Abstract
Isometric feature mapping (ISOMAP), locally linear embedding (LLE) and Laplacian eigenmaps (LE) are recently proposed nonlinear dimensionality reduction methods of manifolds. When these methods are satisfied with some specific constraints, some hidden connections can be found between principal component analysis (PCA) and those manifolds learning based approaches. In this paper, some derivations are presented to validate the idea and then some conclusions are drawn.
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Li, B., Liu, J. (2012). The Connections between Principal Component Analysis and Dimensionality Reduction Methods of Manifolds. In: Huang, DS., Gan, Y., Gupta, P., Gromiha, M.M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2011. Lecture Notes in Computer Science(), vol 6839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25944-9_83
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DOI: https://doi.org/10.1007/978-3-642-25944-9_83
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