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.

Abstract
In this chapter, we present clustering methods for symbolic data. We start by recalling that symbolic data is data presenting inherent variability, and the motivations for the introduction of this new paradigm.We then proceed by defining the different types of variables that allow for the representation of symbolic data, and recall some distance measures appropriate for the new data types. Then we present clustering methods for different types of symbolic data, both hierarchical and nonhierarchical. An application illustrates two well-known methods for clustering symbolic data. © 2016 by Taylor & Francis Group, LLC.

Abstract
Data Mining (DM) researchers often focus on the development and testing of models for a single decision (e.g., direct mailing, churn detection, etc.). In practice, however, multiple decisions have often to be made simultaneously which are not independent and the best global solution is often not the combination of the best individual solutions. This problem can be addressed by searching for the overall best solution by using optimization methods based on the predictions made by the DM models. We describe one case study were this approach was used to optimize the layout of a retail store in order to maximize predicted sales. A metaheuristic is used to search different hypothesis of space allocations for multiple product categories, guided by the predictions made by regression models that estimate the sales for each category based on the assigned space. We test three metaheuristics and three regression algorithms on this task. Results show that the Particle Swam Optimization method guided by the models obtained with Random Forests and Support Vector Machines models obtain good results. We also provide insights about the relationship between the correctness of the regression models and the metaheuristics performance.

Abstract
The problem of Label Ranking is receiving increasing attention from several research communities. The algorithms that have developed/adapted to treat rankings as the target object follow two different approaches: distribution-based (e.g., using Mallows model) or correlation-based (e.g., using Spearman's rank correlation coefficient). Decision trees have been adapted for label ranking following both approaches. In this paper we evaluate an existing correlation-based approach and propose a new one, Entropy-based Ranking trees. We then compare and discuss the results with a distribution-based approach. The results clearly indicate that both approaches are competitive.

Abstract
Traditionally, a single model is developed for a data mining task. As more data is being collected at a more detailed level, organizations are becoming more interested in having specific models for distinct parts of data (e. g. customer segments). From the business perspective, data can be divided naturally into different dimensions. Each of these dimensions is usually hierarchically organized (e. g. country, city, zip code), which means that, when developing a model for a given part of the problem (e. g. a zip code) the training data may be collected at different levels of this nested hierarchy (e. g. the same zip code, the city and the country it is located in). Selecting different levels of granularity may change the performance of the whole process, so the question is which level to use for a given part. We propose a metalearning model which recommends a level of granularity for the training data to learn the model that is expected to obtain the best performance. We apply decision tree and random forest algorithms for metalearning. At the base level, our experiment uses results obtained by outlier detection methods on the problem of detecting errors in foreign trade transactions. The results show that using metalearning help finding the best level of granularity.