Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns
Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Supervised nonlinear dimensionality reduction for visualization and classification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Expert Systems with Applications: An International Journal
| Hi-index | 12.05 |
Data visualization of high-dimensional data is possible through the use of dimensionality reduction techniques. However, in deciding which dimensionality reduction techniques to use in practice, quantitative metrics are necessary for evaluating the results of the transformation and visualization of the lower dimensional embedding. In this paper, we propose a manifold visualization metric based on the pairwise correlation of the geodesic distance in a data manifold. This metric is compared with other metrics based on the Euclidean distance, Mahalanobis distance, City Block metric, Minkowski metric, cosine distance, Chebychev distance, and Spearman distance. The results of applying different dimensionality reduction techniques on various types of nonlinear manifolds are compared and discussed. Our experiments show that our proposed metric is suitable for quantitatively evaluating the results of the dimensionality reduction techniques if the data lies on an open planar nonlinear manifold. This has practical significance in the implementation of knowledge-based visualization systems and the application of knowledge-based dimensionality reduction methods.