Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections

Benign and Malignant Breast Tumor Classification in Ultrasound and Mammography Images via Fusion of Deep Learning and Handcraft Features

Breast cancer is a disease that affects women in different countries around the world. The real cause of breast cancer is particularly challenging to determine, and early detection of the disease is necessary for reducing the death rate, due to the high risks associated with breast cancer. Treatment in the early period can increase the life expectancy and quality of life for women. CAD (Computer Aided Diagnostic) systems can perform the diagnosis of the benign and malignant lesions of breast cancer using technologies and tools based on image processing, helping specialist doctors to obtain a more precise point of view with fewer processes when making their diagnosis by giving a second opinion. This study presents a novel CAD system for automated breast cancer diagnosis. The proposed method consists of different stages. In the preprocessing stage, an image is segmented, and a mask of a lesion is obtained; during the next stage, the extraction of the deep learning features is performed by a CNN-specifically, DenseNet 201. Additionally, handcrafted features (Histogram of Oriented Gradients (HOG)-based, ULBP-based, perimeter area, area, eccentricity, and circularity) are obtained from an image. The designed hybrid system uses CNN architecture for extracting deep learning features, along with traditional methods which perform several handcraft features, following the medical properties of the disease with the purpose of later fusion via proposed statistical criteria. During the fusion stage, where deep learning and handcrafted features are analyzed, the genetic algorithms as well as mutual information selection algorithm, followed by several classifiers (XGBoost, AdaBoost, Multilayer perceptron (MLP)) based on stochastic measures, are applied to choose the most sensible information group among the features. In the experimental validation of two modalities of the CAD design, which performed two types of medical studies-mammography (MG) and ultrasound (US)-the databases mini-DDSM (Digital Database for Screening Mammography) and BUSI (Breast Ultrasound Images Dataset) were used. Novel CAD systems were evaluated and compared with recent state-of-the-art systems, demonstrating better performance in commonly used criteria, obtaining ACC of 97.6%, PRE of 98%, Recall of 98%, F1-Score of 98%, and IBA of 95% for the abovementioned datasets.

Comparison of Positivity in Two Epidemic Waves of COVID-19 in Colombia with FDA

We use the functional data methodology to examine whether there are significant differences between two waves of contagion by COVID-19 in Colombia between 7 July 2020 and 20 July 2021. A pointwise functional t-test is initially used, then an alternative statistical test proposal for paired samples is presented, which has a theoretical distribution and performs well in small samples. Our statistical test generates a scalar p-value, which provides a global idea about the significance of the positivity curves, complementing the existing punctual tests, as an advantage.

Classifying COVID-19 based on amino acids encoding with machine learning algorithms

COVID-19 disease causes serious respiratory illnesses. Therefore, accurate identification of the viral infection cycle plays a key role in designing appropriate vaccines. The risk of this disease depends on proteins that interact with human receptors. In this paper, we formulate a novel model for COVID-19 named "amino acid encoding based prediction" (AAPred). This model is accurate, classifies the various coronavirus types, and distinguishes SARS-CoV-2 from other coronaviruses. With the AAPred model, we reduce the number of features to enhance its performance by selecting the most important ones employing statistical criteria. The protein sequence of SARS-CoV-2 for understanding the viral infection cycle is analyzed. Six machine learning classifiers related to decision trees, k-nearest neighbors, random forest, support vector machine, bagging ensemble, and gradient boosting are used to evaluate the model in terms of accuracy, precision, sensitivity, and specificity. We implement the obtained results computationally and apply them to real data from the National Genomics Data Center. The experimental results report that the AAPred model reduces the features to seven of them. The average accuracy of the 10-fold cross-validation is 98.69%, precision is 98.72%, sensitivity is 96.81%, and specificity is 97.72%. The features are selected utilizing information gain and classified with random forest. The proposed model predicts the type of Coronavirus and reduces the number of extracted features. We identify that SARS-CoV-2 has similar physicochemical characteristics in some regions of SARS-CoV. Also, we report that SARS-CoV-2 has similar infection cycles and sequences in some regions of SARS CoV indicating the affectedness of vaccines on SARS-CoV-2. A comparison with deep learning shows similar results with our method.

A New Algorithm for Computing Disjoint Orthogonal Components in the Three-Way Tucker Model

One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for computing disjoint orthogonal components facilitating the analysis of three-way data and the interpretation of results. We observe in the computational experiments carried out that our novel algorithm ameliorates this drawback, generating final loading matrices with a simple structure and then easier to interpret. Illustrations with real data are provided to show potential applications of the algorithm.