Measuring What Matters: Intrinsic Distance Preservation as a Robust Metric for Embedding Quality

Unsupervised embeddings are fundamental to numerous machine learning applications, yet their evaluation remains a challenging task. Traditional assessment methods often rely on extrinsic variables, such as performance in downstream tasks, which can introduce confounding factors and mask the true quality of embeddings. This paper introduces the Intrinsic Distance Preservation Evaluation (IDPE) method, a novel approach for assessing embedding quality based on the preservation of Mahalanobis distances between data points in the original and embedded spaces. We demonstrate the limitations of extrinsic evaluation methods through a simple example, highlighting how they can lead to misleading conclusions about embedding quality. IDPE addresses these issues by providing a task-independent measure of how well embeddings preserve the intrinsic structure of the original data. Our method leverages efficient similarity search techniques to make it applicable to large-scale datasets. We compare IDPE with established intrinsic metrics like trustworthiness and continuity, as well as extrinsic metrics such as Average Rank and Mean Reciprocal Rank. Our results show that IDPE offers a more comprehensive and reliable assessment of embedding quality across various scenarios. We evaluate PCA and t-SNE embeddings using IDPE, revealing insights into their performance that are not captured by traditional metrics. This work contributes to the field by providing a robust, efficient, and interpretable method for embedding evaluation. IDPE's focus on intrinsic properties offers a valuable tool for researchers and practitioners seeking to develop and assess high-quality embeddings for diverse machine learning applications.