Effective representation of data is crucial in various machine learning tasks, as it captures the underlying structure and context of the data. Embeddings have emerged as a powerful technique for data representation, but evaluating their quality and capacity to preserve structural and contextual information remains a challenge. In this paper, we address this need by proposing a method to measure the \textit{representation capacity} of embeddings. The motivation behind this work stems from the importance of understanding the strengths and limitations of embeddings, enabling researchers and practitioners to make informed decisions in selecting appropriate embedding models for their specific applications. By combining extrinsic evaluation methods, such as classification and clustering, with t-SNE-based neighborhood analysis, such as neighborhood agreement and trustworthiness, we provide a comprehensive assessment of the representation capacity. Additionally, the use of optimization techniques (bayesian optimization) for weight optimization (for classification, clustering, neighborhood agreement, and trustworthiness) ensures an objective and data-driven approach in selecting the optimal combination of metrics. The proposed method not only contributes to advancing the field of embedding evaluation but also empowers researchers and practitioners with a quantitative measure to assess the effectiveness of embeddings in capturing structural and contextual information. For the evaluation, we use $3$ real-world biological sequence (proteins and nucleotide) datasets and performed representation capacity analysis of $4$ embedding methods from the literature, namely Spike2Vec, Spaced $k$-mers, PWM2Vec, and AutoEncoder.

翻译：数据的高效表示在各类机器学习任务中至关重要，因其能够捕捉数据的潜在结构与上下文。嵌入技术已成为数据表示的强大工具，但评估其质量及保持结构与上下文信息的能力仍是一项挑战。本文针对此需求，提出一种衡量嵌入表示能力的方法。该研究动机源于理解嵌入优势与局限的重要性，使研究人员和实践者能够针对特定应用明智地选择嵌入模型。通过结合分类与聚类等外部评估方法，以及基于t-SNE的邻域分析（如邻域一致性与可信度），我们提供了对表示能力的全面评估。此外，采用优化技术（贝叶斯优化）对权重进行优化（针对分类、聚类、邻域一致性与可信度），确保了选择最佳指标组合时的客观性与数据驱动性。所提方法不仅推进了嵌入评估领域的发展，还为研究人员和实践者提供了一种量化手段，以评估嵌入在捕捉结构与上下文信息方面的有效性。在评估中，我们使用了3个真实世界的生物序列（蛋白质与核苷酸）数据集，并对文献中的4种嵌入方法（即Spike2Vec、Spaced k-mers、PWM2Vec和AutoEncoder）进行了表示能力分析。