Vector quantization and signal compression
Vector quantization and signal compression
The nature of statistical learning theory
The nature of statistical learning theory
Self-organization as an iterative kernel smoothing process
Neural Computation
Clustering Algorithms
Letter-Level Shape Description by Skeletonization in Faded Documents
WACV '98 Proceedings of the 4th IEEE Workshop on Applications of Computer Vision (WACV'98)
A Unified Model for Probabilistic Principal Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Piecewise Linear Skeletonization Using Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
A k-segments algorithm for finding principal curves
Pattern Recognition Letters
A Soft k-Segments Algorithm for Principal Curves
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Data visualisation and manifold mapping using the ViSOM
Neural Networks - New developments in self-organizing maps
Regularized principal manifolds
The Journal of Machine Learning Research
Neural Networks
A robust algorithm for image principal curve detection
Pattern Recognition Letters
Principal Surfaces from Unsupervised Kernel Regression
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistics and Computing
Incremental Nonlinear Dimensionality Reduction by Manifold Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automatic parameter selection for a k-segments algorithm for computing principal curves
Pattern Recognition Letters
Learning Nonlinear Image Manifolds by Global Alignment of Local Linear Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
A strategy for feature extraction of high dimensional noisy data
MIC'06 Proceedings of the 25th IASTED international conference on Modeling, indentification, and control
A curve tracing algorithm using level set based affine transform
Pattern Recognition Letters
Finding alternatives and reduced formulations for process-based models
Evolutionary Computation
Neurocomputing
Nonlinear Coordinate Unfolding Via Principal Curve Projections with Application to Nonlinear BSS
Neural Information Processing
Dimensionality reduction for heterogeneous dataset in rushes editing
Pattern Recognition
Extraction of curvilinear features from noisy point patterns using principal curves
Pattern Recognition Letters
A non-probabilistic recognizer of stochastic signals based on KLT
Signal Processing
Measuring non-linear dependence for two random variables distributed along a curve
Statistics and Computing
IEEE Transactions on Signal Processing
International Journal of Applied Mathematics and Computer Science - Selected Problems of Computer Science and Control
Medial set, boundary, and topology of random point sets
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Detecting the boundary curve of planar random point set
MLDM'03 Proceedings of the 3rd international conference on Machine learning and data mining in pattern recognition
Principal curves with feature continuity
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Similarity preserving principal curve: an optimal 1-D feature extractor for data representation
IEEE Transactions on Neural Networks
An effective principal curves extraction algorithm for complex distribution dataset
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
Statistics of shape via principal geodesic analysis on lie groups
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Locally Defined Principal Curves and Surfaces
The Journal of Machine Learning Research
Skeletonization of low-quality characters based on point cloud model
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
A Skeletonizing Reconfigurable Self-Organizing Model: Validation Through Text Recognition
Neural Processing Letters
Nonlinear visualization of incomplete data sets
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Construction algorithm of principal curves in the sense of limit
AI'05 Proceedings of the 18th Australian Joint conference on Advances in Artificial Intelligence
Constraint k-segment principal curves
ICIC'06 Proceedings of the 2006 international conference on Intelligent Computing - Volume Part I
A new principal curve algorithm for nonlinear principal component analysis
ICIC'06 Proceedings of the 2006 international conference on Intelligent Computing - Volume Part I
Clustering based on principal curve
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
A flexible object model for recognising and synthesising facial expressions
AVBPA'05 Proceedings of the 5th international conference on Audio- and Video-Based Biometric Person Authentication
Object shape extraction based on the piecewise linear skeletal representation
ICIAR'05 Proceedings of the Second international conference on Image Analysis and Recognition
SINOBIOMETRICS'04 Proceedings of the 5th Chinese conference on Advances in Biometric Person Authentication
Regression transfer learning based on principal curve
ISNN'10 Proceedings of the 7th international conference on Advances in Neural Networks - Volume Part I
Journal of Visual Communication and Image Representation
CrowdAtlas: self-updating maps for cloud and personal use
Proceeding of the 11th annual international conference on Mobile systems, applications, and services
Regularization-free principal curve estimation
The Journal of Machine Learning Research
A generative model and a generalized trust region Newton method for noise reduction
Computational Optimization and Applications
Hierarchical Clustering of High- Throughput Expression Data Based on General Dependences
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Principal curves have been defined as 驴self-consistent驴 smooth curves which pass through the 驴middle驴 of a d-dimensional probability distribution or data cloud. They give a summary of the data and also serve as an efficient feature extraction tool. We take a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution. The new definition makes it possible to theoretically analyze principal curve learning from training data and it also leads to a new practical construction. Our theoretical learning scheme chooses a curve from a class of polygonal lines with $k$ segments and with a given total length to minimize the average squared distance over $n$ training points drawn independently. Convergence properties of this learning scheme are analyzed and a practical version of this theoretical algorithm is implemented. In each iteration of the algorithm, a new vertex is added to the polygonal line and the positions of the vertices are updated so that they minimize a penalized squared distance criterion. Simulation results demonstrate that the new algorithm compares favorably with previous methods, both in terms of performance and computational complexity, and is more robust to varying data models.