@article {48, title = {Multitask Classification Hypothesis Space With Improved Generalization Bounds}, journal = {Neural Networks and Learning Systems, IEEE Transactions on}, volume = {26}, year = {2015}, pages = {1468-1479}, abstract = {This paper presents a pair of hypothesis spaces (HSs) of vector-valued functions intended to be used in the context of multitask classification. While both are parameterized on the elements of reproducing kernel Hilbert spaces and impose a feature mapping that is common to all tasks, one of them assumes this mapping as fixed, while the more general one learns the mapping via multiple kernel learning. For these new HSs, empirical Rademacher complexity-based generalization bounds are derived, and are shown to be tighter than the bound of a particular HS, which has appeared recently in the literature, leading to improved performance. As a matter of fact, the latter HS is shown to be a special case of ours. Based on an equivalence to Group-Lasso type HSs, the proposed HSs are utilized toward corresponding support vector machine-based formulations. Finally, experimental results on multitask learning problems underline the quality of the derived and validate this paper{\textquoteright}s analysis.}, keywords = {Context, Hilbert space, Kernel, Learning systems, Machine learning, pattern recognition, statistical learning, supervised learning, Support vector machines, Training, Upper bound}, issn = {2162-237X}, doi = {10.1109/TNNLS.2014.2347054}, author = {Cong Li and Michael Georgiopoulos and Georgios C. Anagnostopoulos} } @article {31, title = {A Unifying Framework for Typical Multitask Multiple Kernel Learning Problems}, journal = {Neural Networks and Learning Systems, IEEE Transactions on}, volume = {25}, year = {2013}, month = {July}, pages = {1287-1297}, abstract = {

Over the past few years, multiple kernel learning (MKL) has received significant attention among data-driven feature selection techniques in the context of kernel-based learning. MKL formulations have been devised and solved for a broad spectrum of machine learning problems, including multitask learning (MTL). Solving different MKL formulations usually involves designing algorithms that are tailored to the problem at hand, which is, typically, a nontrivial accomplishment. In this paper we present a general multitask multiple kernel learning (MT-MKL) framework that subsumes well-known MT-MKL formulations, as well as several important MKL approaches on single-task problems. We then derive a simple algorithm that can solve the unifying framework. To demonstrate the flexibility of the proposed framework, we formulate a new learning problem, namely partially-shared common space MT-MKL, and demonstrate its merits through experimentation.

}, keywords = {Algorithm design and analysis, Closed-form solutions, Kernel, Learning systems, Machine learning, Optimization, optimization methods, pattern recognition, supervised learning, Support vector machines, support vector machines (SVMs), support vector machines (SVMs)., Vectors}, issn = {2162-237X}, doi = {10.1109/TNNLS.2013.2291772}, author = {Cong Li and Michael Georgiopoulos and Georgios C. Anagnostopoulos} } @article {38, title = {Efficient Revised Simplex Method for SVM Training}, journal = {Neural Networks, IEEE Transactions on}, volume = {22}, year = {2011}, month = {Oct.}, pages = {1650-1661}, abstract = {

Existing active set methods reported in the literature for support vector machine (SVM) training must contend with singularities when solving for the search direction. When a singularity is encountered, an infinite descent direction can be carefully chosen that avoids cycling and allows the algorithm to converge. However, the algorithm implementation is likely to be more complex and less computationally efficient than would otherwise be required for an algorithm that does not have to contend with the singularities. We show that the revised simplex method introduced by Rusin provides a guarantee of nonsingularity when solving for the search direction. This method provides for a simpler and more computationally efficient implementation, as it avoids the need to test for rank degeneracies and also the need to modify factorizations or solution methods based upon those rank degeneracies. In our approach, we take advantage of the guarantee of nonsingularity by implementing an efficient method for solving the search direction and show that our algorithm is competitive with SVM-QP and also that it is a particularly effective when the fraction of nonbound support vectors is large. In addition, we show competitive performance of the proposed algorithm against two popular SVM training algorithms, SVMLight and LIBSVM.

}, keywords = {active set method, learning (artificial intelligence), LIBSVM algorithm, quadratic programming, rank degeneracy, set theory, simplex method, support vector machine, Support vector machines, SVM training, SVMLight algorithm}, issn = {1045-9227}, doi = {10.1109/TNN.2011.2165081}, author = {Christopher G. Sentelle and Georgios C. Anagnostopoulos and Michael Georgiopoulos} } @conference {39, title = {Kernel principal subspace Mahalanobis distances for outlier detection}, booktitle = {Neural Networks (IJCNN), The 2011 International Joint Conference on}, year = {2011}, note = {

Acceptance rate 75\% (468/620).

}, month = {July}, publisher = {Institute of Electrical and Electronics Engineers (IEEE)}, organization = {Institute of Electrical and Electronics Engineers (IEEE)}, address = {San Jose, California, USA }, abstract = {

Over the last few years, Kernel Principal Component Analysis (KPCA) has found several applications in outlier detection. A relatively recent method uses KPCA to compute the reconstruction error (RE) of previously unseen samples and, via thresholding, to identify atypical samples. In this paper we propose an alternative method, which performs the same task, but considers Mahalanobis distances in the orthogonal complement of the subspace that is utilized to compute the reconstruction error. In order to illustrate its merits, we provide qualitative and quantitative results on both artificial and real datasets and we show that it is competitive, if not superior, for several outlier detection tasks, when compared to the original RE-based variant and the One-Class SVM detection approach.

}, keywords = {Image reconstruction, Kernel, kernel principal component analysis, Mahalanobis distance, Manifolds, orthogonal subspace complement, outlier detection, principal component analysis, reconstruction error, Single photon emission computed tomography, Support vector machines, Training}, doi = {10.1109/IJCNN.2011.6033548}, author = {Cong Li and Michael Georgiopoulos and Georgios C. Anagnostopoulos} } @conference {40, title = {Multinomial Squared Direction Cosines Regression}, booktitle = {Neural Networks (IJCNN), The 2011 International Joint Conference on}, year = {2011}, note = {

Acceptance rate 75\% (468/620).

}, month = {July}, publisher = {Institute of Electrical and Electronics Engineers (IEEE)}, organization = {Institute of Electrical and Electronics Engineers (IEEE)}, address = {San Jose, California, USA }, abstract = {

In this paper we introduce Multinomial Squared Direction Cosines Regression as an alternative Multinomial Response Model. The proposed model offers an intuitive geometric interpretation to the task of estimating posterior class probabilities in multi-class problems. In specific, the latter probabilities correspond to the squared direction cosines between a given pattern and representative class exemplars that form a basis in the decision space. We demonstrate that the model allows for efficient training via a trust region based Newton{\textquoteright}s Method, provided that the number of model parameters is not too large. Experimental results on several benchmark classification problems show that it compares competitively against Logistic Regression Classifiers, Support Vector Machines, and Classification and Regression Tree models.

}, keywords = {benchmark classification problem, Computational modeling, decision space, decision theory, geometric interpretation, Kernel, logistic regression classifier, Mathematical model, model parameter, multiclass problem, multinomial response model, multinomial squared direction cosines regression, Newton method, pattern classification, regression analysis, Regression tree analysis, regression tree model, support vector machine, Support vector machines, Training}, doi = {10.1109/IJCNN.2011.6033620}, author = {Naveed H. Iqbal and Georgios C. Anagnostopoulos} }