Magnification factors for the SOM and GTM algorithms

Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

A stage-oriented model (SOM) for e-commerce adoption:a study of Saudi Arabian organisations

Purpose - The purpose of this paper is to construct a new e-commerce innovation and adoption model that takes into account various stages of e-commerce adoption (interactive, non-interactive and stabilised) and covers technological, organisational and environmental factors. This was tested using data collected from manufacturing and service companies in Saudi Arabia (SA) to reveal inhibitors and catalysts for e-commerce adoption. Design/methodology/approach - This study uses new data from surveys from 202 companies and then uses exploratory factor analysis and structural equation modelling for analyses. Findings - This study shows that the new stage-oriented model (SOM) is valid and can reveal specific detailed nuances of e-commerce adoption within a particular setting. Surprising results show that SA is not so very different to developed western countries in respect to e-commerce adoption. However there are some important differences which are discussed in detail. Research limitations/implications - A new SOM for e-commerce adoption is provided which may be used by other IS adoption researchers. Practical implications - Managers responsible for the adoption of e-commerce in SA, the Middle East and beyond can learn from these findings to speed up adoption rates and make e-commerce more effective. Social implications - This work may help spread e-commerce use throughout SA, the Middle East and to other developing nations. Originality/value - The results add to the extremely limited number of empirical studies that has been conducted to investigate e-commerce adoption in the context of Arabic countries.