@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 {42, title = {Metric representations of data via the Kernel-based Sammon Mapping}, booktitle = {Neural Networks (IJCNN), The 2010 International Joint Conference on}, year = {2010}, note = {

Acceptance rate 71.5\% (621/868).

}, 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 generalization of Sammon{\textquoteright}s Mapping (SM), which is a popular, metric multi-dimensional scaling technique used in data analysis and visualization. The new approach, namely the Kernel-based Sammon Mapping (KSM), yields the classic SM and other much related techniques as special cases. Apart from being able to approximate distance-preserving projections, it can also learn to metrically represent arbitrarily-defined dissimilarities or similarities between samples. Moreover, it can handle equally well numeric, categorical or mixed-type data. It is able to accomplish all this by modeling its projections as linear combinations of appropriate kernel functions. We report experimental results, which showcase KSM{\textquoteright}s capabilities in visually representing several meaningful relationships between samples of selected datasets.

}, keywords = {data analysis, data visualisation, data visualization, distance-preserving projections, kernel-based Sammon mapping, metric multidimensional scaling technique, metric representations, Visualization}, doi = {10.1109/IJCNN.2010.5596662}, author = {Mingbo Ma and Ryan Gonet and RuiZhi Yu and Georgios C. Anagnostopoulos} }