Multidimensional Scaling on Multiple Input Distance Matrices

Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have multiple heterogeneous representations. How to do multidimensional scaling on multiple input distance matrices is still unsolved to our best knowledge. In this paper, we first define this new task formally. Then, we propose a new algorithm called Multi-View Multidimensional Scaling (MVMDS) by considering each input distance matrix as one view. Our algorithm is able to learn the weights of views (i.e., distance matrices) automatically by exploring the consensus information and complementary nature of views. Experimental results on synthetic as well as real datasets demonstrate the effectiveness of MVMDS. We hope that our work encourages a wider consideration in many domains where MDS is needed

Probabilistic Learning on Manifolds: an overview of the algorithm

PLoM és un algorisme disenyat per generar realitzacions d'un determinat conjunt de dades. També es pot utilitzar amb certes restriccions aplicades sobre les noves realitzacions. Aquesta segona aplicació ajunta diversos passos i necessita condicions específiques per a converger. Té una interminable llista de possibles aplicacions, moltes en el camp de l'estadística i de la inteligencia artificial. En aquest projecte, aquest algorisme ha sigut revisat i provat amb alguns exemples.PLoM es un algoritmo diseñado para generar realizaciones de un determinado conjunto de datos. También puede ser usado con ciertas restricciones aplicadas sobre las nuevas realizaciones. Esta segunda aplicación junta varios pasos y necesita condiciones específicas para converger. Tiene una interminable lista de posibles aplicaciones, muchas en el campo de la estadística y de la inteligencia artificial. En este proyecto, este algoritmo ha sido revisado y provado con algunos ejemplos.PLoM is an algorithm focused on generating realizations of a given data set. It can be used with some constraints applied to the new realizations. This second application puts together many steps and needs specific conditions to converge. It has an endless list of applications most in the field of statistics and artificial intelligence. In this project, this algorithm has been reviewed and tested.Outgoin