@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} } @conference {41, title = {Accelerated learning of Generalized Sammon Mappings}, 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 = {

The Sammon Mapping (SM) has established itself as a valuable tool in dimensionality reduction, manifold learning, exploratory data analysis and, particularly, in data visualization. The SM is capable of projecting high-dimensional data into a low-dimensional space, so that they can be visualized and interpreted. This is accomplished by representing inter-sample dissimilarities in the original space by Euclidean inter-sample distances in the projection space. Recently, Kernel Sammon Mapping (KSM) has been shown to subsume the SM and a few other related extensions to SM. Both of the aforementioned models feature a set of linear weights that are estimated via Iterative Majorization (IM). While IM is significantly faster than other standard gradient-based methods, tackling data sets of larger than moderate sizes becomes a challenging learning task, as IM{\textquoteright}s convergence significantly slows down with increasing data set cardinality. In this paper we derive two improved training algorithms based on Successive Over-Relaxation (SOR) and Parallel Tangents (PARTAN) acceleration, that, while still being first-order methods, exhibit faster convergence than IM. Both algorithms are relatively easy to understand, straightforward to implement and, performance-wise, are as robust as IM. We also present comparative results that illustrate their computational advantages on a set of benchmark problems.

}, keywords = {accelerated learning, Acceleration, Convergence, data visualization, dimensionality reduction, Euclidean inter-sample distances, exploratory data analysis, generalized Sammon mappings, inter-sample dissimilarities, iterative majorization, Kernel, kernel Sammon mapping, learning (artificial intelligence), manifold learning, parallel tangents acceleration, projection space, Prototypes, standard gradient-based methods, Stress, successive over-relaxation, Training}, doi = {10.1109/IJCNN.2011.6033609}, author = {Yinjie Huang 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} }