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The least squares support vector machine (LS-SVM), like the SVM, is based on the margin-maximization performing structural risk and has excellent power of generalization. In this paper, we consider its use in semisupervised learning. We propose two algorithms to perform this task deduced from the transductive SVM idea. Algorithm 1 is based on combinatorial search guided by certain heuristics while Algorithm 2 iteratively builds the decision function by adding one unlabeled sample at the time. In term of complexity, Algorithm 1 is faster but Algorithm 2 yields a classifier with a better generalization capacity with only a few labeled data available. Our proposed algorithms are tested in several benchmarks and give encouraging results, confirming our approach.

Non invasive classification system of scoliosis curve types using least-squares support vector machines." Artificial Intelligence in Medicine, Vol. 56, no. 2 (2012): pp. 99-107.The final publication is available via the DOI: http://dx.doi.org/10.1016/j.artmed.2012.07.002The manuscript, in a draft version prior to being accepted by the publisher, is reproduced in the following pages. Mathias AbstractObjective: To determine scoliosis curve types using non invasive acquisition, without any prior knowledge on X-ray data.Methods: Classification of scoliosis deformities according to curve type is used to plan management of scoliosis patients. In this work, we propose a robust system that can determine the scoliosis curve type from non invasive acquisition of 3D back surface of the patients. The 3D image of back surface of the trunk is divided into patches and local geometric descriptors characterizing the surface of the back are computed from each patch and forming the features. We perform the reduction of the dimensionality by using principal component analysis and retain 53 components using overlap criterion combined with the total variance in the observed variables. In this work a multi-class classifier is built with leastsquares support vector machine (LS-SVM). The original LS-SVM formulation was modified by weighting differently the positive and negative samples and a new kernel was designed in order to achieve a robust classifier. The proposed system was validated using data of 165 patients with different scoliosis curve types. A comparison of the results of a non invasive classification was done with those obtained by an expert using X-ray images.Results: The average rate of successful classification was computed using * Corresponding author Email addresses: mathias-mahouzonsou.adankon@polymtl.ca (Mathias M. Adankon), jean.dansereau@polymtl.ca (Jean Dansereau), hubert.labelle@recherche-ste-justine.qc.ca (Hubert Labelle), farida.cheriet@polymtl.ca (Farida Cheriet) Preprint submitted to ElsevierJuly 16, 2012 leave-one-out cross-validation procedure. The overall accuracy of the system was 95%. Considering the correct classification rate per class, we obtained 96%, 84% and 97% respectively for thoracic major curve, double major curve and lumbar/thoracolumbar major curve. Conclusion: This study shows that it is possible to find a relationship between the internal deformity and the back surface deformity in scoliosis with machine learning methods.The proposed system uses non invasive acquisition which is safety for the patient, no radiation. Also, a design of a specific kernel improved classification performance.

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