Isometric sliced inverse regression for nonlinear manifold learning

Authors:
Wei-Ting Yao;Han-Ming Wu
Affiliations:
Department of Mathematics, Tamkang University, New Taipei City, Taiwan, R.O.C. 25137;Department of Mathematics, Tamkang University, New Taipei City, Taiwan, R.O.C. 25137
Venue:
Statistics and Computing
Year:
2013

Citing 17
Cited 0

Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Sparse Greedy Matrix Approximation for Machine Learning

ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
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
Learning a kernel matrix for nonlinear dimensionality 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
Approximate geodesic distances reveal biologically relevant structures in microarray data

Bioinformatics
Selection of the optimal parameter value for the Isomap algorithm

Pattern Recognition Letters
Supervised Isomap with Explicit Mapping

ICICIC '06 Proceedings of the First International Conference on Innovative Computing, Information and Control - Volume 3
RSIR: regularized sliced inverse regression for motif discovery

Bioinformatics
Iterative sliced inverse regression for segmentation of ultrasound and MR images

Pattern Recognition
Nonlinear Dimension Reduction with Kernel Sliced Inverse Regression

IEEE Transactions on Knowledge and Data Engineering
GAP: A graphical environment for matrix visualization and cluster analysis

Computational Statistics & Data Analysis
The dynamical neighborhood selection based on the sampling density and manifold curvature for isometric data embedding

Pattern Recognition Letters
Supervised nonlinear dimensionality reduction for visualization and classification

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Reduced Support Vector Machines: A Statistical Theory

IEEE Transactions on Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

Sliced inverse regression (SIR) was developed to find effective linear dimension-reduction directions for exploring the intrinsic structure of the high-dimensional data. In this study, we present isometric SIR for nonlinear dimension reduction, which is a hybrid of the SIR method using the geodesic distance approximation. First, the proposed method computes the isometric distance between data points; the resulting distance matrix is then sliced according to K-means clustering results, and the classical SIR algorithm is applied. We show that the isometric SIR (ISOSIR) can reveal the geometric structure of a nonlinear manifold dataset (e.g., the Swiss roll). We report and discuss this novel method in comparison to several existing dimension-reduction techniques for data visualization and classification problems. The results show that ISOSIR is a promising nonlinear feature extractor for classification applications.