Quaternion Information Theoretic Learning Adaptive Algorithms for Nonlinear Adaptive

Information Theoretic Learning (ITL) is gaining popularity for designing adaptive filters for a non-stationary or non-Gaussian environment [1] [2] . ITL cost functions such as the Minimum Error Entropy (MEE) have been applied to both linear and nonlinear adaptive filtering with better overall performance compared with the typical mean squared error (MSE) and least-squares type adaptive filtering, especially for nonlinear systems in higher-order statistic noise environments [3]. Quaternion valued data processing is beneficial in applications such as robotics and image processing, particularly for performing transformations in 3-dimensional space. Particularly the benefit for quaternion valued processing includes performing data transformations in a 3 or 4-dimensional space in a more convenient fashion than using vector algebra [4, 5, 6, 7, 8]. Adaptive filtering in quaterion domain operates intrinsically based on the augmented statistics which the quaternion input vector covariance is taken into account naturally and as a result it incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input [9]. The generalized Hamilton-real calculus (GHR) for the quaternion data simplified product and chain rules and allows us to calculate the gradient and Hessian of quaternion based cost function of the learning algorithms eciently [10][11] . The quaternion reproducing kernel Hilbert spaces and its uniqueness provide a mathematical foundation to develop the quaternion value kernel learning algorithms [12]. The reproducing property of the feature space replace the inner product of feature samples with kernel evaluation. In this dissertation, we first propose a kernel adaptive filter for quaternion data based on minimum error entropy cost function. The new algorithm is based on error entropy function and is referred to as the quaternion kernel minimum error entropy (QKMEE) algorithm [13]. We apply generalized Hamilton-real (GHR) calculus that is applicable to quaternion Hilbert space for evaluating the cost function gradient to develop the QKMEE algorithm. The minimum error entropy (MEE) algorithm [3, 14, 15] minimizes Renyis quadratic entropy of the error between the lter output and desired response or indirectly maximizing the error information potential. ITL methodology improves the performance of adaptive algorithm in biased or non-Gaussian signals and noise enviorments compared to the mean squared error (MSE) criterion algorithms such as the kernel least mean square algorithm. Second, we develop a kernel adaptive filter for quaternion data based on normalized minimum error entropy cost function [14]. We apply generalized Hamilton-real GHR) calculus that is applicable to Hilbert space for evaluating the cost function gradient to develop the quaternion kernel normalized minimum error entropy (QKNMEE) algorithm [16]. The new proposed algorithm enhanced QKMEE algorithm where the filter update stepsize selection will be independent of the input power and the kernel size. Third, we develop a kernel adaptive lter for quaternion domain data, based on information theoretic learning cost function which could be useful for quaternion based kernel applications of nonlinear filtering. The new algorithm is based on error entropy function with fiducial point and is referred to as the quaternion kernel minimum error entropy with fiducial point (QKMEEF) algorithm [17]. In our previous work we developed quaternion kernel adaptive lter based on minimum error entropy referred to as the QKMEE algorithm [13]. Since entropy does not change with the mean of the distribution, the algorithm may converge to a set of optimal weights without having zero mean error. Traditionally, to make the zero mean output error, the output during testing session was biased with the mean of errors of training session. However, for non-symmetric or heavy tails error PDF the estimation of error mean is problematic [18]. The minimum error entropy criterion, minimizes Renyi\u27s quadratic entropy of the error between the filter output and desired response or indirectly maximizing the error information potential [19]. Here, the approach is applied to quaternions. Adaptive filtering in quaterion domain intrinsically incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input. We apply generalized Hamilton-real (GHR) calculus that is applicable to Hilbert space for evaluating the cost function gradient to develop the Quaternion Minimum Error Entropy Algorithm with Fiducial point. Simulation results are used to show the behavior of the new algorithm (QKMEEF) when signal is non-Gaussian in presence of unimodal noise versus bi-modal noise distributions. Simulation results also show that the new algorithm QKMEEF can track and predict the 4-Dimensional non-stationary process signals where there are correlations between components better than quadruple real-valued KMEEF and Quat-KLMS algorithms. Fourth, we develop a kernel adaptive filter for quaternion data, using stochastic information gradient (SIG) cost function based on the information theoretic learning (ITL) approach. The new algorithm (QKSIG) is useful for quaternion-based kernel applications of nonlinear ltering [20]. Adaptive filtering in quaterion domain intrinsically incorporates component-wise real valued cross-correlation or the coupling within the dimensions of the quaternion input. We apply generalized Hamilton-real (GHR) calculus that is applicable to quaternion Hilbert space for evaluating the cost function gradient. The QKSIG algorithm minimizes Shannon\u27s entropy of the error between the filter output and desired response and minimizes the divergence between the joint densities of input-desired and input-output pairs. The SIG technique reduces the computational complexity of the error entropy estimation. Here, ITL with SIG approach is applied to quaternion adaptive filtering for three different reasons. First, it reduces the algorithm computational complexity compared to our previous work quaternion kernel minimum error entropy algorithm (QKMEE). Second, it improves the filtering performance by considering the coupling within the dimensions of the quaternion input. Third, it performs better in biased or non-Gaussian signal and noise environments due to ITL approach. We present convergence analysis and steady-state performance analysis results of the new algorithm (QKSIG). Simulation results are used to show the behavior of the new algorithm QKSIG in quaternion non-Gaussian signal and noise environments compared to the existing ones such as quadruple real-valued kernel stochastic information gradient (KSIG) and quaternion kernel LMS (QKLMS) algorithms. Fifth, we develop a kernel adaptive filter for quaternion data, based on stochastic information gradient (SIG) cost function with self adjusting step-size. The new algorithm (QKSIG-SAS) is based on the information theoretic learning (ITL) approach. The new algorithm (QKSIG-SAS) has faster speed of convergence as compared to our previous work QKSIG algorithm

Hedging options including transaction costs in incomplete markets

In this paper we study a hedging problem for European options taking into account the presence of transaction costs. In incomplete markets, i.e. markets without classical restriction, there exists a unique martingale measure. Our approach is based on the Föllmer-Schweizer-Sondermann concept of risk minimizing. In discret time Markov market mo del we construct a risk minimizing strategy by backwards iteration. The strategy gives a closed-form formula. A continuous time market mo del using martingale price pro cess shows the existence of a risk minimizing hedging strateg

Approaches to Active Tourism in the Urals and in Perm Krai

Located in the south of Ural, Perm Krai, apart from mineral resources and well-developed industry, can boast vast areas that lend themselves to active and qualified tourism, with the quality of an amateur sport. The development of these forms of tourism often requires large expenditure needed for adjusting the space to various types of activity. It also requires a correlation between a given character of the space and the preferred form of tourism, which often leads to environmental conflicts between the development of tourism and nature protection. The article presents the most important elements of the tourism potential in Perm Krai, as well as the sports tourism development perspectives in the context of real and potential environmental conflicts

Analysis of stochastic technical trading algorithms

We apply the well-known CUSUM, the Girshick-Rubin, the Graversen-Peskir-Shiryaev and an improved alteration of the Brodsky-Darkovsky algorithm as trading strategies involving only mutually exclusive long positions in cash and the DAX at Xetra intraday auction prices. We select optimal pairs of fixed thresholds for up- and downmovements from a pre-defined two-dimensional grid, hence, admitting asymmetric intervals. We show that under three different scenarios for transaction costs, the improved Brodsky-Darkovsky technique not only outperforms the passive investment in the DAX but also the other three presented algorithms

Potentiometric mapping for wind turbine power plant installation Guilan Province in Iran

The use of renewable energy in different parts of the world is increasing in recent years, therefore, understanding the way and how to use these energies is very important. Today, the use of climate and productive energies has attracted more researchers. The purpose of this research is to determine the potential of the wind turbine power plant and mapping in guilan province based on fuzzy logic and AHP. In this research, wind direction and speed data of 4 synoptic stations of guilan province were provided to assess the potential, mapping and determine the establishment of a wind turbine plant in guilan province for sustainable development using fuzzy logic in a statistical period for each synoptic station since its establishment until 2014. In this systemic model, the monthly and seasonal wind speed were scored using the fuzzy method and WindRose Plot and SabaWind software were used to determine the wind direction. Wind speed mapping map was drawn to establish a wind turbine plant with scores obtained for each of the stations using the GIS. The findings of the research show that fuzzy logic method showed a large variation to establish wind turbine power plants using wind speed and wind direction. In total, the Manjil station with the highest windy with the score of 29.29 were ranked first in the construction of wind turbines after obtaining the final rating each of the 4 stations in guilan province to build a high-confidence wind power plant and other stations are the next priorities in the province of Gilan for the establishment of the turbine plant with the scores (Bandar Anzali: 22.79, Astara: 20.37 and Rasht: 17.91). guilan province is suitable for establishing a turbine plant, because of the potential and windy favorable conditions to use it to meet the needs of various energies, including the electricity of the area. Therefore, it is necessary to take steady steps in order to develop this important industry.Keywords: Wind direction and Speed, Potentiometric, Fuzzy logic, Wind power plant, Statistical analysi

Be Thou Exalted, Volume 3: O Lord, By Thee Delivered: Vocal

Pages 1-4 in Be Thou Exalted, Volume 3: Vocal

El moralismo ingenuo de un cine cálido y humano

Safarian, R. (2001). El moralismo ingenuo de un cine cálido y humano. La madriguera. (34):62-65. http://hdl.handle.net/10251/41926.Importación Masiva62653