Основные понятия
HUMAP is a novel hierarchical dimensionality reduction technique that effectively preserves both global and local structures in the low-dimensional representation of high-dimensional datasets, while maintaining the mental map across hierarchy levels.
Аннотация
The paper presents HUMAP, a novel hierarchical dimensionality reduction (HDR) technique that aims to address the limitations of existing HDR methods. HUMAP is based on the UMAP algorithm and creates a hierarchy on the dataset by encoding both global and local similarity information between data points.
The key highlights of HUMAP are:
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Hierarchy Construction:
- Uses a kernel function and Finite Markov Chain to determine the connection strengths and identify the most visited landmarks (representative data points) for higher hierarchy levels.
- Computes the similarity between landmarks based on the intersection of their global and local neighborhoods.
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Projection:
- Incorporates the hierarchy levels in response to user demand for more specific data.
- Maintains the mental map as the user drills down the hierarchy by using projected data points from higher levels to influence the low-dimensional representation of lower hierarchy levels.
The paper provides experimental evidence that HUMAP addresses the key design considerations of HDR techniques - preserving global and local relations, and maintaining the mental map across hierarchy levels. Quantitative evaluations on various datasets show that HUMAP outperforms existing HDR techniques in terms of runtime, neighborhood preservation, and ability to represent complex structures.
A case study on a COVID-19 tweet dataset further demonstrates HUMAP's ability to reveal dominant structures and detailed information about these structures through hierarchical exploration.
Статистика
HUMAP outperforms existing HDR techniques in terms of runtime execution, especially when embedding the whole dataset.
HUMAP maintains the mental map across hierarchy levels, unlike HSNE and Multiscale PHATE.
HUMAP achieves higher DEMaP scores compared to HSNE, UMAP, and GPU-based HSNE, indicating its ability to better represent complex structures such as clusters and manifolds.
When projecting subsets of data, HUMAP consistently outperforms HSNE in terms of DEMaP.
Цитаты
"HUMAP successfully reveals complex structures present in the numerous granularities of a dataset while maintaining the mental map as the user drills down the hierarchy by using projected data points from higher levels to influence the low-dimensional representation of lower hierarchy levels."
"We provide experimental evidence that HUMAP addresses the aforementioned design considerations through visual and quantitative evaluation."