Growing a tree classifier with imprecise data

Classification of histogram-valued data with support histogram machines

The current large amounts of data and advanced technologies have produced new types of complex data, such as histogram-valued data. The paper focuses on classification problems when predictors are observed as or aggregated into histograms. Because conventional classification methods take vectors as input, a natural approach converts histograms into vector-valued data using summary values, such as the mean or median. However, this approach forgoes the distributional information available in histograms. To address this issue, we propose a margin-based classifier called support histogram machine (SHM) for histogram-valued data. We adopt the support vector machine framework and the Wasserstein-Kantorovich metric to measure distances between histograms. The proposed optimization problem is solved by a dual approach. We then test the proposed SHM via simulated and real examples and demonstrate its superior performance to summary-value-based methods.

An interval prototype classifier based on a parameterized distance applied to breast thermographic images

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.