Manifold learning algorithms have been shown to be useful for many applications of numerical analysis. Unfortunately, existing algorithms often produce noisy results, do not scale well, and are unable to benefit from prior knowledge about the expected results. We propose a new algorithm that iteratively discovers manifolds by preserving the local structure among neighboring data points while scaling down the values in unwanted dimensions. This algorithm produces less noisy results than existing algorithms, and it scales better when the number of data points is much larger than the number of dimensions. Additionally, this algorithm is able to benefit from existing knowledge by operating in a semi-supervised manner.
College and Department
Physical and Mathematical Sciences; Computer Science
BYU ScholarsArchive Citation
Gashler, Michael S., "Manifold Sculpting" (2007). All Theses and Dissertations. 876.
manifold learning, dimensionality reduction, NLDR