Development of machine-learning techniques via collective dynamical systems

Machine learning consists of concepts and techniques that enable computers to improve their performance with experience, i.e., learn from data. Unsupervised and semi-supervised learning are important categories of machine learning, which respectively consists of inferring patterns in datasets whose data have no label (class) and classifying data in partially-labeled datasets. Although intensively studied, machine learning is still a field full of challenges and with many open topics. Collective dynamical systems, in turn, are systems made of a large group of individuals, each one a dynamical system by itself, such that all of them behave collectively, i.e., the action of each individual is influenced by the action of its neighbors. A remarkable feature of those systems is that global patterns may spontaneously emerge from the local interactions among individuals, a phenomenon known as emergence. Their relevance and intrinsic challenges motivate research in various branches of science and engineering. In this doctorate research, we develop and analyze collective dynamical models for their usage in machine-learning tasks, specifically unsupervised and semi-supervised ones. Image segmentation and network community detection are also addressed, as they are related to machine learning as well. In particular, we propose to work on models in which the objects motion is determined by the location and velocity of their neighbors. By doing so, the dynamical system reaches a configuration in which the patterns developed by the set of individuals highlight underlying patterns of the dataset. Due to their self-organizing nature, it is also expected that the models can be robust and the information generated during the process (values of the system variables) can be rich and reveal, for example, features to perform soft labeling and determine overlapping classes. (AU)