Elements of information theory
Elements of information theory
Self-Organizing Maps
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
A Computational Framework for Nonlinear Dimensionality Reduction and Clustering
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
The Exploration Machine --- A Novel Method for Data Visualization
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
Adaptive relevance matrices in learning vector quantization
Neural Computation
Information Retrieval Perspective to Nonlinear Dimensionality Reduction for Data Visualization
The Journal of Machine Learning Research
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
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Objective: While dimension reduction has been previously explored in computer aided diagnosis (CADx) as an alternative to feature selection, previous implementations of its integration into CADx do not ensure strict separation between training and test data required for the machine learning task. This compromises the integrity of the independent test set, which serves as the basis for evaluating classifier performance. Methods and materials: We propose, implement and evaluate an improved CADx methodology where strict separation is maintained. This is achieved by subjecting the training data alone to dimension reduction; the test data is subsequently processed with out-of-sample extension methods. Our approach is demonstrated in the research context of classifying small diagnostically challenging lesions annotated on dynamic breast magnetic resonance imaging (MRI) studies. The lesions were dynamically characterized through topological feature vectors derived from Minkowski functionals. These feature vectors were then subject to dimension reduction with different linear and non-linear algorithms applied in conjunction with out-of-sample extension techniques. This was followed by classification through supervised learning with support vector regression. Area under the receiver-operating characteristic curve (AUC) was evaluated as the metric of classifier performance. Results: Of the feature vectors investigated, the best performance was observed with Minkowski functional 'perimeter' while comparable performance was observed with 'area'. Of the dimension reduction algorithms tested with 'perimeter', the best performance was observed with Sammon's mapping (0.84+/-0.10) while comparable performance was achieved with exploratory observation machine (0.82+/-0.09) and principal component analysis (0.80+/-0.10). Conclusions: The results reported in this study with the proposed CADx methodology present a significant improvement over previous results reported with such small lesions on dynamic breast MRI. In particular, non-linear algorithms for dimension reduction exhibited better classification performance than linear approaches, when integrated into our CADx methodology. We also note that while dimension reduction techniques may not necessarily provide an improvement in classification performance over feature selection, they do allow for a higher degree of feature compaction.