The visual display of quantitative information
The visual display of quantitative information
Treemaps: visualizing hierarchical and categorical data
Treemaps: visualizing hierarchical and categorical data
Visualizing multi-dimensional clusters, trends, and outliers using star coordinates
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Visualizing Data
Designing Pixel-Oriented Visualization Techniques: Theory and Applications
IEEE Transactions on Visualization and Computer Graphics
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
Exploring N-dimensional databases
VIS '90 Proceedings of the 1st conference on Visualization '90
Parallel coordinates: a tool for visualizing multi-dimensional geometry
VIS '90 Proceedings of the 1st conference on Visualization '90
Visualization of high-dimensional data with relational perspective map
Information Visualization
Distance-Preserving Projection of High-Dimensional Data for Nonlinear Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient locally linear embeddings of imperfect manifolds
MLDM'03 Proceedings of the 3rd international conference on Machine learning and data mining in pattern recognition
A new model of self-organizing neural networks and its application in data projection
IEEE Transactions on Neural Networks
Artificial neural networks for feature extraction and multivariate data projection
IEEE Transactions on Neural Networks
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Using the geodesic distance metric instead of the Euclidean distance metric, ISOMAP can visualize the convex but intrinsically flat manifolds such as the swiss roll data set nicely. But it's well known that ISOMAP performs well only when the data belong to a single well-sampled manifold, and fails when the data lie on disjoint manifolds or imperfect manifolds. Generally speaking, as the data points are farer from each other on the manifold, the approximation of the shortest path to the geodesic distance is worse, especially for imperfect manifolds, that is, long distances are approximated generally worse than short distances, which makes the classical MDS algorithm used in ISOMAP unsuitable and thus often leads to the overlapping or ”overclustering” of the data. To solve this problem, we improve the original ISOMAP algorithm by replacing the classical MDS algorithm with the Sammon's mapping algorithm, which can limit the effects of generally worse-approximated long distances to a certain extent, and thus better visualization results are obtained. As a result, besides imperfect manifolds, intrinsically curved manifolds such as the fishbowl data set can also be visualized nicely. In addition, based on the characteristics of the Euclidean distance metric, a faster Dijkstra-like shortest path algorithm is used in our method. Finally, experimental results verify our method very well.