Non-linear dimensionality reduction techniques for classification and visualization
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Convex Optimization
GPCA: an efficient dimension reduction scheme for image compression and retrieval
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Learning a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A spatio-temporal extension to Isomap nonlinear dimension reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A kernel view of the dimensionality reduction of manifolds
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Analysis and extension of spectral methods for nonlinear dimensionality reduction
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning sparse metrics via linear programming
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Manifold-adaptive dimension estimation
Proceedings of the 24th international conference on Machine learning
Nonlinear Dimensionality Reduction
Nonlinear Dimensionality Reduction
Embedding new data points for manifold learning via coordinate propagation
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Nearest manifold approach for face recognition
FGR' 04 Proceedings of the Sixth IEEE international conference on Automatic face and gesture recognition
Spline embedding for nonlinear dimensionality reduction
ECML'06 Proceedings of the 17th European conference on Machine Learning
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This paper proposes a new algorithm for nonlinear dimensionality reduction. Our basic idea is to explore and exploit the local geometry of the manifold with relative distance comparisons. All such comparisons derived from local neighborhoods are enumerated to constrain the manifold to be learned. The task is formulated as a problem of quadratically constrained quadratic programming (QCQP). However, such a QCQP problem is not convex. We relax it to be a problem of semi-definite programming (SDP), from which a globally optimal embedding is obtained. Experimental results illustrate the validity of our algorithm.