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The LLE and a linear mapping
Wu, F. C.; Hu, Z. Y.
AbstractThe locally linear embedding (LLE) is considered an effective algorithm for dimensionality reduction. In this short note, some of its key properties are studied. In particular, we show that: (1) there always exists a linear mapping from the high-dimensional space to the low-dimensional space such that all the constraint conditions in the LLE can be satisfied. The implication of the existence of such a linear mapping is that the LLE cannot guarantee a one-to-one mapping from the high-dimensional space to the low-dimensional space for a given data set: (2) if the LLE is required to globally preserve distance, it must be a PCA mapping; (3) for a given high-dimensional data set, there always exists a local distance-preserving LLE. The above results can bring some new insights into a better understanding of the LLE. (c) 2006 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
KeywordLocally Linear Embedding (Lle) Linear Mapping Principal Component Analysis (Pca)
WOS HeadingsScience & Technology ; Technology
Indexed BySCI
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS IDWOS:000239050200020
Citation statistics
Document Type期刊论文
AffiliationChinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Wu, F. C.,Hu, Z. Y.. The LLE and a linear mapping[J]. PATTERN RECOGNITION,2006,39(9):1799-1804.
APA Wu, F. C.,&Hu, Z. Y..(2006).The LLE and a linear mapping.PATTERN RECOGNITION,39(9),1799-1804.
MLA Wu, F. C.,et al."The LLE and a linear mapping".PATTERN RECOGNITION 39.9(2006):1799-1804.
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