A Note on Laplacian Eigenmaps
A Note on Laplacian Eigenmaps
摘要
In this note,we show that the image of Laplcian eigenmap in 2-dimensional Edclidean space is lied in a parabola.
In this note, we show that the image of Laplcian eigenmap in 2-dimensional Edclidean space is lied in a parabola.
基金
the National Natural Science Foundation of China (No.10531070)
the National Basic Research Program (973) of China (No.2006CB805901)
the National High Technology Research and Development Program (863) of China (No.2006AA11Z209)
the Grant of Science and Technology Commission of Shanghai Municipality (STCSM No.09XD1402500)
参考文献11
-
1David L. Donoho,Carrie Grimes.Image Manifolds which are Isometric to Euclidean Space[J].Journal of Mathematical Imaging and Vision.2005(1)
-
2Cvetkovic′D,Doob M,Sachs H.Spectra of graphs—Theory and applications[]..1995
-
3Donoho DL,Grimes C.Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data[].Proceedings of the National Academy of Sciences of the United States of Amercia.2003
-
4Roweis ST,Saul LK.Nonlinear dimensionality reduction by locally linear embedding[].Science.2000
-
5Tenenbaum JB,de Silva V,Langford JC.A global geometric framework for nonlinear dimensionality reduction[].Science.2000
-
6Belkin M,Niyogi P.Laplacian eigenmaps for dimensionality reduction and data representation[].Neural Computation.2003
-
7Merris R.Laplacian matrics of graphs: a survey[].Linear Algebra and Its Applications.1994
-
8Bondy JA,Murty USR.Graph Theory with Applications[]..1976
-
9M. Belkin,P. Niyogi.Laplacian eigenmaps and spectral techniques for embedding and clustering[].Advances in Neural Information Processing Systems.2002
-
10Kim Y,and Mesbahi M.On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian[].IEEE Transactions on Automatic Control.2006
-
1刘恋.山外有什么[J].初中生辅导,2004,0(13):20-20.
-
2方匡雕.高考数学的新热点——类比思想的应用[J].中学数学研究（华南师范大学）（上半月）,2004,11(8):4-6. 被引量：1
-
3李睿,赵晓.融合DCT和LBP特征的表情识别[J].计算机工程与应用,2013,49(15):171-174. 被引量：3
-
4余熙.A thank-you note[J].第二课堂（A）,2015(5):24-24.
-
5柳羽颜.note-taking[J].英语画刊（中级）,2016(3):23-23.
-
6张超.A Note[J].语数外学习（初中版）（中旬）,2010(5):44-45.
-
7Thank-you Note[J].考试与评价（英语八年级专刊）,2010(6):12-12.
-
8聂秀山,乔建苹,秦丰林.基于拉普拉斯特征映射的鲁棒视频哈希方法[J].计算机工程与设计,2011,32(11):3799-3802. 被引量：2
-
9庄玮.学得课堂:类比法给力数学教学[J].新课程（综合版）,2014,0(8):72-73.
-
10魏祖成.由博弈到概率[J].中学生数学（初中版）,2007(2):21-22.
