Pattern recognition and artificial neural networks have for the most part focused on classification in Euclidean feature spaces. Cognitive psychologists have long known that human judgment of similarities is also non-metric. In this talk I will discuss the computational implications of non-metric matching techniques on supervised classification. I will describe many problems, and address a few of them. In particular, I will focus on the absence of transitivity as a major problem for data reduction, and present a simple algorithm to achieve data reduction in non-metric data sets.
Simulations show the superior performance of our method under various conditions.
I will discuss in detail a novel curve matching algorithm, which uses the robust median distance and is therefore non-metric. Visibility constraints lead to new challenges for computing motion strategies when considered in addition to geometric constraints that are typical in basic motion planning. This talk will focus on two visibility-based planning problems. The second problem involves computing motion strategies that attempt to maintain visibility of a moving target that may or may not be predictable, while optimizing additional criteria such as the total distance traveled. Several computed results and mobile robot experiments will be presented.