Abstract: This paper presents two of the most knowing kernel
adaptive filtering (KAF) approaches, the kernel least mean squares
and the kernel recursive least squares, in order to predict a new output
of nonlinear signal processing. Both of these methods implement a
nonlinear transfer function using kernel methods in a particular space
named reproducing kernel Hilbert space (RKHS) where the model is
a linear combination of kernel functions applied to transform the
observed data from the input space to a high dimensional feature
space of vectors, this idea known as the kernel trick. Then KAF is the
developing filters in RKHS. We use two nonlinear signal processing
problems, Mackey Glass chaotic time series prediction and nonlinear
channel equalization to figure the performance of the approaches
presented and finally to result which of them is the adapted one.
Abstract: In this paper, we study the application of Extreme
Learning Machine (ELM) algorithm for single layered feedforward
neural networks to non-linear chaotic time series problems. In this
algorithm the input weights and the hidden layer bias are randomly
chosen. The ELM formulation leads to solving a system of linear
equations in terms of the unknown weights connecting the hidden
layer to the output layer. The solution of this general system of
linear equations will be obtained using Moore-Penrose generalized
pseudo inverse. For the study of the application of the method we
consider the time series generated by the Mackey Glass delay
differential equation with different time delays, Santa Fe A and
UCR heart beat rate ECG time series. For the choice of sigmoid,
sin and hardlim activation functions the optimal values for the
memory order and the number of hidden neurons which give the
best prediction performance in terms of root mean square error are
determined. It is observed that the results obtained are in close
agreement with the exact solution of the problems considered
which clearly shows that ELM is a very promising alternative
method for time series prediction.
Abstract: Many systems in the natural world exhibit chaos or non-linear behavior, the complexity of which is so great that they appear to be random. Identification of chaos in experimental data is essential for characterizing the system and for analyzing the predictability of the data under analysis. The Lyapunov exponents provide a quantitative measure of the sensitivity to initial conditions and are the most useful dynamical diagnostic for chaotic systems. However, it is difficult to accurately estimate the Lyapunov exponents of chaotic signals which are corrupted by a random noise. In this work, a method for estimation of Lyapunov exponents from noisy time series using unscented transformation is proposed. The proposed methodology was validated using time series obtained from known chaotic maps. In this paper, the objective of the work, the proposed methodology and validation results are discussed in detail.
Abstract: A neurofuzzy approach for a given set of input-output training data is proposed in two phases. Firstly, the data set is partitioned automatically into a set of clusters. Then a fuzzy if-then rule is extracted from each cluster to form a fuzzy rule base. Secondly, a fuzzy neural network is constructed accordingly and parameters are tuned to increase the precision of the fuzzy rule base. This network is able to learn and optimize the rule base of a Sugeno like Fuzzy inference system using Hybrid learning algorithm, which combines gradient descent, and least mean square algorithm. This proposed neurofuzzy system has the advantage of determining the number of rules automatically and also reduce the number of rules, decrease computational time, learns faster and consumes less memory. The authors also investigate that how neurofuzzy techniques can be applied in the area of control theory to design a fuzzy controller for linear and nonlinear dynamic systems modelling from a set of input/output data. The simulation analysis on a wide range of processes, to identify nonlinear components on-linely in a control system and a benchmark problem involving the prediction of a chaotic time series is carried out. Furthermore, the well-known examples of linear and nonlinear systems are also simulated under the Matlab/Simulink environment. The above combination is also illustrated in modeling the relationship between automobile trips and demographic factors.