arXiv:2412.15426cs.LG2024-12AAAI被引 15

通过动态调整局部图结构,提升高维数据降维中的聚类分离效果。

Dimension Reduction with Locally Adjusted Graphs

  • 基于局部子图动态重构,实时优化相似性图结构。
  • 在生物数据集上实现更清晰的聚类分离,优于传统方法。
  • 适合需要精准聚类的高维数据分析场景,如单细胞转录组。

降维算法在理解大规模高维数据集方面极为有用,尤其在识别转录组数据中的簇方面表现突出。这类方法的初始阶段通常将原始高维数据转换为图,其中每条边代表数据点之间的相似性或相异性。然而,由于高维距离不可靠以及从高维数据中提取的信息有限,该图常不理想,且随着数据集规模增大问题加剧。若通过选择嵌入特定区域的点来缩小数据集,所提取的子图更可靠,降维后观察到的簇也更易分离。本文提出LocalMAP,一种新型降维算法,通过动态且局部地调整图结构以应对这一挑战。它能够实时提取子图并更新图结构,从而识别并分离其他降维方法可能忽略或合并的真实簇。通过生物数据集的案例研究,验证了LocalMAP在帮助用户更准确识别真实世界问题中的聚类方面的有效性。

原文摘要 · Abstract (English)

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often involves converting the original high-dimensional data into a graph. In this graph, each edge represents the similarity or dissimilarity between pairs of data points. However, this graph is frequently suboptimal due to unreliable high-dimensional distances and the limited information extracted from the high-dimensional data. This problem is exacerbated as the dataset size increases. If we reduce the size of the dataset by selecting points for a specific sections of the embeddings, the clusters observed through DR are more separable since the extracted subgraphs are more reliable. In this paper, we introduce LocalMAP, a new dimensionality reduction algorithm that dynamically and locally adjusts the graph to address this challenge. By dynamically extracting subgraphs and updating the graph on-the-fly, LocalMAP is capable of identifying and separating real clusters within the data that other DR methods may overlook or combine. We demonstrate the benefits of LocalMAP through a case study on biological datasets, highlighting its utility in helping users more accurately identify clusters for real-world problems.

降维聚类图学习生物信息学

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