@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} } @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} } @conference {43, title = {Multi-objective memetic evolution of ART-based classifiers}, booktitle = {Evolutionary Computation (CEC), 2010 IEEE Congress on}, year = {2010}, note = {

Nominated for Best Paper Award.

Acceptance rate 60\% (622/1027).

}, month = {July}, publisher = {Institute of Electrical and Electronics Engineers (IEEE)}, organization = {Institute of Electrical and Electronics Engineers (IEEE)}, address = {Barcelona, Spain}, abstract = {

In this paper we present a novel framework for evolving ART-based classification models, which we refer to as MOME-ART. The new training framework aims to evolve populations of ART classifiers to optimize both their classification error and their structural complexity. Towards this end, it combines the use of interacting sub-populations, some traditional elements of genetic algorithms to evolve these populations and a simulated annealing process used for solution refinement to eventually give rise to a multi-objective, memetic evolutionary framework. In order to demonstrate its capabilities, we utilize the new framework to train populations of semi-supervised Fuzzy ARTMAP and compare them with similar networks trained via the recently published MO-GART framework, which has been shown as being very effective in yielding high-quality ART-based classifiers. The experimental results show clear advantages of MOME-ART in terms of Pareto Front quality and density, as well as parsimony properties of the resulting classifiers.

}, keywords = {adaptive resonance theory, ART classifiers, ART-based classification models, ART-based classifiers, classification error, Complexity theory, Cooling, Electronic mail, fuzzy set theory, genetic algorithms, interacting subpopulations, Mathematical model, MO-GART framework, MOME-ART, multiobjective memetic evolutionary framework, Pareto front quality, Pareto optimisation, parsimony property, pattern classification, semisupervised fuzzy ARTMAP, simulated annealing, simulated annealing process, solution refinement, structural complexity, Subspace constraints, Training, training framework}, doi = {10.1109/CEC.2010.5586385}, author = {Rong Li and Timothy R. Mersch and Oriana X. Wen and Assem Kaylani and Georgios C. Anagnostopoulos} }