Power Transformed Density Ridge Estimation

Hengchao Chen

doi:10.1109/LSP.2025.3549699

Power Transformed Density Ridge Estimation

2025-01-01

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AI

DOI：10.1109/LSP.2025.3549699

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This paper proposes to control ridge estimation with nonlinear transformations. We establish an inclusion relationship between ridges with/without transformations: R(f degrees p) subset of R(p), where R(p) is the d-dimensional ridge of p : R-D -> R and f is a strictly increasing and concave map defined on range(p). This finding reveals the benefit of applying an increasing and concave transformation before ridge estimation. As f(q)(y) = y(q)/q, q <= 1 are increasing and concave on R+, we use these power transformations to positive density functions, and then perform ridge estimation. The algorithm, named power-transformed subspace-constrained mean-shift (PSCMS), outperforms its competitors in numerical experiments.

Keyword:

Estimation

Hafnium

Symmetric matrices

Manifolds

Manifold learning

High dimensional data

Eigenvalues and eigenfunctions

Density functional theory

Vectors

Training

Ridge estimation

increasing and concave transformations

inclusion relationship

power transformations

Power Transformed Density Ridge Estimation

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