Xin Yang
ABSTRACT
The problem of nonlinear dimensionality reduction is considered. We focus on problems where prior information is available, namely, semi-supervised dimensionality reduction. It is shown that basic nonlinear dimensionality reduction algorithms, such as Locally Linear Embedding (LLE), Isometric feature mapping (ISOMAP), and Local Tangent Space Alignment (LTSA), can be modified by taking into account prior information on exact mapping of certain data points. The sensitivity analysis of our algorithms shows that prior information will improve stability of the solution. We also give some insight on what kind of prior information best improves the solution. We demonstrate the usefulness of our algorithm by synthetic and real life examples.
- Chan, R., & Ng, M. (1996). Conjugate gradient methods for Toeplitz systems. SIAM Review, 38(3), 427--482. Google Scholar
Digital Library
- de Silva, V., & Tenenbaum, J. (2004). Sparse multidimensional scaling using landmark points (Technical Report). Stanford University.Google Scholar
- Golub, G., & Van Loan, C. (Eds.). (1996). Matrix computations. Baltimore: The Johns Hopkins University Press.Google Scholar
- Hastie, T., Tibshirani, R., & Friedman, J. (Eds.). (2001). The elements of statistical learning: data mining, inference, and prediction. New York: Springer.Google ScholarCross Ref
- Rahimi, A., Recht, B., & Darrell, T. (2005). Learning appearance manifolds from video. Computer Vision and Pattern Recognition (CVPR). Google ScholarDigital Library
- Roweis, S., & Saul, L. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323--2326.Google ScholarCross Ref
- Saul, L., & Roweis, S. (2003). Think globally, fit locally: unsupervised learning of nonlinear manifolds. Journal of Machine Learning Research, 4, 119--155. Google ScholarDigital Library
- Tenebaum, J., de Silva, V., & Langford, J. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500), 2319--2323.Google ScholarCross Ref
- Weinberger, K., Packer, B., & Saul, L. (2005). Nonlinear dimensionality reduction by semidefinite programming and kernel matrix factorization. Proceedings of the tenth international workshop on artificial intelligence and statistics, 381--388.Google Scholar
- Zha, H., & Zhang, Z. (2005). Spectral analysis of alignment in manifold learning. IEEE International Conference on Acoustics, Speech, and Signal Processing.Google Scholar
- Zhang, Z., & Zha, H. (2004). Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM Journal on Scientific Computing, 26(1), 313--338. Google ScholarDigital Library
Index Terms
- Semi-supervised nonlinear dimensionality reduction
Recommendations
Local Fisher discriminant analysis for supervised dimensionality reduction
ICML '06: Proceedings of the 23rd international conference on Machine learningDimensionality reduction is one of the important preprocessing steps in high-dimensional data analysis. In this paper, we consider the supervised dimensionality reduction problem where samples are accompanied with class labels. Traditional Fisher ...
A unified framework for semi-supervised dimensionality reduction
In practice, many applications require a dimensionality reduction method to deal with the partially labeled problem. In this paper, we propose a semi-supervised dimensionality reduction framework, which can efficiently handle the unlabeled data. Under ...
Semi-supervised dimensionality reduction of hyperspectral imagery using pseudo-labels
A new semi-supervised feature reduction approach is proposed.Pseudo-labels are generated using Dirichlet Process Mixing Model, which are then used for learning a semi-supervised dimensionality reduction projection that simultaneously preserves ...
Comments