Abstract
Symbolic Data Analysis (SDA) provides a framework for the representation and analysis of data that comprehends inherent variability. While in Data Mining and classical Statistics the data to be analyzed usually presents one single value for each variable, that is no longer the case when the entities under analysis are not single elements, but groups gathered on the basis of some given criteria. Then, for each variable, variability inherent to each group should be taken into account. Also, when analysing concepts, such as botanic species, disease descriptions, car models, and so on, data entail intrinsic variability, which should be explicitly considered. To this purpose, new variable types have been introduced, whose realizations are not single real values or categories, but sets, intervals, or, more generally, distributions over a given domain. SDA provides methods for the (multivariate) analysis of such data, where the variability expressed in the data representation is taken into account, using various approaches. (C) 2014 John Wiley & Sons, Ltd.

Abstract
In this work, we study reverse complementary genomic word pairs in the human DNA, by comparing both the distance distribution and the frequency of a word to those of its reverse complement. Several measures of dissimilarity between distance distributions are considered, and it is found that the peak dissimilarity works best in this setting. We report the existence of reverse complementary word pairs with very dissimilar distance distributions, as well as word pairs with very similar distance distributions even when both distributions are irregular and contain strong peaks. The association between distribution dissimilarity and frequency discrepancy is also explored, and it is speculated that symmetric pairs combining low and high values of each measure may uncover features of interest. Taken together, our results suggest that some asymmetries in the human genome go far beyond Chargaff's rules. This study uses both the complete human genome and its repeat-masked version.

Abstract
In this work we explore the dissimilarity between symmetric word pairs, by comparing the inter-word distance distribution of a word to that of its reversed complement. We propose a new measure of dissimilarity between such distributions. Since symmetric pairs with different patterns could point to evolutionary features, we search for the pairs with the most dissimilar behaviour. We focus our study on the complete human genome and its repeat-masked version. © Springer International Publishing AG 2017.

Abstract
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-to define a graph structure and the underlying network in the context of complex data objects. A Network Symbolic description is defined according to the statistical characterization of the network topological properties. We use suitable network measures, which are represented by means of symbolic variables. Their study through multidimensional data analysis, allows for 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.

Abstract
Building on probabilistic models for interval-valued variables, parametric classification rules, based on Normal or Skew-Normal distributions, are derived for interval data. The performance of such rules is then compared with distancebased methods previously investigated. The results show that Gaussian parametric approaches outperform Skew-Normal parametric and distance-based ones in most conditions analyzed. In particular, with heterocedastic data a quadratic Gaussian rule always performs best. Moreover, restricted cases of the variance-covariance matrix lead to parsimonious rules which for small training samples in heterocedastic problems can outperform unrestricted quadratic rules, even in some cases where the model assumed by these rules is not true. These restrictions take into account the particular nature of interval data, where observations are defined by both MidPoints and Ranges, which may or may not be correlated. Under homocedastic conditions linear Gaussian rules are often the best rules, but distance-based methods may perform better in very specific conditions.

Abstract
In this paper we address the problem of clustering interval data, adopting a model-based approach. To this purpose, parametric models for interval-valued variables are used which consider configurations for the variance-covariance matrix that take the nature of the interval data directly into account. Results, both on synthetic and empirical data, clearly show the well-founding of the proposed approach. The method succeeds in finding parsimonious heterocedastic models which is a critical feature in many applications. Furthermore, the analysis of the different data sets made clear the need to explicitly consider the intrinsic variability present in interval data.