Beyond PCA: Manifold Dimension Estimation via Local Graph Structure

arXiv — cs.LGTuesday, November 4, 2025 at 5:00:00 AM

Beyond PCA: Manifold Dimension Estimation via Local Graph Structure

A new framework for manifold dimension estimation has been proposed, which enhances traditional local principal component analysis by incorporating adjustments for curvature. This approach aims to improve the accuracy of estimating the intrinsic dimensions of complex data structures, addressing limitations in existing methods. By leveraging local graph structures, the framework provides a more nuanced understanding of manifold geometry. The enhancement over local PCA is designed to capture subtle variations in data that standard techniques might overlook. As a result, this method offers promising potential for applications requiring precise dimension estimation in high-dimensional datasets. The proposal, detailed in a recent arXiv publication, contributes to ongoing research in machine learning and data analysis. Overall, this development represents a positive step toward more accurate and reliable manifold dimension estimation.

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