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The LLE and a linear mapping
Wu, F. C.; Hu, Z. Y.
Source PublicationPATTERN RECOGNITION
2006-09-01
Volume39Issue:9Pages:1799-1804
SubtypeArticle
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
WOS KeywordNONLINEAR DIMENSIONALITY REDUCTION
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS IDWOS:000239050200020
Citation statistics
Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9201
Collection09年以前成果
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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