Interpretation of Structural Preservation in Low-Dimensional Embeddings

• Published in: IEEE transactions on knowledge and data engineering Vol. 34; no. 5; pp. 2227 - 2240
• Main Authors: Ghosh, Aindrila, Nashaat, Mona, Miller, James, Quader, Shaikh
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; algorithms for data and knowledge management; Approximation algorithms; Bridges; data and knowledge visualization; Data visualization; Datasets; Dimensionality reduction; Embedding; Interactive data exploration and discovery; Manifolds; Optimization; Reduction; Visualization
• ISSN: 1041-4347; 1558-2191
• DOI: 10.1109/TKDE.2020.3005878

Despite being commonly used in big-data analytics; the outcome of dimensionality reduction remains a black-box to most of its users. Understanding the quality of a low-dimensional embedding is important as not only it enables trust in the transformed data, but it can also help to select the most appropriate dimensionality reduction algorithm in a given scenario. As existing research primarily focuses on the visual exploration of embeddings, there is still a need for enhancing interpretability of such algorithms. To bridge this gap, we propose two novel interactive explanation techniques for low-dimensional embeddings obtained from any dimensionality reduction algorithm. The first technique LAPS produces a local approximation of the neighborhood structure to generate interpretable explanations on the preserved locality for a single instance. The second method GAPS explains the retained global structure of a high-dimensional dataset in its embedding, by combining non-redundant local-approximations from a coarse discretization of the projection space. We demonstrate the applicability of the proposed techniques using 16 real-life tabular, text, image, and audio datasets. Our extensive experimental evaluation shows the utility of the proposed techniques in interpreting the quality of low-dimensional embeddings, as well as with selecting the most suitable dimensionality reduction algorithm for any given dataset.