Algorithms for ridge estimation with convergence guarantees
This work addresses the need for reliable filament extraction in data analysis, offering theoretical assurances for convergence, though it is incremental as it builds upon existing ridge estimation methods.
The paper tackles the problem of extracting filamentary structures from point clouds by modeling them as density ridges, proposing two novel algorithms with asymptotic convergence guarantees to recover the full ridge set, unlike the existing SCMS algorithm which lacks such theoretical support.
The extraction of filamentary structure from a point cloud is discussed. The filaments are modeled as ridge lines or higher dimensional ridges of an underlying density. We propose two novel algorithms, and provide theoretical guarantees for their convergences, by which we mean that the algorithms can asymptotically recover the full ridge set. We consider the new algorithms as alternatives to the Subspace Constrained Mean Shift (SCMS) algorithm for which no such theoretical guarantees are known.