Kernel PCA and de-noising in feature spaces
Proceedings of the 1998 conference on Advances in neural information processing systems II
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neighbor search with global geometry: a minimax message passing algorithm
Proceedings of the 24th international conference on Machine learning
Penalized preimage learning in kernel principal component analysis
IEEE Transactions on Neural Networks
Population Shape Regression from Random Design Data
International Journal of Computer Vision
The pre-image problem in kernel methods
IEEE Transactions on Neural Networks
Foundations and Trends® in Computer Graphics and Vision
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We propose a technique to represent a pathological pattern as a deviation from normality along a manifold structure. Each subject is represented by a map of local motion abnormalities, obtained from a statistical atlas of motion built from a healthy population. The algorithm learns a manifold from a set of patients with varying degrees of the same pathology. The approach extends recent manifold-learning techniques by constraining the manifold to pass by a physiologically meaningful origin representing a normal motion pattern. Individuals are compared to the manifold population through a distance that combines a mapping to the manifold and the path along the manifold to reach its origin. The method is applied in the context of cardiac resynchronization therapy (CRT), focusing on a specific motion pattern of intra-ventricular dyssynchrony called septal flash (SF). We estimate the manifold from 50 CRT candidates with SF and test it on 38 CRT candidates and 21 healthy volunteers. Experiments highlight the need of nonlinear techniques to learn the studied data, and the relevance of the computed distance for comparing individuals to a specific pathological pattern.