Gravitational Dimensionality Reduction Using Newtonian Gravity and Einstein's General Relativity

Due to the effectiveness of using machine learning in physics, it has been widely received increased attention in the literature. However, the notion of applying physics in machine learning has not been given much awareness to. This work is a hybrid of physics and machine learning where concepts of physics are used in machine learning. We propose the supervised Gravitational Dimensionality Reduction (GDR) algorithm where the data points of every class are moved to each other for reduction of intra-class variances and better separation of classes. For every data point, the other points are considered to be gravitational particles, such as stars, where the point is attracted to the points of its class by gravity. The data points are first projected onto a spacetime manifold using principal component analysis. We propose two variants of GDR -- one with the Newtonian gravity and one with the Einstein's general relativity. The former uses Newtonian gravity in a straight line between points but the latter moves data points along the geodesics of spacetime manifold. For GDR with relativity gravitation, we use both Schwarzschild and Minkowski metric tensors to cover both general relativity and special relativity. Our simulations show the effectiveness of GDR in discrimination of classes

Comprehensive Taxonomies of Nature- and Bio-inspired Optimization: Inspiration Versus Algorithmic Behavior, Critical Analysis Recommendations

In recent algorithmic family simulates different biological processes observed in Nature in order to efficiently address complex optimization problems. In the last years the number of bio-inspired optimization approaches in literature has grown considerably, reaching unprecedented levels that dark the future prospects of this field of research. This paper addresses this problem by proposing two comprehensive, principle-based taxonomies that allow researchers to organize existing and future algorithmic developments into well-defined categories, considering two different criteria: the source of inspiration and the behavior of each algorithm. Using these taxonomies we review more than three hundred publications dealing with nature- inspired and bio-inspired algorithms, and proposals falling within each of these categories are examined, leading to a critical summary of design trends and similarities between them, and the identification of the most similar classical algorithm for each reviewed paper. From our analysis we conclude that a poor relationship is often found between the natural inspiration of an algorithm and its behavior. Furthermore, similarities in terms of behavior between different algorithms are greater than what is claimed in their public disclosure: specifically, we show that more than one-third of the reviewed bio-inspired solvers are versions of classical algorithms. Grounded on the conclusions of our critical analysis, we give several recommendations and points of improvement for better methodological practices in this active and growing research field

Comprehensive Taxonomies of Nature- and Bio-inspired Optimization: Inspiration versus Algorithmic Behavior, Critical Analysis and Recommendations

In recent years, a great variety of nature- and bio-inspired algorithms has been reported in the literature. This algorithmic family simulates different biological processes observed in Nature in order to efficiently address complex optimization problems. In the last years the number of bio-inspired optimization approaches in literature has grown considerably, reaching unprecedented levels that dark the future prospects of this field of research. This paper addresses this problem by proposing two comprehensive, principle-based taxonomies that allow researchers to organize existing and future algorithmic developments into well-defined categories, considering two different criteria: the source of inspiration and the behavior of each algorithm. Using these taxonomies we review more than three hundred publications dealing with nature-inspired and bio-inspired algorithms, and proposals falling within each of these categories are examined, leading to a critical summary of design trends and similarities between them, and the identification of the most similar classical algorithm for each reviewed paper. From our analysis we conclude that a poor relationship is often found between the natural inspiration of an algorithm and its behavior. Furthermore, similarities in terms of behavior between different algorithms are greater than what is claimed in their public disclosure: specifically, we show that more than one-third of the reviewed bio-inspired solvers are versions of classical algorithms. Grounded on the conclusions of our critical analysis, we give several recommendations and points of improvement for better methodological practices in this active and growing research field.Comment: 76 pages, 6 figure