A robust routing algorithm was developed based on reinforcement learning that uses (1) reward-weighted principal component analysis, which compresses the state space of a network with a large number of nodes and eliminates the adverse effects of various types of attacks or disturbance noises, (2) activity-oriented index allocation, which adaptively constructs a basis that is used for approximating routing probabilities, and (3) newly developed space compression based on a potential model that reduces the space for routing probabilities. This algorithm takes all the network states into account and reduces the adverse effects of disturbance noises. The algorithm thus works well, and the frequencies of causing routing loops and falling to a local optimum are reduced even if the routing information is disturbed.

A state space compression method based on multivariate analysis was developed and applied to reinforcement learning for high-dimensional continuous state spaces. First, useful components in the state variables of an environment are extracted and meaningless ones are removed by using multiple regression analysis. Next, the state space of the environment is compressed by using principal component analysis so that only a few principal components can express the dynamics of the environment. Then, a basis of a feature space for function approximation is constructed based on orthonormal bases of the important principal components. A feature space is thus autonomously construct without preliminary knowledge of the environment, and the environment is effectively expressed in the feature space. An example synchronization problem for multiple logistic maps was solved using this method, demonstrating that it solves the curse of dimensionality and exhibits high performance without suffering from disturbance states.

A method for a genuinely multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. It is applied to EEG data from a psychological experiment, obtaining results which indicate a possible relevance of this method in the context of cognitive science as well as in other fields.

Many methods have been proposed to detect intrusions; for example, the pattern matching method on known intrusion patterns and the statistical approach to detecting deviation from normal activities. We investigated a new method for detecting intrusions based on the number of system calls during a user's network activity on a host machine. This method attempts to separate intrusions from normal activities by using discriminant analysis, a kind of multivariate analysis. We can detect intrusions by analyzing only 11 system calls occurring on a host machine by discriminant analysis with the Mahalanobis' distance, and can also tell whether an unknown sample is an intrusion. Our approach is a lightweight intrusion detection method, given that it requires only 11 system calls for analysis. Moreover, our approach does not require user profiles or a user activity database in order to detect intrusions. This paper explains our new method for the separation of intrusions and normal behavior by discriminant analysis, and describes the classification method by which to identify an unknown behavior.