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.

翻译：无监督嵌入是众多机器学习应用的基础，然而其评估仍是一项具有挑战性的任务。传统的评估方法通常依赖于外部变量，例如在下游任务中的性能表现，这可能会引入混杂因素并掩盖嵌入的真实质量。本文提出了内在距离保持评估方法，这是一种基于马氏距离在原始空间与嵌入空间之间保持程度来评估嵌入质量的新方法。我们通过一个简单示例展示了外部评估方法的局限性，强调了它们如何导致对嵌入质量的误导性结论。IDPE通过提供一种与任务无关的度量来解决这些问题，该度量反映了嵌入保持原始数据内在结构的程度。我们的方法利用高效的相似性搜索技术，使其适用于大规模数据集。我们将IDPE与既有的内在度量指标（如可信度与连续性）以及外部度量指标（如平均排名与平均倒数排名）进行比较。结果表明，IDPE能在多种场景下提供更全面可靠的嵌入质量评估。我们使用IDPE评估了PCA和t-SNE嵌入，揭示了传统度量方法未能捕捉到的性能特征。本研究的贡献在于为嵌入评估提供了一种鲁棒、高效且可解释的方法。IDPE对内在特性的关注为研究人员和实践者提供了一个有价值的工具，有助于开发和评估适用于多样化机器学习应用的高质量嵌入。