title: Classification of small lesions on dynamic breast MRI: Integrating dimension reduction and out-of-sample extension into CADx methodology.
abstract: 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
  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.
authors.affiliation: Department of Imaging Sciences, University of Rochester, 430 Elmwood Avenue, Rochester, NY 14627, USA; Department of Biomedical Engineering, University of Rochester, 430 Elmwood Avenue, Rochester, NY 14627, USA. Electronic address: mahesh.nagarajan@rochester.edu.
authors.forename: Mahesh B
authors.initials: MB
authors.lastname: Nagarajan
authors.affiliation: Department of Imaging Sciences, University of Rochester, 430 Elmwood Avenue, Rochester, NY 14627, USA; Department of Biomedical Engineering, University of Rochester, 430 Elmwood Avenue, Rochester, NY 14627, USA.
authors.forename: Markus B
authors.initials: MB
authors.lastname: Huber
authors.affiliation: Department of Radiology, Ludwig Maximilians University, Klinikum Innenstadt, Ziemssenstr. 1, 80336 Munich, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Schlossbauer
authors.affiliation: Department of Radiology, Ludwig Maximilians University, Klinikum Innenstadt, Ziemssenstr. 1, 80336 Munich, Germany.
authors.forename: Gerda
authors.initials: G
authors.lastname: Leinsinger
authors.affiliation: Department of Radiology, SUNY Upstate Medical University, 750 E. Adams St, Syracuse, NY 13210, USA.
authors.forename: Andrzej
authors.initials: A
authors.lastname: Krol
authors.affiliation: Department of Imaging Sciences, University of Rochester, 430 Elmwood Avenue, Rochester, NY 14627, USA; Department of Biomedical Engineering, University of Rochester, 430 Elmwood Avenue, Rochester, NY 14627, USA; Department of Radiology, Ludwig Maximilians University, Klinikum Innenstadt, Ziemssenstr. 1, 80336 Munich, Germany.
authors.forename: Axel
authors.initials: A
authors.lastname: Wismüller
mesh_terms: D001940:Breast / Q000473:pathology*; D005260:Female; D006801:Humans; D008279:Magnetic Resonance Imaging / Q000379:methods*
keywords: Automated lesion classification; Dimension reduction; Dynamic breast magnetic resonance imaging; Feature selection; Minkowski functionals; Out-of-sample extension; Topological texture features