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Super-parameter optimization method based on pre-trained stochastic Fourier eigenkernel LMS

An optimization method and LMS algorithm technology, applied in the field of hyperparameter optimization, to overcome the instability of steady-state performance, improve coupling, and improve accuracy

Active Publication Date: 2019-01-15
HARBIN UNIV OF SCI & TECH
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Problems solved by technology

[0011] The purpose of the present invention is to solve the problem of how to obtain a set of hyperparameter values ​​in order to ensure the accuracy performance of the algorithm and reduce the computational complexity

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  • Super-parameter optimization method based on pre-trained stochastic Fourier eigenkernel LMS
  • Super-parameter optimization method based on pre-trained stochastic Fourier eigenkernel LMS
  • Super-parameter optimization method based on pre-trained stochastic Fourier eigenkernel LMS

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specific Embodiment approach 1

[0029] Specific implementation mode one: combine figure 2 This embodiment will be described. The hyperparameter optimization method based on the pre-trained random Fourier feature kernel LMS described in this embodiment, the method includes the following steps:

[0030] Step 1. Given a set of training sets x(i) represents the input signal of the i-th group, d(i) represents the expected signal of the i-th group, and M represents the sample size of the training set; P samples are randomly selected from the training set to obtain the pre-training set Among them: the value range of P is (1,M);

[0031] Step 2. Determine the value of the kernel parameter σ, and pre-set the values ​​of the m dimension parameters as [D 1 ,D 2 ,...,D j ,...,D m ], where: D 1 ,D 2 ,D j and D m respectively represent the value of the first dimension parameter, the value of the second dimension parameter, the value of the jth dimension parameter and the value of the mth dimension parameter; ...

specific Embodiment approach 2

[0039] Specific embodiment two: this embodiment further defines the hyperparameter optimization method based on the pre-trained random Fourier characteristic kernel LMS described in the first embodiment, the value range of the kernel parameter σ in the step two is [0.01, 2].

[0040] The value method of the kernel parameter: It takes multiple attempts to determine the value according to the effect of the training error.

specific Embodiment approach 3

[0041] Specific embodiment three: This embodiment further defines the hyperparameter optimization method based on the pre-trained random Fourier feature kernel LMS described in the first embodiment, the jth dimension parameter D in the second step j The value range of is [10, 1000], where: j=1,2,...,m.

[0042] Dimension parameter D j Value method: recommended multiple value method: such as D j+1 2 times D j ;D j+2 2 times D j+1 ; and so on;

[0043] The steady-state error under multiple kernel parameters is obtained through training, the kernel parameter value with the smallest steady-state error is selected, and m dimension parameters are determined according to the actual computational complexity and storage requirements; The steady-state error of σ continuously adjusts the kernel parameter σ value and the parameter values ​​of the m dimensions.

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Abstract

The invention provides a super-parameter optimization method based on pre-trained stochastic Fourier eigenkernel LMS. The method is used in super-parameter optimization of kernel adaptive filters. Theinvention solves the problem of how to obtain a group of super parameter values in order to guarantee the precision performance of the algorithm and reduce the computational complexity of the algorithm. On the basis of the pre-training set, to realize the performance evaluation of stochastic Fourier feature in every dimension, under the minimum mean square error criterion, a set of Fourier feature super-parameter values under the optimal dimension can be determined by the minimum mean square error values obtained by pre-training, The method of the invention reduces the dimension of the randomFourier feature required to reach the precision condition, thereby reducing the complexity, and improves the coupling degree between the modeled system and the random Fourier feature network in the adaptive filter system, thereby overcoming the problem that the steady-state performance is unstable due to the random sampling difference in the super-parameter value. The invention can be applied tothe field of super-parameter optimization technology of a nuclear adaptive filter.

Description

technical field [0001] The invention belongs to the technical field of hyperparameter optimization of a kernel adaptive filter, and in particular relates to a hyperparameter optimization method based on a pre-trained random Fourier characteristic kernel LMS (Least Mean Square, least mean square algorithm). Background technique [0002] Kernel adaptive filter is a filtering technique combining kernel learning method and traditional adaptive filtering method. The idea of ​​transforming the nonlinear problem in the original space into a linear optimization problem in the high-dimensional feature space is introduced. In many fields of nonlinear signal processing (nonlinear system identification, nonlinear time series prediction, echo cancellation, etc.), it has been widely proved that it has good nonlinear system modeling ability. [0003] The stochastic Fourier characteristic kernel least mean square algorithm is a kind of kernel adaptive filtering algorithm based on kernel ap...

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Application Information

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IPC IPC(8): H03H21/00
CPCH03H21/0043
Inventor 陈寅生罗中明刘玉奇
Owner HARBIN UNIV OF SCI & TECH
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