Titlebook: Geometric Structure of High-Dimensional Data and Dimensionality Reduction; Jianzhong Wang Book 2012 Higher Education Press, Beijing and Sp

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Geometric Structure of High-Dimensional Datahe data geometry is inherited from the manifold. Since the underlying manifold is hidden, it is hard to know its geometry by the classical manifold calculus. The data graph is a useful tool to reveal the data geometry. To construct a data graph, we first find the neighborhood system on the data, whi

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Data Models and Structures of Kernels of DRrs, which represent the objects of interest. In the second type, the data describe the similarities (or dissimilarities) of objects that cannot be digitized or hidden. The output of a DR processing with an input of the first type is a low-dimensional data set, having the same cardinality as the inpu

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Random Projectionus norm of the matrix of data difference. The reduced data of PCA consists of several leading eigenvectors of the covariance matrix of the data set. Hence, PCA may not preserve the local separation of the original data. To respect local properties of data in dimensionality reduction (DR), we employ

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