arXiv subjects
Publications and source records attributed to Marie Cottrell.
We study a system of interacting renewal processes which is a model for neuronal activity. We show that the system possesses an exponentially large number (with respect to the number of neurons in the network) of limiting configurations of the "firing neurons". These we call patterns. Furthermore, under certain conditions of symmetry we find an algorithm to control limiting patterns by means of the connection parameters.
Using the Panel Study of Income Dynamics data on the period 1982-1992, this paper investigates some mechanisms of the labor market in the United States. This market is analyzed as a stable structure constituted of segments which present contrasted characteristics under the usual distinction between primary and secondary sectors. Using a neural network algorithm applied on quantitative variables measured at the level of heads of household, a broad classification in four classes of situations is constructed. It shows a clear hierarchy going from situations of very precarious work or no work at all, to situations of stable jobs with higher wages than the average. A Markov chain, constructed with the trajectories between the different situations of these workers, shows a very stable structure of this segmented labor market. Keywords: segmented labor market, unemployment, trajectories, Kohonen algorithm, Markov chain.
In France, for administrative reasons, unemployed workers may actually be involved in occasional work while remaining identified as unemployed (and receiving the corresponding benefit). This is due to the fact that the unemployed are deemed to be seeking full-time jobs and non-fixed term contracts of employment. This situation may be analysed as evidence of a special type of secondary segment of the labour market in a context of massive unemployment. The authors consider the effects of this situation both on the duration of unemployment and its recurrence may be usefully investigated.
This study focuses on recurring unemployment, that is people with two or more spells of unemployment during the period of observation (July 1993 - August 1996). First, a classification is obtained which is then used to examine the specific role of occasional jobs during a spell of unemployment and, in this context, the influence of the received unemployment benefits on the duration of this spell. This paper is a continuation of previous analyses of unemployment in France, based on long-term data from the unemployed register held by ANPE (National Employment Bureau). The present analysis conducted using additional information about unemployment benefits received by the unemployed from UNEDIC (Unemployment Benefits Office).
In the analysis of poverty and social exclusion, indicators of living conditions are some interesting non-monetary complements to the usual measurements in terms of current or annual income. Living conditions depend in fact on longer term factors than income, and provide further information on households' actual resources that allow to compare more accurately between living standards. But in counterpart, a difficulty comes from the qualitative nature of the information, and the large number of dimensions and items that may be taken into account; in other words, living conditions are difficult to "measure". A consequence is that very often, the information is either used only partly, or reduced into a global score of (bad) living conditions, that results from counting "negative" items, and the qualitative dimension is lost. In this paper, we propose to use the Kohonen algorithm first to describe how the elements of living conditions are combined, and secondly to classify households according to their living conditions. The main interest of a classification is to make appear not only quantitative differences in the "levels" of living conditions, but also qualitative differences within similar "levels".
Kohonen self-organisation maps are a well know classification tool, commonly used in a wide variety of problems, but with limited applications in time series forecasting context. In this paper, we propose a forecasting method specifically designed for multi-dimensional long-term trends prediction, with a double application of the Kohonen algorithm. Practical applications of the method are also presented.
The processing of data which contain missing values is a complicated and always awkward problem, when the data come from real-world contexts. In applications, we are very often in front of observations for which all the values are not available, and this can occur for many reasons: typing errors, fields left unanswered in surveys, etc. Most of the statistical software (as SAS for example) simply suppresses incomplete observations. It has no practical consequence when the data are very numerous. But if the number of remaining data is too small, it can remove all significance to the results. To avoid suppressing data in that way, it is possible to replace a missing value with the mean value of the corresponding variable, but this approximation can be very bad when the variable has a large variance. So it is very worthwhile seeing that the Kohonen algorithm (as well as the Forgy algorithm) perfectly deals with data with missing values, without having to estimate them beforehand. We are particularly interested in the Kohonen algorithm for its visualization properties.
Pseudo panels constituted with repeated cross-sections are good substitutes to true panel data. But individuals grouped in a cohort are not the same for successive periods, and it results in a measurement error and inconsistent estimators. The solution is to constitute cohorts of large numbers of individuals but as homogeneous as possible. This paper explains a new way to do this: by using a self-organizing map, whose properties are well suited to achieve these objectives. It is applied to a set of Canadian surveys, in order to estimate income elasticities for 18 consumption functions..
Results of neural network learning are always subject to some variability, due to the sensitivity to initial conditions, to convergence to local minima, and, sometimes more dramatically, to sampling variability. This paper presents a set of tools designed to assess the reliability of the results of Self-Organizing Maps (SOM), i.e. to test on a statistical basis the confidence we can have on the result of a specific SOM. The tools concern the quantization error in a SOM, and the neighborhood relations (both at the level of a specific pair of observations and globally on the map). As a by-product, these measures also allow to assess the adequacy of the number of units chosen in a map. The tools may also be used to measure objectively how the SOM are less sensitive to non-linear optimization problems (local minima, convergence, etc.) than other neural network models.
Self-organizing maps (SOM) are widely used for their topology preservation property: neighboring input vectors are quantified (or classified) either on the same location or on neighbor ones on a predefined grid. SOM are also widely used for their more classical vector quantization property. We show in this paper that using SOM instead of the more classical Simple Competitive Learning (SCL) algorithm drastically increases the speed of convergence of the vector quantization process. This fact is demonstrated through extensive simulations on artificial and real examples, with specific SOM (fixed and decreasing neighborhoods) and SCL algorithms.
Bootstrap techniques (also called resampling computation techniques) have introduced new advances in modeling and model evaluation. Using resampling methods to construct a series of new samples which are based on the original data set, allows to estimate the stability of the parameters. Properties such as convergence and asymptotic normality can be checked for any particular observed data set. In most cases, the statistics computed on the generated data sets give a good idea of the confidence regions of the estimates. In this paper, we debate on the contribution of such methods for model selection, in the case of feedforward neural networks. The method is described and compared with the leave-one-out resampling method. The effectiveness of the bootstrap method, versus the leave-one-out methode, is checked through a number of examples.
Seeking to determine which working patterns have a specific effect on part-time work, in 1998-99 France's INSEE statistical agency carried out a Timetable survey that questioned the homogeneity of this form of employment (again in terms of the working patterns upon which it is based). A neuronal method was used to classify an entire sample of part-time employees according to their weekly working patterns -the end result being that part-time work was shown to be a very heterogeneous form of employment. This was not only reflected by the existence of many different groups of part-time employees, each with highly differentiated individual and professional characteristics, but also (and above all) by the diversity of their weekly working patterns.
This paper shows how to use the Kohonen algorithm to represent multidimensional data, by exploiting the self-organizing property. It is possible to get such maps as well for quantitative variables as for qualitative ones, or for a mixing of both. The contents of the paper come from various works by SAMOS-MATISSE members, in particular by E. de Bodt, B. Girard, P. Letrémy, S. Ibbou, P. Rousset. Most of the examples have been studied with the computation routines written by Patrick Letrémy, with the language IML-SAS, which are available on the WEB page http://samos.univ-paris1.fr.
In the present article, we attempt to devise a typology of forms of part-time employment by applying a widely used neuronal methodology called Kohonen maps. Starting out with data that we describe using category-specific variables, we show how it is possible to represent observations and the modalities of the variables that define them simultaneously, on a single map. This allows us to ascertain, and to try to describe, the main categories of part-time employment.
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 Université Paris I Panthéon Sorbonne (SAMOS-MATISSE research centre) organized WSOM 2005 in Paris on September 5-8, 2005.
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.
It is well known that the SOM algorithm achieves a clustering of data which can be interpreted as an extension of Principal Component Analysis, because of its topology-preserving property. But the SOM algorithm can only process real-valued data. In previous papers, we have proposed several methods based on the SOM algorithm to analyze categorical data, which is the case in survey data. In this paper, we present these methods in a unified manner. The first one (Kohonen Multiple Correspondence Analysis, KMCA) deals only with the modalities, while the two others (Kohonen Multiple Correspondence Analysis with individuals, KMCA\_ind, Kohonen algorithm on DISJonctive table, KDISJ) can take into account the individuals, and the modalities simultaneously.
Neural Gas (NG) constitutes a very robust clustering algorithm given euclidian data which does not suffer from the problem of local minima like simple vector quantization, or topological restrictions like the self-organizing map. Based on the cost function of NG, we introduce a batch variant of NG which shows much faster convergence and which can be interpreted as an optimization of the cost function by the Newton method. This formulation has the additional benefit that, based on the notion of the generalized median in analogy to Median SOM, a variant for non-vectorial proximity data can be introduced. We prove convergence of batch and median versions of NG, SOM, and k-means in a unified formulation, and we investigate the behavior of the algorithms in several experiments.