Search results for "Polygons"

PolyACO+: a multi-level polygon-based ant colony optimisation classifier

2017

Ant Colony Optimisation for classification has mostly been limited to rule based approaches where artificial ants walk on datasets in order to extract rules from the trends in the data, and hybrid approaches which attempt to boost the performance of existing classifiers through guided feature reductions or parameter optimisations. A recent notable example that is distinct from the mainstream approaches is PolyACO, which is a proof of concept polygon-based classifier that resorts to ant colony optimisation as a technique to create multi-edged polygons as class separators. Despite possessing some promise, PolyACO has some significant limitations, most notably, the fact of supporting classific…

Exacus: Efficient and Exact Algorithms for Curves and Surfaces

2005

We present the first release of the Exacus C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness, clarity of the design, modularity, flexibility, and ease of use. We present the generic design and structure of the libraries, which currently compute arrangements of curves and curve segments of low algebraic degree, and boolean operations on polygons bounded by such segments.

Historical Notes on Star Geometry in Mathematics, Art and Nature

2018

Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”

Distributed Learning Automata-based S-learning scheme for classification

2019

This paper proposes a novel classifier based on the theory of Learning Automata (LA), reckoned to as PolyLA. The essence of our scheme is to search for a separator in the feature space by imposing an LA-based random walk in a grid system. To each node in the grid, we attach an LA whose actions are the choices of the edges forming a separator. The walk is self-enclosing, and a new random walk is started whenever the walker returns to the starting node forming a closed classification path yielding a many-edged polygon. In our approach, the different LA attached to the different nodes search for a polygon that best encircles and separates each class. Based on the obtained polygons, we perform …

Distributed learning automata-based scheme for classification using novel pursuit scheme

2020

Learning Automata (LA) is a popular decision making mechanism to “determine the optimal action out of a set of allowable actions” (Agache and Oommen, IEEE Trans Syst Man Cybern-Part B Cybern 2002(6): 738–749, 2002). The distinguishing characteristic of automata-based learning is that the search for the optimising parameter vector is conducted in the space of probability distributions defined over the parameter space, rather than in the parameter space itself (Thathachar and Sastry, IEEE Trans Syst Man Cybern-Part B Cybern 32(6): 711–722, 2002). Recently, Goodwin and Yazidi pioneered the use of Ant Colony Optimisation (ACO) for solving classification problems (Goodwin and Yazidi 2016). In th…

Creating “mathematically” sustainable world: from the spirograph, a reverse path

2014

The approach to the subject of mathematic learning, represents, in the pedagogical-educational field, a problematic situation. Nowadays we attend to an heated discussion on the character of the basic mathematical concepts, on the analytical-critical succession between processes and objects. The purpose of these notes is to recover and to value the contribution of the autopoiesis theory in the characterization of the mathematical domain going beyond the mere reiteration, inspecting and testing new and generative paths of ideas. In this mechanism we would insert the use of the spirograph as a disturbing, uncertain element able to nourish the “mind-system”.

From the fourteenth century to Cabrì: convuleted constructions of star polygons

2014

I poligoni stellati: origini storiche ed implicazioni didattiche

2019

The genesis of mathematical concepts in the evolutionary line of human thought in the long story and the genesis in individual optics possess evident analogies. Starting from this assumption, we describe an activity presented to 15-year-old students; the aim was to consolidate fundamental concepts of Euclidean geometry related to regular polygons. The experimentation has used a didactic approach based on the historical evolution of the formal definition of regular star polygon through the centuries. The activity and the results obtained in terms of internalization of the concepts in the students are showed.