Abstract
Principal curves were proposed as the nonlinear generalization of PCA. However, for the tasks of feature extraction for signal representation at which PCA is adept, existing definitions of principal curves have some weakness in their theoretical bases thus fail to get reasonable results in many situations. In this paper, a new definition of principal curves - Principal Curve with Feature Continuity (PCFC) is proposed. PCFC focuses on both reconstruction error minimization and feature continuity. It builds a continuous mapping from samples to the extracted features so the features preserve the inner structures of the sample set, which benefits the researchers to learn the properties of the sample set. The existence and the differential properties of PCFC are studied and the results are presented in this paper.
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Sun, Mm., Yang, Jy. (2007). Principal Curves with Feature Continuity. In: Zhou, ZH., Li, H., Yang, Q. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2007. Lecture Notes in Computer Science(), vol 4426. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71701-0_86
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DOI: https://doi.org/10.1007/978-3-540-71701-0_86
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71700-3
Online ISBN: 978-3-540-71701-0
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