Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation
While diffusion models enable new approaches for estimating Local Intrinsic Dimension (LID), existing methods fail in high-dimensional spaces where noise from vast normal directions overwhelms the tangent signal. We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension $D$. Experiments on synthetic and real data confirm LHSD's superior robustness and its utility i...
| Authors | Genki Osada |
|---|---|
| Primary category | cs.LG |
| Published | 2 May 2026 |
| Last updated at source | 22 June 2026 |
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