Density-Preserving Reconstruction and Clustering for High-Dimensional Data: A UMAP-Based Approach with Distribution Alignment

To address the issue of degraded clustering performance caused by the loss of local density information during highdimensional data dimensionality reduction, this paper proposes a density-preserving UMAP reconstruction method (DP-UMAP). This method introduces a density alignment term based on kernel density estimation into the UMAP loss function, constraining the consistency of density distributions between the lowdimensional embedding space and the original high-dimensional space, thereby alleviating density distortion after dimensionality reduction. Subsequently, experiments are conducted on multiple datasets, where DP-UMAP is first applied for dimensionality reduction, followed by the Density Peak Clustering (DPC) algorithm to cluster the reduced-dimensional data. The experimental results demonstrate that, compared to other clustering algorithms, DP-UMAP not only preserves local density structures but also more effectively enhances the clustering performance of DPC. Particularly on high-dimensional complex datasets, DP-UMAP exhibits superior cluster separation and clustering consistency, validating the effectiveness of the proposed method in high-dimensional data dimensionality reduction and clustering tasks.