Adaptive Resonance Theory and Diffusion Maps for Clustering Applications in Pattern Analysis

Adaptive Resonance is primarily a theory that learning is regulated by resonance phenomena in neural circuits. Diffusion maps are a class of kernel methods on edge-weighted graphs. While either of these approaches have demonstrated success in image analysis, their combination is particularly effective. These techniques are reviewed and some example applications are given

Path planning for general mazes

Path planning is used in, but not limited to robotics, telemetry, aerospace, and medical applications. The goal of the path planning is to identify a route from an origination point to a destination point while avoiding obstacles. This path might not always be the shortest in distance as time, terrain, speed limits, and many other factors can affect the optimality of the path. However, in this thesis, the length, computational time, and the smoothness of the path are the only constraints that will be considered with the length of the path being the most important. There are a variety of algorithms that can be used for path planning but Ant Colony Optimization (ACO), Neural Network, and A* will be the only algorithms explored in this thesis. The problem of solving general mazes has been greatly researched, but the contributions of this thesis extended Ant Colony Optimization to path planning for mazes, created a new landscape for the Neural Network to use, and added a bird\u27s eye view to the A* Algorithm. The Ant Colony Optimization that was used in this thesis was able to discover a path to the goal, but it was jagged and required a larger computational time compared to the Neural Network and A* algorithm discussed in this thesis. The Hopfield-type neural network used in this thesis propagated energy to create a landscape and used gradient decent to find the shortest path in terms of distance, but this thesis modified how the landscape was created to prevent the neural network from getting trapped in local minimas. The last contribution was applying a bird\u27s eye view to the A* algorithm to learn more about the environment which helped to create shorter and smoother paths