Consistance d'un estimateur de minimum de variance étendue

National audienceWe consider a generalization of the criterion minimized by the K-means algorithm, where a neighborhood structure is used in the calculus of the variance. Such tool is used, for example with Kohonen maps, to measure the quality of the quantification preserving the neighborhood relationships. If we assume that the parameter vector is in a compact Euclidean space and all it components are separated by a minimal distance, we show the strong consistency of the set of parameters almost realizing the minimum of the empirical extended variance

A new approach for data visualization problem

Data visualization is the process of transforming data, information, and knowledge into visual form, making use of humans’ natural visual capabilities which reveals relationships in data sets that are not evident from the raw data, by using mathematical techniques to reduce the number of dimensions in the data set while preserving the relevant inherent properties. In this paper, we formulated data visualization as a Quadric Assignment Problem (QAP), and then presented an Artificial Bee Colony (ABC) to solve the resulted discrete optimization problem. The idea behind this approach is to provide mechanisms based on ABC to overcome trapped in local minima and improving the resulted solutions. To demonstrate the application of ABC on discrete optimization in data visualization, we used a database of electricity load and compared the results to other popular methods such as SOM, MDS and Sammon's map. The results show that QAP-ABC has high performance with compared others

Analyse of artificial neural network clustering ability for deformation analysis

In this work the clustering abilities of artificial neural network are tested. So, this thesis is a practical test of clustering abilities of the geodynamic velocity vectors, however, the results are not meant to be used by geologists, but only for learning about the neural network workings and abilities. Clustering is a procedure of connecting similar objects to groups. In this work, the objects are represented by velocity vectors. The network I was using is a simplified version of Kohonen self organising map. I am using a single layer of neurons with Kohonen competitive learning rule. Neurons are not topologically ordered. Learning is a procedure of representing input data to the network. In each step the properties of neurons are adapted. Speaking for competitive training, all neurons at the same time receive input vector but parameters are adapted only to a neuron that fits vector best. The neuron is adapted in such a way that it will even better correspond when represented by similar vectors. The computations were done by using Matlab's Neural network toolbox, where some types and learning rules are already contained. For representing results of clustering I used AutoCad 2005. The procedure was tested by solving four tasks. I made data for first three by myself and the fourth was a practical test of method on real observations of geodynamic velocities from California. I found that neural network is a very interesting way of clustering for we can not assume what the results will be like in common clustering methods. But at the same time I show that the method is unreliable, so we should not use it for tasks, where results have to be precise