhance the cluster formation and lower the complexity of calculation.Neighborhood representation using Voronoi and indexing using tree techniques speeds up similarity search, and improves scalability in large data sets.Through numerical evaluation the accuracy of the clustering, execution time, and geometric consistency have been shown to be improved in comparison to conventional methods.The framework offers a mathematically sound, efficient and scalable analysis solution for high dimensional data in a variety of computational and data-driven applications.