Using semi-tensor product of matrices, the controllability and stabilizability of nite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms. Based on this algebraic description, a necessary and suf cient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to nd all the control sequences of an arbitrary length. Moreover, the stabilizability of nite automata is considered, and a necessary and suf cient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples veri es the correctness of the presented results/algorithms.

Extreme Learning Machine (ELM) as a fast and efficient neural network model in pattern recognition and machine learning will decline when the labeled training sample is insufficient. Transfer learning helps the target task to learn a reliable model by using plentiful labeled samples from the different but relevant domain. In this paper, we propose a supervised Extreme Learning Machine with knowledge transferability, called Transfer Extreme Learning Machine with Output Weight Alignment (TELM-OWA). Firstly, it reduces the distribution difference between domains by aligning the output weight matrix of the ELM trained by the labeled samples from the source and target domains. Secondly, the approximation between the interdomain ELM output weight matrix is added to the objective function to further realize the cross-domain transfer of knowledge. Thirdly, we consider the objective function as the least square problem and transform it into a standard ELM model to be efficiently solved. Finally, the effectiveness of the proposed algorithm is verified by classification experiments on 16 sets of image datasets and 6 sets of text datasets, and the result demonstrates the competitive performance of our method with respect to other ELM models and transfer learning approach.

No abstract

No abstract