کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
531210 | 869818 | 2006 | 6 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The LLE and a linear mapping The LLE and a linear mapping](/preview/png/531210.png)
The 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.
Journal: Pattern Recognition - Volume 39, Issue 9, September 2006, Pages 1799–1804