@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} } @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} }