LIAAD

"Starting from the main idea of Symbolic Data Analysis to extend statistics and data mining methods from first-order to second-order objects, we focus on network data as defined in the
framework of Social Network Analysis in order to define a graph structure and the underlying network in the context of complex data objects. A Network Symbolic Object is defined according to the statistical characterization of the network topological properties. We deal with the choice of suitable network measures transformed in symbolic variables. Their study through multidimensional data analysis, allows the synthetic representation of a network as a point onto a metric space. The proposed approach is discussed on the basis of a simulation study considering three classical network growth processes."

This paper introduces a partitioning clustering method for objects described by interval data. It follows the dynamic clustering approach and uses and L 2 distance. Particular emphasis is put on the standardization problem where we propose and investigate three standardization techniques for interval-type variables. Moreover, various tools for cluster interpretation are presented and illustrated by simulated and real-case data.

A parametric modelling for interval data is proposed, assuming a multivariate Normal or Skew-Normal
distribution for the midpoints and log-ranges of the interval variables. The intrinsic nature of the interval
variables leads to special structures of the variance–covariance matrix, which is represented by five
different possible configurations. Maximum likelihood estimation for both models under all considered
configurations is studied. The proposed modelling is then considered in the context of analysis of variance
and multivariate analysis of variance testing. To access the behaviour of the proposed methodology, a simulation
study is performed. The results show that, for medium or large sample sizes, tests have good power
and their true significance level approaches nominal levels when the constraints assumed for the model are
respected; however, for small samples, sizes close to nominal levels cannot be guaranteed. Applications to
Chinese meteorological data in three different regions and to credit card usage variables for different card
designations, illustrate the proposed methodology.

Symbolic objects (Diday (1987, 1992), Brito, Diday (1990), Brito (1991)) allow to model data on the form of descriptions by intension, thus generalizing the usual tabular model of data analysis. This modelisation allows to take into account variability within a set. The formalism of symbolic objects has some notions in common with VL1, proposed by Michalski (1980); however VL1 is mainly based on prepositional and predicate calculus, while the formalism of symbolic objects allows for an explicit interpretation within its framework, by considering the duality intension-extension. That is, given a set of observations, we consider the couple (symbolic object — extension in the given set). This results from the wish to keep a statistics point of view. The need to represent non-deterministic knowledge, that is, data for which the values for the different variables are assigned a weight, led to considering an extension of assertion objects to probabilist objects (Diday 1992). In this case, data are represented by probability distributions on the variables observation sets. The notions previously defined for assertion objects are the generalized to this new kind of symbolic objects. Other extensions can be found in Diday (1992). In order to obtain a clustering structure on the data, we propose a pyramidal symbolic clustering method. Methods of conceptual clustering have known a great improvement in the last years. These methods aim at obtaining a system of interpreted clusters. In the eighties a large number of conceptual clustering methods have been developed, mention should be made to Michalski (1980), Michalski, Diday and Stepp (1982), Fisher (1987). The pyramidal model (Diday (1984,1986), Bertrand (1986)) generalizes hierarchical clustering by presenting an overlapping instead of a partition at each level; pyramidal clustering produces a structure which is nevertheless much simpler than the lattice structure, since each cluster should be an interval of a total order θ (as a consequence, pyramids present no crossing in the graphic representation). So, the pyramidal model supplies a structure which is richer than hierarchical trees (in that it keeps more information), and that, compared to lattices, are easily interpretable. The method we present builds a pyramid by an agglomerative algorithm. Each cluster is represented by a symbolic object whose extension — that is the set of elements verifying it — is the cluster itself. Hence a cluster is represented by a couple extension — intension. An application on textual data modelled by probabilist objects (texts described by frequency of key-words) allowed to obtain a pyramid whose clusters (representing though groups of texts) are themselves represented by probabilist objects, we thus identify groups of texts refering to close subjects.