A fuzzy-set-based Reconstructed Phase Space method for identification of temporal patterns in complex time series

The new time series data mining framework proposed in this paper applies Reconstructed Phase Space (RPS) to identify temporal patterns that are characteristic and predictive of significant events in a complex time series. The new framework utilizes the fuzzy set and the Gaussian-shaped membership function to define temporal patterns in the time-delay embedding phase space. The resulting objective function represents not only the overall value of the event function, but also the weight of the vector in the temporal pattern cluster to which it contributes. Also, the new objective function is continuously differentiate so the gradient descent optimization such as quasiNewton's method can be applied to search the optimal temporal patterns with much faster speed of convergence. The computational stability is significantly improved over the genetic algorithm originally used in our early framework. A new simple but effective two-step optimization strategy is proposed which further improves the search performance. Another significant contribution is the use of mutual information and false neighbors methods to estimate the time delay and the phase space dimension. We also implemented two experimental applications to demonstrate the effectiveness of the new framework with comparisons to the original framework and to the neural network prediction approach.