Nonlinear Feature Space Research Articles

Evolving kernel principal component analysis for fault diagnosis

Feature extraction is the core of a fault diagnosis system. This paper presents a novel approach, called evolving kernel principal component analysis (EKPCA), to transform the original features to a more effective nonlinear combination in fault classification. EKPCA is based on the integration of kernel principal component analysis (KPCA) and an improved evolutionary optimization algorithm. As a coordinate transformation technique, KPCA is a superset of principal component analysis (PCA), which is utilized to project the original data space to a nonlinear feature space via the appropriate kernel function, and then PCA is performed in the projected feature space. Compared with PCA, KPCA is more flexible in extracting a group of new nonlinear features. However, the efficiency of KPCA in real-world applications depends mainly on the kernel function chosen a priori. It remains an issue of how to select the kernel function from the viewpoint of optimization. This paper addresses this issue using the techniques from evolutionary computation (EC). An improved evolutionary algorithm incorporated with a Gaussian mutation operator that is inspired from evolutionary strategies (ES) and evolutionary programming (EP) can enhance both the global and the local search performances without substantially increasing the computational effort. The application in fault diagnosis to a large-scale rotating machine shows that EKPCA is effective and efficient in discovering the optimal nonlinear features corresponding to real-world operational data. Thus, this method can improve the recognition power of a fault diagnosis system.

Beyond Black–Scholes: A Neural Networks-Based Approach to Options Pricing

The paper presents two alternative schemes for pricing European and American call options, both based on artificial neural networks. The first method uses binomial trees linked to an innovative stochastic volatility model. The volatility model is based on wavelets and artificial neural networks. Wavelets provide a convenient signal/noise decomposition of the volatility in the non-linear feature space. Neural networks are used to infer future volatility levels from the wavelets feature space in an iterative manner. The bootstrap method provides the 95% confidence intervals for the options prices. In the second approach neural networks are trained with genetic algorithms in order to reverse-engineer the Black–Scholes formulae. The standard Black–Scholes model provides a starting point for an evolutionary training process, which yields improved options prices. Market options prices as quoted on the Chicago Board Options Exchange are used for performance comparison between the Black–Scholes model and the proposed options pricing schemes. The proposed models produce as good as and often better options prices than the conventional Black–Scholes formulae.

Stochastic volatility options pricing with wavelets and artificial neural networks

The paper describes an alternative options pricing method which uses a binomial tree linked to an innovative stochastic volatility model. The volatility model is based on wavelets and artificial neural networks. Wavelets provide a convenient signal/noise decomposition of the volatility in the nonlinear feature space. Neural networks are used to infer future volatility from the wavelets feature space in an iterative manner. The bootstrap method provides the 95% confidence intervals for the options prices. Market options prices as quoted on the Chicago Board Options Exchange are used for performance comparison between the Black‐Scholes model and a new options pricing scheme. The proposed dynamic volatility model produces as good as and often better options prices than the conventional Black‐Scholes formulae.

Patterns and symbols treated in a three-layered associative memory network

This paper presents a new network for inference using patterns and symbols. Patterns are spatial distributions of feature vectors in nonlinear feature space made from original images. The new network is for acquiring concepts and inferring meanings of original images. Simulations using similar/different patterns are done to show the unique feature of the proposed network.