Distributed density support approximation and topology-preserving dimensionality reduction.
碩士 === 國立東華大學 === 應用數學系 === 103 === This work explores topology-preserving dimensionality reduction based on novel distributed density support approximation. Given training data are assumed as a sample from a d-dimensional density support. Under the assumption, the underlying density suppo...
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2015
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| Online Access: | http://ndltd.ncl.edu.tw/handle/00226405468659469146 |
| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 103 === This work explores topology-preserving dimensionality reduction based on novel distributed density support approximation. Given training data are assumed as a sample from a d-dimensional density support. Under the assumption, the underlying density support is approximated by the union of distributed regular supports, respectively centered at local means of clusters derived by the novel annealed K-means algorithm. Distances and neighboring relations of centers of regular local supports are defined. A mapping for topology preserving dimensionality reduction is stated as a task of seeking images of local means on a plane that reserve distances of the original high dimensional space as well as possible. Distances inside density support are determined by the Dijkstra's shortest path algorithm based on neighboring relations of centers of distributed local supports. A nonlinear system for optimal planar images of centers of local supports is presented and resolved by the LM (Levenberg–Marquardt) method. The proposed approach effective and reliable is shown effective and reliable by numerical simulations.
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