Data pruning and ordered training are two methods used to train a learner with heterogeneous data. The former is a typical procedure that attempts to factor out noise from the data; the latter is a novel method that partitions the data into a number of categories and assigns training times to those assuming that data size and training time have a polynomial relation. In its current form, ordered training is an approximate and a priori data-emphasizing method. Both methods have been applied to a time-delay neural network - which is one of the main learners in Microsoft's Tablet PC handwriting recognition system. Their effect on the learner is presented in this paper. The handwriting data and the chosen language are Italian.

tFPR is a hybrid fuzzy and structural pattern recognition system that uses fuzzy sets to represent multi-variate pattern classes that can be either static or dynamic depending on time or some other parameter space. The membership functions of the fuzzy sets that represent pattern classes are modeled by sigmoidal functions. The choice of sigmoidal functions was motivated by their ability to represent efficiently and concisely different multi-variate pattern classes. Given a set of input data and a pattern class specification, that is defined as a fuzzy set, tFPR estimates how closely the data match the pattern class specification using the grade of membership of the data in the fuzzy set. The input data may be a number of time-dependent signals whose past values may influence the evaluation of the pattern class. In that case, structural pattern recognition methods, in addition to fuzzy ones, are employed in order to match multi-dimensional curves (rather than points) in the input domain. Two different structural (segmentation) methods are presented. The first is an efficient greedy algorithm that is linear to the number of input data points while the second is an algorithm that is optimal under certain conditions but is slower than the first method. Although efficiency is a very important consideration in tFPR, the main issues are knowledge acquisition and knowledge representation (in terms of pattern classes). tFPR has been implemented in the BB1 blackboard architecture. It is currently being applied in a system for medical monitoring. Potential applications in other domains are under investigation.

A formal analysis of probabilities, possibilities, and fuzzy sets is presented in this paper. A number of theorems proved show the above measures have equal representational power when their domains are infinite. However, for finite domains, it is proved that probabilities have a higher representational power than both possibilities and fuzzy sets. The cost of this increased power is high computational complexity and reduced computational efficiency. The resulting trade-off of high complexity and representational power versus computational efficiency is discussed under the spectrum of experimental systems and applications.