The authors have opened a new window on the problem of learning process and learning theory in artificial intelligence (AI) systems, including classification in a complex, dynamic environment. It has been extended by them with the use of multiclass dynamics found in continuous dynamic systems. The author’s base of observations was the maximum likelihood estimation. To it they added the model of learning several classes at once.

In regard to learning with stochastic observation, the authors explained the hidden Markov model by using the expectation-maximization (EM) algorithm as the base for dynamic learning problem solving. They found that exact methods for separating expected movements (Kalman and smoothing filters) are available, but are not flexible enough for for multiclass and complex dynamics. The authors thus found it valuable to introduce approximations based on the propagation of particle sets (a particle smoothing filter). The motion process in complex dynamic systems observation within the learning process is shown through the forward filter based on the CONDENSATION algorithm, so it becomes the CONDENSATION forward algorithm.

The authors also give the results of practical learning scenarios of complex dynamics, combining the EM algorithm with the CONDENSATION algorithm to achieve space for exploring multiclass dynamics. Observations were made with two and three classes in which the EM learning algorithm was taking on the very considerable computational load. The solution is also given by partial importance sampling. The combination of CONDENSATION (particle filtering) and the EM algorithm is used as the EM-C algorithm, which proved to be a learning algorithm for complex dynamic learning. At the same time, the partial importance sampling was used to reduce computation time.

The authors suggest that the EM-C algorithm can solve the problem of learning of complex dynamics in motion process data acquisition. They found that the computational resources could be reduced to a reasonable and effective level by introducing the observation of particle sets, where partial importance sampling using an importance function forms the basis for appropriate recognition of motion by the AI system. The facts and results are correctly and clearly described, giving valuable insight into the area of learning processes in system design and conceptualizing vision of motion dynamics classification criteria and development.

The authors present a significant improvement in the theory and practice of understanding learning problems of complex dynamics needed for most AI system design scenarios. This paper will be interesting reading for those working in or studying the area of AI system design, machine intelligence, and human-computer interface.