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Model selection plays an important role in cost-sensitive SVM (CS-SVM). It has been proven that the global minimum cross validation (CV) error can be efficiently computed based on the solution path for one parameter learning problems. However, it is a challenge to obtain the global minimum CV error for CS-SVM based on one-dimensional solution path and traditional grid search, because CS-SVM is with two regularization parameters. In this paper, we propose a solution and error surfaces based CV approach (CV-SES). More specifically, we first compute a two-dimensional solution surface for CS-SVM based on a bi-parameter space partition algorithm, which can fit solutions of CS-SVM for all values of both regularization parameters. Then, we compute a two-dimensional validation error surface for each CV fold, which can fit validation errors of CS-SVM for all values of both regularization parameters. Finally, we obtain the CV error surface by superposing $K$ validation error surfaces, which can find the global minimum CV error of CS-SVM. Experiments are conducted on seven datasets for cost sensitive learning and on four datasets for imbalanced learning. Experimental results not only show that our proposed CV-SES has a better generalization ability than CS-SVM with various hybrids between grid search and solution path methods, and than recent proposed cost-sensitive hinge loss SVM with three-dimensional grid search, but also show that CV-SES uses less running time. [ABSTRACT FROM AUTHOR]

Clinical routine often requires to analyze spinal images of multiple anatomic structures in multiple anatomic planes from multiple imaging modalities (M^3). Unfortunately, existing methods for segmenting spinal images are still limited to one specific structure, in one specific plane or from one specific modality (S^3). In this paper, we propose a novel approach, Regression Segmentation, that is for the first time able to segment M^3 spinal images in one single unified framework. This approach formulates the segmentation task innovatively as a boundary regression problem: modeling a highly nonlinear mapping function from substantially diverse M^3 images directly to desired object boundaries. Leveraging the advancement of sparse kernel machines, regression segmentation is fulfilled by a multi-dimensional support vector regressor (MSVR) which operates in an implicit, high dimensional feature space where M^3 diversity and specificity can be systematically categorized, extracted, and handled. The proposed regression segmentation approach was thoroughly tested on images from 113 clinical subjects including both disc and vertebral structures, in both sagittal and axial planes, and from both MRI and CT modalities. The overall result reaches a high dice similarity index (DSI) 0.912 and a low boundary distance (BD) 0.928 mm. With our unified and expendable framework, an efficient clinical tool for M^3 spinal image segmentation can be easily achieved, and will substantially benefit the diagnosis and treatment of spinal diseases. [ABSTRACT FROM AUTHOR]