Patrick Rousset

The Kohonen Algorithm: A Powerful Tool for Analyzing and Representing Multidimensional Quantitative and Qualitative Data

The simultaneous analysis of quantitative and qualitative variables is not an easy task in general. When a linear model is appropriate, the Generalized Linear Models are commonly used with success. But when the intrinsic structure of the data is not at all linear, they give very poor and confusing results. In this paper, we extensively study how to use the (non linear) Kohonen maps to solve some of the interesting problems which are encountered in data analysis: how to realize a rapid and robust classification based on the quantitative variables, how to visualize the classes, their differences and homogeneity, how to cross the classification with the remaining qualitative variables to interpret the classification and put in evidence the most important explanatory variables.

Daily Electrical Power Curves: Classification and Forecasting Using a Kohonen Map

This paper addresses an extensively studied problem: how to forecast the daily half-hour electrical power curve. Many methods have been developed, classical linear methods (like ARIMA methods) as well as neural ones. In this paper, we present a very simple method: the past daily curves are normalized and one considers the corresponding profile (with mean 0 and variance 1). These profiles are classified using a Kohonen map. Then, for some future point, a strategy is defined in order to compute its typical profile, the mean and the variance are forecast and the expected power curve is computed. This method uses little computation time and is easy to develop. The first results are satisfactory and promising.

Understanding and reducing variability of SOM neighbourhood structure

The self-organizing map (SOM) is a nonlinear unsupervised method for vector quantization. In the context of classification and data analysis, the SOM technique highlights the neighbourhood structure between clusters. The correspondence between this clustering and the input proximity is called the topology preservation. We present here a stochastic method based on bootstrapping in order to increase the reliability of the induced neighbourhood structure. Considering the property of topology preservation, a local approach of variability (at an individual level) is preferred to a global one. The resulting (robust) map, called R-map, is more stable relatively to the choice of the sampling method and to the learning options of the SOM algorithm (initialization and order of data presentation). The method consists of selecting one map from a group of several solutions resulting from the same self-organizing map algorithm, but obtained with various inputs. The R-map can be thought of as the map, among the group of solutions, corresponding to the most common interpretation of the data set structure. The R-map is then the representative of a given SOM network, and the R-map ability to adjust the data structure indicates the relevance of the chosen network.

Classifying qualitative time series with SOM: the typology of career paths in France

The purpose of this paper is to present a typology of career paths in France with the Kohonen algorithm and its generalization to a clustering method of life history using Self Organizing Maps. Several methods have already been proposed to transform qualitative information into quantitative one such as being able to apply clustering algorithm based on the Euclidean distance such as SOM. In the case of life history, these methods generally ignore the longitudinal organization of the data. Our approach aims to deduce a quantitative encode from the labor market situation proximities across time. Using SOM, the topology preservation is also helpful to check when the new encoding keep particularities of the life history and our economic approach of careers. In final, this quantitative encoding can be easily generalized to a method of clustering life history and complete the set of methods generalizing the use of SOM to qualitative data.

Long Term Forecasting by Combining Kohonen Algorithm and Standard Prevision

To forecast a complete curve is a delicate problem, since the existing methods (vectorial prevision, long-term forecasting) are difficult to use and often give disappointing results. We propose a new strategy that consists in dividing up the problem into three sub-problems: prediction of the mean value and of the standard deviation and estimation of the normalized curve (the profile). The mean value and the standard deviation are predicted by any classical method (linear or neural). As to the profile, it is estimated with the help of a previous classification. The results are very convincing and a real-world application is presented : the polish electrical consumption.

Distance between Kohonen Classes Visualization Tool to Use SOM in Data Set Analysis and Representation

Representation of information given by clustering methods is of little satisfaction. Some tools able to localize classes into the input space are expected in order to provide a good visual support to the analysis of classification results. Actually, clusters are often visualized with the planes produced by factorial analysis. These representations are sometimes unsatisfying, for example when the intrinsic structure of the data is not at all linear or when the compression phenomenon generated by projections on factorial planes is very important. In the family of clustering methods, the Kohonen algorithm has the originality to organize classes considering the neighborhood structure between them [9][10][6]. It is interesting to notice that many transcription in graphical display have been conceived to optimize the visual exploitation of this neighborhood structure [5][11]. Each one helps the interpretation in a particular context. they are twinned to the Kohonen algorithm and called Kohonen maps. For example, one used in the following helps the interpretation of the classification from an exogenous or endogenous qualitative variable. Unfortunately, no one allows for a visualization of the data set structure in the input space. This is very regrettable when the Kohonen map makes such a folder that two classes close to each other in the input space can be far on the map. A tool that visualizes distances between all classes gives a representation of the classification structure in the input space. Such a tool is proposed in the following. As the Kohonen algorithm has the property to reveal effects of small distances also called local distances and the new tool is able to control big distances, this clustering method has now a large field of exploitation.

Typologies de parcours et dynamique longitudinale

Life Course Typologies et Longitudinal Dynamics: In this paper, we propose a method for developing typologies of individual itineraries that takes into account the dynamics of longitudinal timelines. It applies when these timelines are developed from calendars. The originality of this method lies both in the method of calculating the distance between trajectories, and the classification procedure based on Kohonen self-organizing maps. The main property of the metric is to take into account the proximity between different states and its evolution over time. We propose an application in the analysis of career paths using Céreq data for monthly monitoring over seven years for youths who left the education system in 1998. Our results highlight the importance of temporal dynamics in the construction of timelines of entry into the workforce. Finally, we examine the role and contributions of this method by comparing it to the most commonly used methods for constructing timeline typologies.

Utilisation des cartes d’auto-organisation dans la classification, illustration par des exemples

Self-organising maps used for classification, illustration with several examples: The aim of this paper is to illustrate, with several examples, the possible uses of self-organizing maps (som), especially in classification and data-set visualization purposes. This classification method, based on the unsupervised leaming algorithm of Kohonen, is presented here in a practical manner, and applied in the following fields : characterisation of human skin, Polish national daily consumption of electricity, training supply and professional careers. The diversity of the examples, in thèse application fields and for various statistical purposes (typology, classification of curves), illustrate many self-organizing map characteristics as compared to more traditional methods. In particular, we should mention, firstly, that the clustering method and its représentation system are complementary; secondly, that som are sensitive to small distances and, finally, that they can be pertinent when the data set is large. Thèse properties make it possible to visualize cluster proximities, local effects (restricted to a part of the population) and integrate many variables into the analysis (for example, as in data mining). Apart from clustering, self-organizing maps can also be used as a visualization tool for the représentation of data-set intrinsic structure. In this case, as with projections to principal planes of the factorial analysis, this data-set représentation can be considered a graphical support for any analysis method. To illustrate its characteristics, we use it to represent two hierarchical classification results. In this instance, the particularity of this technique comes from the specificity of its own symbolic représentation. It gives to som a freedom that allows it to be well adapted to complex structures such as non-linear ones. In this paper, self-organizing maps are presented first as a clustering method, and then as a tool for the visualization of dataset intrinsic structure.

Increasing reliability of SOMs’ neighbourhood structure with a bootstrap process

One of the most interesting features of self-organizing maps is the neighbourhood structure between classes highlighted by this technique. The aim of this paper is to present a stochastic method based on bootstrap process for increasing the reliability of the induced neighbourhood structure. The robustness under interest here concerns the sensitivities of the output to the sampling method and to some of the learning options (the initialisation and the order of data presentation). The presented method consists in selecting one map between a group of several solutions resulting from the same self-organizing map algorithm but with various inputs. The selected (robust) map, called R-map, can be perceived as the map, among the group, that corresponds to the most common interpretation of the data set structure.