CMET: Clustering guided METric for quantifying embedding quality

2025-07-07

AI Summary

This paper addresses the challenge of efficiently quantifying the preservation of both local and global structures in embedding quality assessment. We propose CMET, a lightweight dual-scale metric featuring a clustering-guided mechanism: CMET_L measures local structure preservation based on neighborhood consistency, while CMET_G evaluates global structure preservation using hierarchical clustering results—jointly achieving substantial reductions in time and space complexity. CMET exhibits high stability, strong robustness to noise, and broad adaptability across diverse data types and embedding methods, enabling rapid evaluation on datasets of varying scales. Extensive experiments on four synthetic, two biological, and two image datasets demonstrate that CMET consistently outperforms state-of-the-art baselines, with particularly notable advantages in scalability and noise robustness.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Due to rapid advancements in technology, datasets are available from various domains. In order to carry out more relevant and appropriate analysis, it is often necessary to project the dataset into a higher or lower dimensional space based on requirement. Projecting the data in a higher-dimensional space helps in unfolding intricate patterns, enhancing the performance of the underlying models. On the other hand, dimensionality reduction is helpful in denoising data while capturing maximal information, as well as reducing execution time and memory.In this context, it is not always statistically evident whether the transformed embedding retains the local and global structure of the original data. Most of the existing metrics that are used for comparing the local and global shape of the embedding against the original one are highly expensive in terms of time and space complexity. In order to address this issue, the objective of this study is to formulate a novel metric, called Clustering guided METric (CMET), for quantifying embedding quality. It is effective to serve the purpose of quantitative comparison between an embedding and the original data. CMET consists of two scores, viz., CMET_L and CMET_G, that measure the degree of local and global shape preservation capability, respectively. The efficacy of CMET has been demonstrated on a wide variety of datasets, including four synthetic, two biological, and two image datasets. Results reflect the favorable performance of CMET against the state-of-the-art methods. Capability to handle both small and large data, low algorithmic complexity, better and stable performance across all kinds of data, and different choices of hyper-parameters feature CMET as a reliable metric.

Problem

• Quantify embedding quality for dimensionality transformations
• Compare local and global structure preservation in embeddings
• Develop efficient metric (CMET) with low complexity

Innovation

• Introduces CMET for embedding quality assessment
• Combines local and global structure metrics
• Low complexity, handles diverse datasets effectively