arXiv:2510.02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis. The standard approach, Local Principal Component Analysis (LPCA), struggles in high-noise setting due to a critical trade-off in choosing the neighborhood size. Selecting an optimal size requires prior knowledge of the geometric and noise characteristics of the data that are often unavailable. In this paper, we propose a spectral method, Laplacian Eigenvector Gradient Orthogonalization (LEGO), that utilizes the global structure of the data to
This research provides an algorithmic improvement for fundamental geometric data analysis, a core component for advancing various AI applications, published ahead of wider machine learning conferences.
Improved tangent space estimation is crucial for more robust and efficient machine learning models, particularly in high-noise environments, leading to more reliable AI systems.
The proposed LEGO method offers a more resilient way to analyze complex data geometries compared to standard LPCA, potentially enhancing the performance of AI algorithms dealing with noisy, high-dimensional data.
- · AI researchers
- · Data scientists
- · Machine learning startups
- · Industries with noisy data
- · Legacy LPCA-dependent methods
- · Models reliant on perfectly clean data
More accurate and robust manifold learning across diverse datasets.
Accelerated development of AI models requiring precise geometric understanding of data.
Potentially enables new AI applications in fields previously hampered by data noise and complexity.
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Read at arXiv cs.LG