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Traditional manifold learning algorithms, such as Locally Linear Embedding, Isomap and Laplacian Eigenmap, only provide the embedding results of training samples. Although many extensions of these approaches try to solve the out-of-sample extension problem, their computations cannot avoid eigen-decomposition of dense matrices which is expensive in both time and memory. To solve this problem, spectral...
Traditional nonlinear dimensionality reduction methods, such as multiple kernel dimensionality reduction and nonlinear spectral regression (SR), are generally regarded as extended versions of linear discriminant analysis (LDA) in the supervised case. As is well known, LDA has the restrictive assumption that the data of each class is of a Gaussian distribution. Thus, the performance of these methods...
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