Generalized Non-metric Multidimensional Scaling

Using Multidimensional Scaling for Assessment Economic Development of Regions

Addressing socio-economic development issues are strategic and most important for any country. Multidimensional statistical analysis methods, including comprehensive index assessment, have been successfully used to address this challenge, but they donchr('39')t cover all aspects of development, leaving some gap in the development of multidimensional metrics. The purpose of the study is to const...

Numerical Geometry of Non-rigid Objects: Embedding Problems

Non-rigid shapes appear at all scales in nature – from our body, its organs and tissues, to tiny bacteria and microscopic protein molecules. Being so ubiquitous, such shapes are often encountered in pattern recognition and computer vision applications. The main challenge appears to be the richness and the amount of degrees of freedom of the class of possible non-rigid deformations. Among the va...

Distance-Based Partial Least Squares Analysis

Distances matrices are traditionally analyzed with statistical methods that represent distances as maps such as Metric Multidimensional Scaling (MDS), Generalized Procrustes Analysis (GPA), Individual Differences Scaling (INDSCAL), and DISTATIS. MDS analyzes only one distance matrix at a time while GPA, INDSCAL and DISTATIS extract similarities between several distance matrices. However, none o...

Multi-Dimensional Scaling Assignment ‘Non-metric multidimensional scaling on data from the USA Beer Market’

An Adaptive Multidimensional Scaling and Principled Nonlinear Manifold

The self-organizing map (SOM) and its variant, the visualization induced SOM (ViSOM), have been linked with principal manifolds. They have also been shown to yield similar results to multidimensional scaling (MDS). However the exact connection has not yet been established. In this paper we first examine their relationship with (generalized) MDS from their cost functions in the aspect of data vi...