Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Mixtures of probabilistic principal component analyzers
Neural Computation
Learning and Design of Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Unified Model for Probabilistic Principal Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Unsupervised Learning of Finite Mixture Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Self-Organizing Maps
Coordinating Principal Component Analyzers
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Face Recognition Using Laplacianfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Self-organizing mixture models
Neurocomputing
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Semantic image classification using statistical local spatial relations model
Multimedia Tools and Applications
Nearest hyperdisk methods for high-dimensional classification
Proceedings of the 25th international conference on Machine learning
Image denoising using mixtures of projected Gaussian scale mixtures
IEEE Transactions on Image Processing
Mixture of the robust L1 distributions and its applications
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
Large margin classifiers based on affine hulls
Neurocomputing
Probabilistic self-organizing maps for continuous data
IEEE Transactions on Neural Networks
IEEE Transactions on Signal Processing
Incremental alignment manifold learning
Journal of Computer Science and Technology - Special issue on natural language processing
Front end analysis of speech recognition: a review
International Journal of Speech Technology
Learning colours from textures by sparse manifold embedding
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
Target reconstruction using manifold-based compressive sensing
IScIDE'11 Proceedings of the Second Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Learning colours from textures by sparse manifold embedding
Signal Processing
Motion planning and reactive control on learnt skill manifolds
International Journal of Robotics Research
Embedding new observations via sparse-coding for non-linear manifold learning
Pattern Recognition
Behaviour generation in humanoids by learning potential-based policies from constrained motion
Applied Bionics and Biomechanics
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Appearance-based methods, based on statistical models of the pixel values in an image (region) rather than geometrical object models, are increasingly popular in computer vision. In many applications, the number of degrees of freedom (DOF) in the image generating process is much lower than the number of pixels in the image. If there is a smooth function that maps the DOF to the pixel values, then the images are confined to a low-dimensional manifold embedded in the image space. We propose a method based on probabilistic mixtures of factor analyzers to 1) model the density of images sampled from such manifolds and 2) recover global parameterizations of the manifold. A globally nonlinear probabilistic two-way mapping between coordinates on the manifold and images is obtained by combining several, locally valid, linear mappings. We propose a parameter estimation scheme that improves upon an existing scheme and experimentally compare the presented approach to self-organizing maps, generative topographic mapping, and mixtures of factor analyzers. In addition, we show that the approach also applies to finding mappings between different embeddings of the same manifold.