Interpretation of Structural Preservation in Low-dimensional Embeddings


In spite of the fact that it is widely used in big-data analytics, the outcome of dimensionality reduction is still a mystery to the vast majority of those who employ it. Understanding the quality of a low-dimensional embedding is important not only because it enables trust in the transformed data, but also because it can help in selecting the most appropriate dimensionality reduction algorithm in a given scenario. This is why it is important to understand the quality of a low-dimensional embedding. Given that the majority of the research that has been done to date has concentrated on the visual exploration of embeddings, there is still a need for improving the interpretability of algorithms of this kind. We propose two novel interactive explanation techniques for low-dimensional embeddings that can be obtained from any dimensionality reduction algorithm. This will help bridge the gap that currently exists. The first method, known as LAPS, produces a local approximation of the neighborhood structure in order to generate interpretable explanations for a single instance based on the locality that has been preserved. The second method, called GAPS, explains the retained global structure of a high-dimensional dataset in its embedding by combining non-redundant local-approximations derived from a coarse discretization of the projection space. This is done in order to reduce the number of projection space discretizations that are required. We use sixteen different real-world datasets, including tabular, text, image, and audio formats, to demonstrate how applicable the proposed techniques are. The extensive experimental evaluation that we conducted demonstrates that the proposed techniques have utility in interpreting the quality of low-dimensional embeddings and in selecting the most appropriate dimensionality reduction algorithm for any given dataset. This utility was demonstrated by the extensive testing that we conducted.

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