Silhouettes: a graphical aid to the interpretation and validation of cluster analysis
Journal of Computational and Applied Mathematics
Active shape models—their training and application
Computer Vision and Image Understanding
Machine Learning
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ensemble Methods in Machine Learning
MCS '00 Proceedings of the First International Workshop on Multiple Classifier Systems
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Spectral Grouping Using the Nyström Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Combining Multiple Clusterings Using Evidence Accumulation
IEEE Transactions on Pattern Analysis and Machine Intelligence
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Robust locally linear embedding
Pattern Recognition
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
The Journal of Machine Learning Research
Manifold alignment using Procrustes analysis
Proceedings of the 25th international conference on Machine learning
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Multiple view semi-supervised dimensionality reduction
Pattern Recognition
Local smoothing for manifold learning
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
Bagging-based spectral clustering ensemble selection
Pattern Recognition Letters
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Gleason patterns of prostate cancer histopathology, characterized primarily by morphological and architectural attributes of histological structures (glands and nuclei), have been found to be highly correlated with disease aggressiveness and patient outcome. Gleason patterns 4 and 5 are highly correlated with more aggressive disease and poorer patient outcome, while Gleason patterns 1-3 tend to reflect more favorable patient outcome. Because Gleason grading is done manually by a pathologist visually examining glass (or digital) slides subtle morphologic and architectural differences of histological attributes, in addition to other factors, may result in grading errors and hence cause high inter-observer variability. Recently some researchers have proposed computerized decision support systems to automatically grade Gleason patterns by using features pertaining to nuclear architecture, gland morphology, as well as tissue texture. Automated characterization of gland morphology has been shown to distinguish between intermediate Gleason patterns 3 and 4 with high accuracy. Manifold learning (ML) schemes attempt to generate a low dimensional manifold representation of a higher dimensional feature space while simultaneously preserving nonlinear relationships between object instances. Classification can then be performed in the low dimensional space with high accuracy. However ML is sensitive to the samples contained in the dataset; changes in the dataset may alter the manifold structure. In this paper we present a manifold regularization technique to constrain the low dimensional manifold to a specific range of possible manifold shapes, the range being determined via a statistical shape model of manifolds (SSMM). In this work we demonstrate applications of the SSMM in (1) identifying samples on the manifold which contain noise, defined as those samples which deviate from the SSMM, and (2) accurate out-of-sample extrapolation (OSE) of newly acquired samples onto a manifold constrained by the SSMM. We demonstrate these applications of the SSMM in the context of distinguish between Gleason patterns 3 and 4 using glandular morphologic features in a prostate histopathology dataset of 58 patient studies. Identifying and eliminating noisy samples from the manifold via the SSMM results in a statistically significant improvement in area under the receiver operator characteristic curve (AUC), 0.832+/-0.048 with removal of noisy samples compared to a AUC of 0.779+/-0.075 without removal of samples. The use of the SSMM for OSE of newly acquired glands also shows statistically significant improvement in AUC, 0.834+/-0.051 with the SSMM compared to 0.779+/-0.054 without the SSMM. Similar results were observed for the synthetic Swiss Roll and Helix datasets.