scholarly journals Sparse representation in Szegő kernels through reproducing kernel Hilbert space theory with applications

2015 ◽  
Vol 13 (04) ◽  
pp. 1550030 ◽  
Author(s):  
Y. Mo ◽  
T. Qian ◽  
W. Mi
Keyword(s):  
Reproducing Kernel ◽  
Linear Time ◽  
Reproducing Kernel Hilbert Space ◽  
Identification Problem ◽  
Support Vector ◽  
Complex Data ◽  
Linear Time Invariant ◽  
Generalization Bounds ◽  
Domain Identification ◽  
Linear Time Invariant System

This paper discusses generalization bounds for complex data learning which serve as a theoretical foundation for complex support vector machine (SVM). Drawn on the generalization bounds, a complex SVM approach based on the Szegő kernel of the Hardy space H2(𝔻) is formulated. It is applied to the frequency-domain identification problem of discrete linear time-invariant system (LTIS). Experiments show that the proposed algorithm is effective in applications.

A Frequency Domain Identification Scheme for Control and Fault Diagnosis

1997 ◽  
Vol 119 (1) ◽  
pp. 48-56 ◽  
Author(s):  
G. Mallory ◽  
R. Doraiswami
Keyword(s):  
Frequency Domain ◽  
Linear Time ◽  
Robot Manipulator ◽  
Physical Parameters ◽  
Linear Time Invariant ◽  
Domain Identification ◽  
Frequency Domain Identification ◽  
Identification Technique ◽  
Manipulator Arm ◽  
Linear Time Invariant System

A robust scheme to estimate a set of models for a linear time-invariant system, subject to perturbations in the physical parameters, from a frequency response data record is proposed. The true model as well as the disturbances affecting the system are assumed unknown. However, the physical parameters are assumed to enter the coefficients of the system transfer function multilinearly. A set of models is identified by perturbing the physical parameters one-at-time and using a frequency domain identification technique. Exploiting the assumed multilinearity, the estimated set of models is validated. The proposed scheme is evaluated on a number of simulated systems, and on a physical robot manipulator arm.

scholarly journals Temporal Variability in the Response of a Linear Time-Invariant Catchment System to a Non-Stationary Inflow Concentration Field

2020 ◽  
Vol 10 (15) ◽  
pp. 5356
Author(s):  
Ching-Min Chang ◽  
Kuo-Chen Ma ◽  
Mo-Hsiung Chuang
Keyword(s):  
Closed Form ◽  
Temporal Variability ◽  
Linear Time ◽  
Concentration Field ◽  
Surface Water Quality ◽  
Catchment Scale ◽  
Input Concentration ◽  
Linear Time Invariant ◽  
Linear Time Invariant System ◽  
Time Invariant

Predicting the effects of changes in dissolved input concentration on the variability of discharge concentration at the outlet of the catchment is essential to improve our ability to address the problem of surface water quality. The goal of this study is therefore dedicated to the stochastic quantification of temporal variability of concentration fields in outflow from a catchment system that exhibits linearity and time invariance. A convolution integral is used to determine the output of a linear time-invariant system from knowledge of the input and the transfer function. This work considers that the nonstationary input concentration time series of an inert solute to the catchment system can be characterized completely by the Langevin equation. The closed-form expressions for the variances of inflow and outflow concentrations at the catchment scale are derived using the Fourier–Stieltjes representation approach. The variance is viewed as an index of temporal variability. The closed-form expressions therefore allow to evaluate the impacts of the controlling parameters on the temporal variability of outflow concentration.

On Learning Vector-Valued Functions

2005 ◽  
Vol 17 (1) ◽  
pp. 177-204 ◽  
Author(s):  
Charles A. Micchelli ◽  
Massimiliano Pontil
Keyword(s):  
Hilbert Space ◽  
Learning Theory ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Support Vector ◽  
Translation Invariant ◽  
Minimal Norm ◽  
Finite Set ◽  
Vector Valued Functions ◽  
Vector Valued

In this letter, we provide a study of learning in a Hilbert space of vector-valued functions. We motivate the need for extending learning theory of scalar-valued functions by practical considerations and establish some basic results for learning vector-valued functions that should prove useful in applications. Specifically, we allow an output space Y to be a Hilbert space, and we consider a reproducing kernel Hilbert space of functions whose values lie in Y. In this setting, we derive the form of the minimal norm interpolant to a finite set of data and apply it to study some regularization functionals that are important in learning theory. We consider specific examples of such functionals corresponding to multiple-output regularization networks and support vector machines, for both regression and classification. Finally, we provide classes of operator-valued kernels of the dot product and translation-invariant type.

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