Applied multivariate statistical analysis
Applied multivariate statistical analysis
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Self-organization as an iterative kernel smoothing process
Neural Computation
Self-organizing maps
A Hierarchical Latent Variable Model for Data Visualization
IEEE Transactions on Pattern Analysis and Machine Intelligence
GTM: the generative topographic mapping
Neural Computation
Neural Computation
Learning and Design of Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
A polygonal line algorithm for constructing principal curves
Proceedings of the 1998 conference on Advances in neural information processing systems II
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Neural Computation and Self-Organizing Maps; An Introduction
Neural Computation and Self-Organizing Maps; An Introduction
Nonlinear dimensionality reduction using probabilistic principal surfaces
Nonlinear dimensionality reduction using probabilistic principal surfaces
A class of neural networks for independent component analysis
IEEE Transactions on Neural Networks
Limitations of nonlinear PCA as performed with generic neural networks
IEEE Transactions on Neural Networks
Principal Surfaces from Unsupervised Kernel Regression
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning Nonlinear Image Manifolds by Global Alignment of Local Linear Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
A model of diatom shape and texture for analysis, synthesis and identification
Machine Vision and Applications
Clustering and visualization approaches for human cell cycle gene expression data analysis
International Journal of Approximate Reasoning
Kernel class-wise locality preserving projection
Information Sciences: an International Journal
Nonlinear Coordinate Unfolding Via Principal Curve Projections with Application to Nonlinear BSS
Neural Information Processing
Nonlinear Principal Manifolds --- Adaptive Hybrid Learning Approaches
HAIS '08 Proceedings of the 3rd international workshop on Hybrid Artificial Intelligence Systems
Active curve axis Gaussian mixture models
Pattern Recognition
An interactive tool for data visualization and clustering
KES'07/WIRN'07 Proceedings of the 11th international conference, KES 2007 and XVII Italian workshop on neural networks conference on Knowledge-based intelligent information and engineering systems: Part III
Adaptive nonlinear manifolds and their applications to pattern recognition
Information Sciences: an International Journal
Similarity preserving principal curve: an optimal 1-D feature extractor for data representation
IEEE Transactions on Neural Networks
Probabilistic self-organizing maps for continuous data
IEEE Transactions on Neural Networks
Locally Defined Principal Curves and Surfaces
The Journal of Machine Learning Research
NEC: a hierarchical agglomerative clustering based on fisher and negentropy information
WIRN'05 Proceedings of the 16th Italian conference on Neural Nets
Construction algorithm of principal curves in the sense of limit
AI'05 Proceedings of the 18th Australian Joint conference on Advances in Artificial Intelligence
Probabilistic principal surface classifier
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part II
SINOBIOMETRICS'04 Proceedings of the 5th Chinese conference on Advances in Biometric Person Authentication
ADA'04 Proceedings of the 3rd international conference on Astronomical Data Analysis
Journal of Medical Systems
Information Sciences: an International Journal
Regularization-free principal curve estimation
The Journal of Machine Learning Research
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Principal curves and surfaces are nonlinear generalizations of principal components and subspaces, respectively. They can provide insightful summary of high-dimensional data not typically attainable by classical linear methods. Solutions to several problems, such as proof of existence and convergence, faced by the original principal curve formulation have been proposed in the past few years. Nevertheless, these solutions are not generally extensible to principal surfaces, the mere computation of which presents a formidable obstacle. Consequently, relatively few studies of principal surfaces are available. Recently, we proposed the probabilistic principal surface (PPS) to address a number of issues associated with current principal surface algorithms. PPS uses a manifold oriented covariance noise model, based on the generative topographical mapping (GTM), which can be viewed as a parametric formulation of Kohonen's self-organizing map. Building on the PPS, we introduce a unified covariance model that implements PPS $\left( 01\right) $ by varying the clamping parameter $\alpha$. Then, we comprehensively evaluate the empirical performance (reconstruction error) of PPS, GTM, and the manifold-aligned GTM on three popular benchmark data sets. It is shown in two different comparisons that the PPS outperforms the GTM under identical parameter settings. Convergence of the PPS is found to be identical to that of the GTM and the computational overhead incurred by the PPS decreases to $40$ percent or less for more complex manifolds. These results show that the generalized PPS provides a flexible and effective way of obtaining principal surfaces.