High Dimensional Correspondences from Low Dimensional Manifolds - An Empirical Comparison of Graph-Based Dimensionality Reduction Algorithms
نویسندگان
چکیده
Linear methods yield data points xn = r1φn,1 +r ∗ 2φn,2 + . . .+ rMφn,M = R φn, which are d-dimensional linear combinations of the original D-dimensional data points φn. . Principal Component Analysis (PCA, Jolliffe (2002)): Preserves the global covariance structure by decomposition of the covariance matrix Σφ,φ = RS R. . Metric Multidimensional Scaling (MDS, Cox & Cox (1994)): Preserves inner products between data points by decomposing the Gram matrix K nm = φn · φm.
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