A Genetic Algorithm as a Learning Method Based on Geometric Representations

A number of different methods combining the use of neural networks and genetic algorithms have been described [1]. This paper discusses an approach for training neural networks based on the geometric representation of the network. In doing so, the genetic algorithm becomes applicable as a common training method for a number of machine learning algorithms that can be similarly represented. The experiments described here were specifically derived to construct claim regions for Fuzzy ARTMAP Neural Networks [2,3]. The adaptation of several principles to guarantee the success in traditional training of neural networks provided a similar level of success for the GA. Especially exciting is that this method provides the rare case of a GA guaranteeing a perfect solution with an increasing probability with each generation. One neural network that has demonstrated good success, specifically for classification problems, is Fuzzy Adaptive Resonance Theory-MAP Neural Networks [2]. Fuzzy-ARTMAP Neural Networks (FAM-NN) provide numerous benefits, the most notable being online learning and notification of inputs that cannot be classified with the current learning [2,3]. FAM-NN constructs claim regions which can be viewed as geometric shapes, i.e. rectangles, cubes or hyper-cubes, in n-dimensional space. Each region has an assigned a category. Based simply on the classification rules, points within these regions are classified as being part of that claim region’s category. Georgiopoulos provides a more detailed discussion on this point as it applies to the rules within FAM-NN [3]. The genetic algorithm for this application used a variable length representation. Each individual consists of m-pairs of points in n-dimensional space. Each pair constitutes the vertices of a rectangle, cube or hyper-cube, depending on the dimensionality of the representational space. Just as in the claim regions in FAM-NN, each pair is also assigned a category according to the classification categories in the training data. The operators selected for this work concentrate on achieving success comparable to the traditional FAM-NN training. By adapting operators that emphasize the best traditional performance, the GA performance is improved and new characteristics emerge further improving the training. The genetic algorithm uses single-point crossover with random selection of parents. Mutation consists of several possibilities, the latter of which are novel. Typical mutation of a randomly selected dimension of a particular vertex occurs at a given probability. Additionally, pairs of points are randomly added, deleted or swapped. Identical pairs of points based on particular input patterns