Neural networks, fuzzy natural logic, fuzzy transform, time series

This chapter focuses on the so-called model-driven approach to data analysis. This approach is closely related to the computations performed by neural networks since the latter follow a specific procedure for transforming the original data into a form well suited to solving the original, usually external, problem. The chapter is divided into two sections, in which we discuss two diferent types of dataembedded in continuous or discrete spaces. In Section 1.1, we analyze the data as continuous functions and discuss three options for representing them in feature space: according to a Cybenko-type approximation, a Kolmogorov-type representation, and an approximate representation using F-transform theory. In Section 2 1.2, we deal with time series data defined in the discrete-time domain. The feature extraction method is based on the composition of two successively applied models derived from the theories of F-transforms and fuzzy natural logic (FNL). We demonstrate the efectiveness of the proposed method in processing long time series.

This chapter focuses on the so-called model-driven approach to data analysis. This approach is closely related to the computations performed by neural networks since the latter follow a specific procedure for transforming the original data into a form well suited to solving the original, usually external, problem. The chapter is divided into two sections, in which we discuss two diferent types of dataembedded in continuous or discrete spaces. In Section 1.1, we analyze the data as continuous functions and discuss three options for representing them in feature space: according to a Cybenko-type approximation, a Kolmogorov-type representation, and an approximate representation using F-transform theory. In Section 2 1.2, we deal with time series data defined in the discrete-time domain. The feature extraction method is based on the composition of two successively applied models derived from the theories of F-transforms and fuzzy natural logic (FNL). We demonstrate the efectiveness of the proposed method in processing long time series.