HUMAP: Hierarchical Uniform Manifold Approximation and Projection

Abstract

Fig. 1: Comparison of traditional dimensionality reduction (DR) techniques (A) vs. hierarchical DR techniques (B).Traditional techniques operate in a single level of detail and focus on delivering a big picture that depicts the dataset as a whole, ignoring fine-grained details of intra-cluster distributions and making it difficult to proceed with more detailed investigations. On the other hand, hierarchical DR (HDR) approaches summarize important intra-cluster information already on the top-level representations of the hierarchy imposed on the input data without affecting the layout's overall organization. Our hierarchical approach, called HUMAP, extends HDR techniques state of the art by preserving the mental map when requesting more details of clusters while balancing the trade-off between global and local relations. This characteristic is apparent in the first three layouts for hierarchical DR results (B). For HUMAP, the projected data subsets in different hierarchy levels resemble superior hierarchy levels, while users receive more information about the similarity among clusters. Furthermore, HUMAP also preserves the mental map of different hierarchy levels; that is, the top-level representation (B) resembles the lowest-level representation (C).

Kumap: Kernel Uniform Manifold Approximation and Projection for Out-of-sample Extensions Problem

“…Over the past few years, UMAP has many improvements. Marcilio-Jr et al [30] introduced the Hierarchical UMAP (HUMAP) algorithm, which enables flexible adjustments to preserve both global and local data structures during dimensionality reduction by parameter tuning, adapting to specific needs. Jeon et al [31] proposed the Uniform Manifold Approximation with Two-phase Optimization (UMATO), which divides the projection of high-dimensional data into two stages.…”