Curvature based Sparse Manifold Learning

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The idea of manifold learning is to treat data distribution via the high-dimensional embedding of the manifold graphs, in the face of mass unstructured data. The core of it is to restore its low-dimensional structure, aiming to realize the efficient and accurate data analysis results; namely, the evaluation of the algorithm improves efficiency as much as possible while ensuring the accuracy of certain data analysis. By studying the dimensionality reduction algorithm that is based on local feature mapping, we find out that there is still an improvement space for algorithm complexity in the known algorithm, and also notice that there are some connections and differences between the local neighborhood and the Euclidean space. Therefore, based on the improvement of Laplacian Eigenmap algorithm, the thesis proposes a new neighborhood partition method, and the concept of curvature is introduced in the feature description of local neighborhood. The improved algorithm (CSLEP) reduces the computational cost of redundant local neighborhoods. Meanwhile, it achieves a more accurate mapping mode of local neighborhood features.