Rafik Abdesselam

Topological comparisons of proximity measures

In many fields of application, the choice of proximity measure directly affects the results of data mining methods, whatever the task might be: clustering, comparing or structuring of a set of objects. Generally, in such fields of application, the user is obliged to choose one proximity measure from many possible alternatives. According to the notion of equivalence, such as the one based on pre-ordering, certain proximity measures are more or less equivalent, which means that they should produce almost the same results. This information on equivalence might be helpful for choosing one such measure. However, the complexity O (n 4 ) of this approach makes it intractable when the size n of the sample exceeds a few hundred. To cope with this limitation, we propose a new approach with less complexity O (n 2 ). This is based on topological equivalence and it exploits the concept of local neighbors. It defines equivalence between two proximity measures as having the same neighborhood structure on the objects. We illustrate our approach by considering 13 proximity measures used on datasets with continuous attributes.

Typology of the French regional development: revealing the refugee versus Schumpeter effects in new-firm start-ups

In this article, we analyse the relationships between unemployment rates and new-firm start-up rates in France. Using a quarterly data basis covering the period 1993 to 2011, we identify, thanks to data analysis methods, different classes that show different types of development among the French regions. For each of these classes, the existence of refugee/Schumpeter effects both in the short run and in the long run is revealed. At the national level, it appears that the refugee effect explains the dynamics of entrepreneurship in France over the period 2000 to 2011. Necessity is the key motivation for new French firms.

Feature selection for multiclass support vector machines

In this paper, we present and evaluate a novel method for feature selection for Multiclass Support Vector Machines (MSVM). It consists in determining the relevant features using an upper bound of generalization error proper to the multiclass case called the multiclass radius margin bound. A score derived from this bound will rank the variables in order of relevance, then, forward method will be used to select the optimal subset. The experiments are firstly conducted on simulated data to test the ability of the score to give the correct order of relevance of variables and the ability of the proposed method to find the subset giving a better error rate than the case where all features are used. Afterward, four real datasets publicly available will be used and the results will be compared with those of other methods of variable selection by MSVM.

Discriminant Analysis on Mixed Predictors

The processing of mixed data – both quantitative and qualitative variables – cannot be carried out as explanatory variables through a discriminant analysis method. In this work, we describe a methodology of a discriminant analysis on mixed predictors. The proposed method uses simultaneously quantitative and qualitative explanatory data with a discrimination and classification aim. It’s a classical discriminant analysis carried out on the principal factors of a Mixed Principal Component Analysis of explanatory mixed variables, i.e. both quantitative and transformed qualitative variables associate to the dummy variables. An example resulting from real data illustrates the results obtained with this method, which are also compared with those of a logistic regression model.

Comparison of Proximity Measures for a Topological Discrimination

The results of any operation of clustering or classification of objects strongly depend on the proximity measure chosen. The user has to select one measure among many existing ones. Yet, according to the notion of topological equivalence chosen, some measures are more or less equivalent. In this paper, we propose a new approach to compare and classify proximity measures in a topological structure and in a context of discrimination. The concept of topological equivalence uses the basic notion of local neighborhood. We define the topological equivalence between two proximity measures, in the context of discrimination, through the topological structure induced by each measure. We propose a criterion for choosing the “best” measure, adapted to the data considered, among some of the most used proximity measures for quantitative or qualitative data. The principle of the proposed approach is illustrated using two real datasets with conventional proximity measures of literature for quantitative and qualitative variables. Afterward, we conduct experiments to evaluate the performance of this discriminant topological approach and to test if the proximity measure selected as the “best” discriminant changes in terms of the size or the dimensions of the used data. The “best” discriminating proximity measure will be verified a posteriori using a supervised learning method of type Support Vector Machine, discriminant analysis or Logistic regression applied in a topological context.

Comparison of Proximity Measures: A Topological Approach

In many application domains, the choice of a proximity measure affect directly the result of classification, comparison or the structuring of a set of objects. For any given problem, the user is obliged to choose one proximity measure between many existing ones. However, this choice depend on many characteristics. Indeed, according to the notion of equivalence, like the one based on pre-ordering, some of the proximity measures are more or less equivalent. In this paper, we propose a new approach to compare the proximity measures. This approach is based on the topological equivalence which exploits the concept of local neighbors and defines an equivalence between two proximity measures by having the same neighborhood structure on the objects.We compare the two approaches, the pre-ordering and our approach, to thirty five proximity measures using the continuous and binary attributes of empirical data sets.

A Test of LBO Firms' Acquisition Rationale: The French Case

We investigate whether the characteristics of Leveraged Buy-Out (LBO) targets before the deal differ from those of targets that have undergone another type of transfer of shares. Specifically, we examine the size, value, industry, quotation and profitability of French targets involved in transfers of shares between 1996 and 2004. Using two different methods (a classical logit regression and a mixed discriminant analysis), results show that LBO targets are more profitable, that they are more frequently unquoted, and that they more often belong to manufacturing industries in comparison with the targets involved in other types of transfers of shares.

Differences in financial and legal system and contribution of private equity funds to transfers of shares in Europe

This article deals with the role of private equity in the financing of transfers of shares in five European countries: France, Germany, Italy, Spain and the United Kingdom. These countries have been chosen because their corporate governance systems still remain different in spite of the process of European integration. We first identify the expected effects of the main characteristics of national financial and legal systems on the activity of private equity funds. Second, we use a sample of deals collected from the Zephyr database to investigate the similarities (and dissimilarities) between European countries in the role played by private equity in transfers of shares. Our results show that the French case is very specific and opposite to the British case. In France, private equity funds play a more important role in the financing of transfers of shares than in other countries. This result supports the thesis of a specific French corporate governance model and leads us to refute the hypothesis of the convergence towards the Anglo-American model for the French corporate governance system.

Sequential decisional discriminant analysis

We are describing here a sequential discriminant analysis method which aim is essentially to classify evolutionary data. This method of decision-making is based on the research of principal axes of a configuration of points in the individual-space with a relational inner product. We are in presence of a discriminant analysis problem, in which the decision must be taken as the partial knowledge evolutionary information of the observations of the statistical unit, which we want to classify. We show here how the knowledge from the observation of the global testimony sample carried out during the entire period, can be of particular benefit to the classifying decision on supplementary statistical units, of which we only have partial information about. An analysis using real data is here described using this method.

A Geometrical Relational Model for Data Analysis

The proposed model allows analyses which are more powerful than Factorial Discriminant or Correspondence Analyses; it may be considered as a useful complement to Multivariate Analysis of Variance. Comparing to MANOVA, statistics are not carried out from variables, but from statistical units. The statistical unit space, linked to the variable space by an isometry, contains two orthogonal subspaces associated to mean and residual values as well.