RESUMO
Interval-valued data have been commonly encountered in practice, and Symbolic Data Analysis provides a solution to the statistical treatment of these data. Regression analysis for interval-valued symbolic data is a topic that has been widely investigated in the literature of symbolic data analysis, and several models from different paradigms have been proposed. There are basic regression assumptions, and it is essential to validate them. This paper introduces an approach to check interval regression model adequacy based on residual analysis. Concepts of ordinary and standardized interval residual are presented, and graphical analysis of these residuals is also proposed. To show the usefulness of the proposed approach, an application for estimating school dropout in the scenario of Brazilian municipalities is performed. We observed some outliers from the interval residuals analysis, and interval robust regression models are more suitable for estimating school dropout.
RESUMO
This paper presents new approaches to fit regression models for symbolic internal-valued variables, which are shown to improve and extend the center method suggested by Billard and Diday and the center and range method proposed by Lima-Neto, E.A.and De Carvalho, F.A.T. Like the previously mentioned methods, the proposed regression models consider the midpoints and half of the length of the intervals as additional variables. We considered various methods to fit the regression models, including tree-based models, K-nearest neighbors, support vector machines, and neural networks. The approaches proposed in this paper were applied to a real dataset and to synthetic datasets generated with linear and nonlinear relations. For an evaluation of the methods, the root-mean-squared error and the correlation coefficient were used. The methods presented herein are available in the the RSDA package written in the R language, which can be installed from CRAN.
RESUMO
Breast cancer is one of the leading causes of death in women. Because of this, thermographic images have received a refocus for diagnosing this cancer type. This work proposes an innovative approach to classify breast abnormalities (malignant, benignant and cyst), employing interval temperature data in order to detect breast cancer. The learning step takes into account the internal variation of the intervals when describing breast abnormalities and uses a way to map these intervals into a space where they can be more easily separated. The method builds class prototypes, and the allocation step is based on a parameterized Mahalanobis distance for interval-valued data. The proposed classifier is applied to a breast thermography dataset from Brazil with 50 patients. We investigate two different scenarios for parameter configuration. The first scenario focuses on the overall misclassification rate and achieves 16 % misclassification rate and 93 % sensitivity to the malignant class. The second scenario maximizes the sensitivity to the malignant class, achieving 100 % sensitivity to this specific class, along with 20 % overall misclassification rate. We compare the performances of our approach and of many methods taken from the literature of interval data classification for the breast thermography task. Results show that our method outperforms competing algorithms.