Carmela Iorio

Parsimonious time series clustering using P-splines

A new parsimonious way to cluster time (data) series is provided.We deal with P-spline framework and non-hierarchical clustering.Simulation studies and two well-known real world case studies are performed. We introduce a parsimonious model-based framework for clustering time course data. In these applications the computational burden becomes often an issue due to the large number of available observations. The measured time series can also be very noisy and sparse and an appropriate model describing them can be hard to define. We propose to model the observed measurements by using P-spline smoothers and then to cluster the functional objects as summarized by the optimal spline coefficients. According to the characteristics of the observed measurements, our proposal can be combined with any suitable clustering method. In this paper we provide applications based on non-hierarchical clustering algorithms. We evaluate the accuracy and the efficiency of our proposal by simulations and by analyzing two real data examples.

Regression trees for multivalued numerical response variables

Abstract In the framework of regression trees, this paper provides a recursive partitioning methodology to deal with a non-standard response variable. Specifically, either multivalued numerical or modal response of the type histogram will be considered. These data are known as symbolic data, which special cases are classical data, imprecise data, conjunctive data as well as fuzzy data. In spite of pre-processing data in order to deal with standard regression tree methodology, this paper provides, as main contribution, a definition of the impurity measure and of the splitting criterion allowing for building the regression tree for multivalued numerical response variable. We analyze and evaluate the performance of our proposal, using simulated data as well as a real-world case studies.

A differential evolution algorithm for finding the median ranking under the Kemeny axiomatic approach

An accurate (meta)heuristic solution to the rank aggregation problem is proposed.The reference paradigm is the KemenySnell axiomatic framework.We specifically adapt the differential evolution algorithm to deal with the median ranking problem.Simulation studies and real data applications are performed. In recent years the analysis of preference rankings has become an increasingly important topic. One of the most important tasks in dealing with preference rankings is the identification of the median ranking, namely that ranking that best represents the preferences of a population of judges. This task is known with several alternative names, such as rank aggregation problem, consensus ranking problem, social choice problem. In this paper we propose a Differential Evolution algorithm for the Consensus Ranking detection (DECoR) within the Kemenys axiomatic framework. The algorithm works with full, partial and incomplete rankings. A simulation study shows that our proposal is particularly feasible when working with a very large number of objects to be ranked, because it is accurate and also faster than other proposals. Some applications on real data sets show the practical utility of our proposal in helping the users in taking decisions.

A P-Spline based clustering approach for portfolio selection

Abstract In the last years, many clustering techniques dealing with time course data have been proposed due to recent interests in studying phenomena that change over time. A new clustering method suitable for time series applications has been recently proposed by exploiting the properties of the P-splines approach. This semi-parametric tool has several advantages, i.e. it facilitates the removal of noise from time series and it ensures a computational time saving. In this paper, we propose to use this clustering approach on financial data with the aim of building a financial portfolio. Our proposal works directly on time series without any pre-processing, except for the computation of the spline coefficients and, eventually, normalizing the series. We show that our strategy is useful to support the investment decisions of financial practitioners.

A New Proposal for Tree Model Selection and Visualization

The most common approach to build a decision tree is based on a two-step procedure: growing a full tree and then prune it back. The goal is to identify the tree with the lowest error rate. Alternative pruning criteria have been proposed in literature. Within the framework of recursive partitioning algorithms by tree-based methods, this paper provides a contribution on both the visual representation of the data partition in a geometrical space and the selection of the decision tree. In our visual approach the identification of the best tree and of the weakest links is immediately evaluable by the graphical analysis of the tree structure without considering the pruning sequence. The results in terms of error rate are really similar to the ones returned by the classification and regression trees (CART) procedure, showing how this new way to select the best tree is a valid alternative to the well-known cost-complexity pruning.

Dynamic recursive tree-based partitioning for malignant melanoma identification in skin lesion dermoscopic images

In this paper, multivalued data or multiple values variables are defined. They are typical when there is some intrinsic uncertainty in data production, as the result of imprecise measuring instruments, such as in image recognition, in human judgments and so on. So far, contributions in symbolic data analysis literature provide data preprocessing criteria allowing for the use of standard methods such as factorial analysis, clustering, discriminant analysis, tree-based methods. As an alternative, this paper introduces a methodology for supervised classification, the so-called Dynamic CLASSification TREE (D-CLASS TREE), dealing simultaneously with both standard and multivalued data as well. For that, an innovative partitioning criterion with a tree-growing algorithm will be defined. Main result is a dynamic tree structure characterized by the simultaneous presence of binary and ternary partitions. A real world case study will be considered to show the advantages of the proposed methodology and main issues of the interpretation of the final results. A comparative study with other approaches dealing with the same types of data will be also shown. The comparison highlights that, even if the results are quite similar in terms of error rates, the proposed D-CLASS tree returns a more interpretable tree-based structure.

P-Splines Based Clustering as a General Framework: Some Applications Using Different Clustering Algorithms

A parsimonious clustering method suitable for time course data applications has been recently introduced. The idea behind this proposal is quite simple but efficient. Each series is first summarized by lower dimensional vectors of P-spline coefficients and then, the P-spline coefficients are partitioned by means of a suitable clustering algorithm. In this paper, we investigate the performance of this proposal through several applications showing examples within both hierarchical and non-hierarchical clustering algorithms.