提出轻量级嵌入质量评估方法CMET，高效衡量降维后数据结构保留程度。
CMET: Clustering guided METric for quantifying embedding quality
- 基于聚类引导设计，分层评估局部与全局结构保留度。
- 在合成、生物、图像等多类数据上优于现有方法，稳定可靠。
- 低复杂度、适配大小数据，适合模型优化与可视化分析场景。
随着技术快速发展，各领域数据日益丰富。为开展更相关和合适的分析，常需将数据投影到高维或低维空间：高维投影有助于揭示复杂模式并提升模型性能；而降维可实现去噪、保留最大信息量、降低计算开销。然而，变换后的嵌入是否保持原始数据的局部与全局结构，往往难以统计判断。现有评估指标在时间与空间复杂度上成本高昂。为此，本文提出一种新型嵌入质量度量方法——聚类引导度量（Clustering guided METric, CMET），包含局部（CMET_L）与全局（CMET_G）两个得分，用于定量比较嵌入与原始数据的结构一致性。该方法在四类合成数据、两类生物数据及两类图像数据上验证，表现优于当前最优方法。CMET具备处理大小数据的能力、低算法复杂度，且在各类数据及超参数设置下均表现出色，是可靠的嵌入质量评估工具。
原文摘要 · Abstract (English)
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.
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