A clustering algorithm based on the Hausdorff distance is analyzed and compared to the single, complete, and average linkage algorithms. The four clustering procedures are applied to a toy example and to the time series of financial data. The dendrograms are scrutinized and their features compared. The Hausdorff linkage relies on firm mathematical grounds and turns out to be very effective when one has to discriminate among complex structures.

A clustering procedure, based on the Hausdorff distance, is introduced and tested on the financial time series of the Dow Jones Industrial Average (DJIA) index.

The COVID-19 pandemic has amplified the urgency of the developments in computer-assisted medicine and, in particular, the need for automated tools supporting the clinical diagnosis and assessment of respiratory symptoms. This need was already clear to the scientific community, which launched an international challenge in 2017 at the International Conference on Biomedical Health Informatics (ICBHI) for the implementation of accurate algorithms for the classification of respiratory sound. In this work, we present a framework for respiratory sound classification based on two different kinds of features: (i) short-term features which summarize sound properties on a time scale of tenths of a second and (ii) long-term features which assess sounds properties on a time scale of seconds. Using the publicly available dataset provided by ICBHI, we cross-validated the classification performance of a neural network model over 6895 respiratory cycles and 126 subjects. The proposed model reached an accuracy of 85%±3% and an precision of 80%±8%, which compare well with the body of literature. The robustness of the predictions was assessed by comparison with state-of-the-art machine learning tools, such as the support vector machine, Random Forest and deep neural networks. The model presented here is therefore suitable for large-scale applications and for adoption in clinical practice. Finally, an interesting observation is that both short-term and long-term features are necessary for accurate classification, which could be the subject of future studies related to its clinical interpretation.