Dimension Reduction with Locally Adjusted Graphs

• URL: http://arxiv.org/abs/2412.15426v1
• Date: Thu, 19 Dec 2024 22:21:39 GMT
• Title: Dimension Reduction with Locally Adjusted Graphs
• Authors: Yingfan Wang, Yiyang Sun, Haiyang Huang, Cynthia Rudin,
• Abstract summary: LocalMAP is a dimensionality reduction algorithm that dynamically and locally adjusts the graph to address this challenge. We demonstrate the benefits of LocalMAP through a case study on biological datasets.
• Score: 20.06041784058165
• License:
• Abstract: 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.

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