TY - GEN
T1 - Out-of-sample embedding of spherical manifold based on constrained least squares
AU - Zhang, Yongpeng
AU - Lin, Zenggang
AU - Yao, Rui
AU - Zhu, Yu
AU - Li, Haisen
PY - 2012
Y1 - 2012
N2 - All of the current state-of-the-art nonlinear dimensionality reduction methods attempt to seek the low-dimensional manifold structure by preserving global or local properties of the original data, but without considering the constraint of the manifold structure, thus, there may be a big contrast between the manifold structure result obtained by the nonlinear techniques and the result that we expected. Therefore, it is necessary for us to study the constrained nonlinear dimensionality reduction. In this paper, we study the embedding of a hidden manifold onto a unit sphere by using SMACOF algorithm and propose a method to solve the out-of-sample problem which usually arises in the manifold learning. By converting it into a constrained least squares problem with the spherical structure information, this method avoids reconstructing the neighborhood graph. The application results of 3-D object pose estimation show the effectiveness of our propose method.
AB - All of the current state-of-the-art nonlinear dimensionality reduction methods attempt to seek the low-dimensional manifold structure by preserving global or local properties of the original data, but without considering the constraint of the manifold structure, thus, there may be a big contrast between the manifold structure result obtained by the nonlinear techniques and the result that we expected. Therefore, it is necessary for us to study the constrained nonlinear dimensionality reduction. In this paper, we study the embedding of a hidden manifold onto a unit sphere by using SMACOF algorithm and propose a method to solve the out-of-sample problem which usually arises in the manifold learning. By converting it into a constrained least squares problem with the spherical structure information, this method avoids reconstructing the neighborhood graph. The application results of 3-D object pose estimation show the effectiveness of our propose method.
KW - constrained least squares
KW - manifold learning
KW - out-of-sample embedding
KW - SMACOF
KW - spherical MDS
UR - http://www.scopus.com/inward/record.url?scp=84865819797&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-31919-8_72
DO - 10.1007/978-3-642-31919-8_72
M3 - 会议稿件
AN - SCOPUS:84865819797
SN - 9783642319181
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 562
EP - 570
BT - Intelligent Science and Intelligent Data Engineering - Second Sino-Foreign-Interchange Workshop, IScIDE 2011, Revised Selected Papers
T2 - 2nd Sino-Foreign-Interchange Workshop on Intelligent Science and Intelligent Data Engineering, IScIDE 2011
Y2 - 23 October 2011 through 25 October 2011
ER -