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The notion of linear separability is used widely in machine learning research. Learning algorithms that use this concept to learn include neural networks (single layer perceptron and recursive deterministic perceptron), and kernel machines (support vector machines). This paper presents an overview of several of the methods for testing linear separability between two classes. The methods are divided into four groups: Those based on linear programming, those based on computational geometry, one based on neural networks, and one based on quadratic programming. The Fisher linear discriminant method is also presented. A section on the quantification of the complexity of classification problems is included.

A key factor in the fight against viral diseases such as the coronavirus (COVID-19) is the identification of virus carriers as early and quickly as possible, in a cheap and efficient manner. The application of deep learning for image classification of chest X-ray images of COVID-19 patients could become a useful pre-diagnostic detection methodology. However, deep learning architectures require large labelled datasets. This is often a limitation when the subject of research is relatively new as in the case of the virus outbreak, where dealing with small labelled datasets is a challenge. Moreover, in such context, the datasets are also highly imbalanced, with few observations from positive cases of the new disease. In this work we evaluate the performance of the semi-supervised deep learning architecture known as MixMatch with a very limited number of labelled observations and highly imbalanced labelled datasets. We demonstrate the critical impact of data imbalance to the model’s accuracy. Therefore, we propose a simple approach for correcting data imbalance, by re-weighting each observation in the loss function, giving a higher weight to the observations corresponding to the under-represented class. For unlabelled observations, we use the pseudo and augmented labels calculated by MixMatch to choose the appropriate weight. The proposed method improved classification accuracy by up to 18%, with respect to the non balanced MixMatch algorithm. We tested our proposed approach with several available datasets using 10, 15 and 20 labelled observations, for binary classification (COVID-19 positive and normal cases). For multi-class classification (COVID-19 positive, pneumonia and normal cases), we tested 30, 50, 70 and 90 labelled observations. Additionally, a new dataset is included among the tested datasets, composed of chest X-ray images of Costa Rican adult patients.

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Biometric based systems for individual authentication are increasingly becoming indispensable for protecting life and property. They provide ways for uniquely and reliably authenticating people, and are difficult to counterfeit. Biometric based authenticity systems are currently used in governmental, commercial and public sectors. However, these systems can be expensive to put in place and often impose physical constraint to the users. This paper introduces an inexpensive, powerful and easy to use hand geometry based biometric person authentication system using neural networks. The proposed approach followed to construct this system consists of an acquisition device, a pre-processing stage, and a neural network based classifier. One of the novelties of this work comprises on the introduction of hand geometry's related, position independent, feature extraction and identification which can be useful in problems related to image processing and pattern recognition. Another novelty of this research comprises on the use of error correction codes to enhance the level of performance of the neural network model. A dataset made of scanned images of the right hand of fifty different people was created for this study. Identification rates and Detection Cost Function (DCF) values obtained with the system were evaluated. Several strategies for coding the outputs of the neural networks were studied. Experimental results show that, when using Error Correction Output Codes (ECOC), up to 100% identification rates and 0% DCF can M. Faundez-Zanuy 123 202 M. Faundez-Zanuy et al.be obtained. For comparison purposes, results are also given for the Support Vector Machine method.