How to use the Kohonen algorithm to simultaneously analyse individuals in a survey

The Kohonen algorithm (SOM, Kohonen,1984, 1995) is a very powerful tool for data analysis. It was originally designed to model organized connections between some biological neural networks. It was also immediately considered as a very good algorithm to realize vectorial quantization, and at the same time pertinent classification, with nice properties for visualization. If the individuals are described by quantitative variables (ratios, frequencies, measurements, amounts, etc.), the straightforward application of the original algorithm leads to build code vectors and to associate to each of them the class of all the individuals which are more similar to this code-vector than to the others. But, in case of individuals described by categorical (qualitative) variables having a finite number of modalities (like in a survey), it is necessary to define a specific algorithm. In this paper, we present a new algorithm inspired by the SOM algorithm, which provides a simultaneous classification of the individuals and of their modalities.Comment: Special issue ESANN 0

Designing Incentive-Alignment Contracts in a Principal-Agent Setting in the Presence of Real Options

We develop a model of incentive compensation for optimal upgrades supplied by an outsourced Information Technology department. We first consider the problem when the rate of technological development is certain and there are no information asymmetries between the parties. We extend this to allow private information between the principal and an agent acting as an external supplier of information technology upgrades. Based on the model in these simple circumstances, we then model uncertain technological improvements, where improvements evolve as Geometric Brownian motion, and there is benefit to flexibility in the timing of the upgrade. We are aware of contracts, known as "evergreen upgrades", where a principal pays for upgrades at specified intervals. We find little support for such a contract in our model, and the loss of flexibility in the timing of upgrades is puzzling. The Stern-Stewart problem encourages us to consider just such instances, where contracts limit flexibility that it may in the interest of both parties to retain

Advances in Self Organising Maps

The Self-Organizing Map (SOM) with its related extensions is the most popular artificial neural algorithm for use in unsupervised learning, clustering, classification and data visualization. Over 5,000 publications have been reported in the open literature, and many commercial projects employ the SOM as a tool for solving hard real-world problems. Each two years, the "Workshop on Self-Organizing Maps" (WSOM) covers the new developments in the field. The WSOM series of conferences was initiated in 1997 by Prof. Teuvo Kohonen, and has been successfully organized in 1997 and 1999 by the Helsinki University of Technology, in 2001 by the University of Lincolnshire and Humberside, and in 2003 by the Kyushu Institute of Technology. The Universit\'{e} Paris I Panth\'{e}on Sorbonne (SAMOS-MATISSE research centre) organized WSOM 2005 in Paris on September 5-8, 2005.Comment: Special Issue of the Neural Networks Journal after WSOM 05 in Pari

Finding structural anomalies in star graphs: A general approach

We develop a general theory for a quantum-walk search on a star graph. A star graph has N edges each of which is attached to a central vertex. A graph G is attached to one of these edges, and we would like to find out to which edge it is attached. This is done by means of a quantum walk, a quantum version of a random walk. This walk contains O(\sqrt{N}) steps, which represents a speedup over a classical search, which would require O(N) steps. The overall graph, star plus G, is divided into two parts, and we find that for a quantum speedup to occur, the eigenvalues associated with these two parts in the N goes to infinity limit must be the same. Our theory tells us how the initial state of the walk should be chosen, and how many steps the walk must make in order to find G.Comment: Replaced with published versio