scholarly journals A cost function to determine the optimum filter and parameters for stabilizing gaze data

2019 ◽  
Vol 12 (2) ◽  
Author(s):  
Pieter Blignaut
Keyword(s):  
Standard Deviation ◽  
Cost Function ◽  
Sliding Window ◽  
Optimum Combination ◽  
Fir Filters ◽  
Eye Tracker ◽  
Optimal Parameters ◽  
Filter Length ◽  
Optimum Filter ◽  
Unfiltered Data

Prior to delivery of data, eye tracker software may apply filtering to correct for noise. Although filtering produces much better precision of data, it may add to the time it takes for the reporting of gaze data to stabilise after a saccade due to the usage of a sliding window. The effect of various filters and parameter settings on accuracy, precision and filter related latency is examined. A cost function can be used to obtain the optimal parameters (filter, length of window, metric and threshold for removal of samples and removal percentage). It was found that for any of the FIR filters, the standard deviation of samples can be used to remove 95% of samples in the window so than an optimum combination of filter related latency and precision can be obtained. It was also confirmed that for unfiltered data, the shape of noise, signified by RMS/STD, is around √2 as expected for white noise, whereas lower RMS/STD values were observed for all filters.

Estimating Optimum Filter Length in Linear Prediction

1997 ◽  
Vol 51 (5) ◽  
pp. 718-720 ◽  
Author(s):  
O.-P. Sievänen
Keyword(s):  
Raman Spectra ◽  
Prediction Error ◽  
Linear Prediction ◽  
Signal To Noise Ratio ◽  
New Method ◽  
Signal To Noise ◽  
Filter Length ◽  
Optimum Filter ◽  
Good Signal ◽  
Prediction Filter

In this article a new method to estimate optimum filter length in linear prediction is described. Linear prediction was used to enhance resolution of a spectrum. In particular, the dependence of prediction error on filter length has been studied. With calculations of simulated spectra it is shown that the prediction error falls rapidly when the filter length attains its optimum value. This effect is quite pronounced when the spectrum has a good signal-to-noise ratio and the modified covariance method is used to calculate prediction filter coefficients. The method is illustrated with applications to real Raman spectra.

scholarly journals Micro-Slit Cutting in an Aluminum Foil Using an Un-Traveling Tungsten Wire

2020 ◽  
Vol 10 (2) ◽  
pp. 665
Author(s):  
Jiacheng Zhu ◽  
Xiaolong Fang ◽  
Ningsong Qu
Keyword(s):  
Surface Roughness ◽  
Standard Deviation ◽  
Tungsten Wire ◽  
Feeding Rate ◽  
Aluminum Foil ◽  
Optimal Parameters ◽  
Cutting Mechanism ◽  
Average Width ◽  
Series Of Experiments ◽  
Secondary Velocity

Microslit cutting in aluminum foils is considered to be difficult as aluminum foils have low hardness and deformability. In this study, a novel cutting method is proposed where a tungsten microwire is utilized as the tool to cut aluminum foil without tool traveling or spinning. A statics simulation is first performed to analyze the cutting mechanism. Further, a tungsten wire with a diameter of 50 μm is utilized as the tool and a series of experiments are carried to discuss how the feeding rate influences slit width and roughness. With optimal parameters, it takes only 100 s to fabricate a 5 mm long microslit with an average width of 48.75 μm, width standard deviation of 1.48 μm, and surface roughness of 0.110 μm when applying initial/secondary velocity of 50/50 μm·s−1.

scholarly journals A Novel Learning Rate Schedule in Optimization for Neural Networks and It’s Convergence

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 660 ◽  
Author(s):  
Jieun Park ◽  
Dokkyun Yi ◽  
Sangmin Ji
Keyword(s):  
Neural Networks ◽  
Cost Function ◽  
Numerical Experiments ◽  
Learning Rate ◽  
Optimal Parameters ◽  
Effective Learning ◽  
Symmetric Optimization ◽  
Constant Rate ◽  
The Cost ◽  
Iteration Time

The process of machine learning is to find parameters that minimize the cost function constructed by learning the data. This is called optimization and the parameters at that time are called the optimal parameters in neural networks. In the process of finding the optimization, there were attempts to solve the symmetric optimization or initialize the parameters symmetrically. Furthermore, in order to obtain the optimal parameters, the existing methods have used methods in which the learning rate is decreased over the iteration time or is changed according to a certain ratio. These methods are a monotonically decreasing method at a constant rate according to the iteration time. Our idea is to make the learning rate changeable unlike the monotonically decreasing method. We introduce a method to find the optimal parameters which adaptively changes the learning rate according to the value of the cost function. Therefore, when the cost function is optimized, the learning is complete and the optimal parameters are obtained. This paper proves that the method ensures convergence to the optimal parameters. This means that our method achieves a minimum of the cost function (or effective learning). Numerical experiments demonstrate that learning is good effective when using the proposed learning rate schedule in various situations.

scholarly journals A comparison between gradient descent and stochastic approaches for parameter optimization of a coupled ocean–sea ice model

2012 ◽  
Vol 9 (6) ◽  
pp. 3593-3642
Author(s):  
H. Sumata ◽  
F. Kauker ◽  
R. Gerdes ◽  
C. Köberle ◽  
M. Karcher
Keyword(s):  
Genetic Algorithms ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Sea Ice ◽  
Cost Function ◽  
Parameter Optimization ◽  
Difference Method ◽  
Gradient Descent ◽  
Optimal Parameters ◽  
Ice Model

Abstract. Two types of optimization methods were applied to a parameter optimization problem in a coupled ocean–sea ice model, and applicability and efficiency of the respective methods were examined. One is a finite difference method based on a traditional gradient descent approach, while the other adopts genetic algorithms as an example of stochastic approaches. Several series of parameter optimization experiments were performed by minimizing a cost function composed of model–data misfit of ice concentration, ice drift velocity and ice thickness. The finite difference method fails to estimate optimal parameters due to an ill-shaped nature of the cost function, whereas the genetic algorithms can effectively estimate near optimal parameters with a practical number of iterations. The results of the study indicate that a sophisticated stochastic approach is of practical use to a parameter optimization of a coupled ocean–sea ice model.

scholarly journals Controller design of isolated power-electricity island using genetic algorithm

2019 ◽  
Vol 70 (1) ◽  
pp. 46-51
Author(s):  
Ivan Sekaj ◽  
Martin Ernek
Keyword(s):  
Genetic Algorithm ◽  
Cost Function ◽  
Controller Design ◽  
Control Design ◽  
Optimal Parameters ◽  
Control Error ◽  
Pi Controllers ◽  
The Cost

Abstract The contribution presents the use of Genetic Algorithm for searching of the optimal parameters of a set of speed controllers of an isolated power-electricity island. Nine PI-controllers are designed. The cost function which is minimised using the Genetic Algorithm represents the integral of the control error area. Robustness aspects of the control design are considered as well.

scholarly journals The Relationship Between Bitcoin and Stock Market

2020 ◽  
Vol 11 (2) ◽  
pp. 22-35 ◽  
Author(s):  
Xin Wang ◽  
Xi Chen ◽  
Peng Zhao
Keyword(s):  
Standard Deviation ◽  
Stock Market ◽  
Sliding Window ◽  
Financial Investment ◽  
Vector Autoregressive ◽  
Applied Study ◽  
Window Technique ◽  
Study Results ◽  
The Mean ◽  
The Relationship

This article analyzes the relationship between Bitcoin and the stock market by using a vector autoregressive model. To enhance the impulse response signal, the Sliding Window technique is applied. Study results show the relationship between Bitcoin and the stock market. First, the S&P 500 has a relatively significant effect on Bitcoin, while the influence caused by the S&P 500 is weak. In addition, after involving the Sliding Window technique, the effects caused by the standard deviation of the S&P 500 and the mean of the Dow Jones are remarkably strong on the mean of Bitcoin and the standard deviation of the S&P 500 has a comparatively significant effect on the standard deviation of Bitcoin as well. Generally, the S&P 500 and the Dow Jones indexes have an advantageous effect on Bitcoin. Financial investment can be made based on this model and conclusion.

scholarly journals A comparison between gradient descent and stochastic approaches for parameter optimization of a sea ice model

Ocean Science ◽  
2013 ◽  
Vol 9 (4) ◽  
pp. 609-630 ◽  
Author(s):  
H. Sumata ◽  
F. Kauker ◽  
R. Gerdes ◽  
C. Köberle ◽  
M. Karcher
Keyword(s):  
Sea Ice ◽  
Cost Function ◽  
Parameter Optimization ◽  
Gradient Descent ◽  
Stochastic Approach ◽  
Optimization Methods ◽  
Horizontal Resolution ◽  
The Arctic ◽  
Optimal Parameters ◽  
Ice Model

Abstract. Two types of optimization methods were applied to a parameter optimization problem in a coupled ocean–sea ice model of the Arctic, and applicability and efficiency of the respective methods were examined. One optimization utilizes a finite difference (FD) method based on a traditional gradient descent approach, while the other adopts a micro-genetic algorithm (μGA) as an example of a stochastic approach. The optimizations were performed by minimizing a cost function composed of model–data misfit of ice concentration, ice drift velocity and ice thickness. A series of optimizations were conducted that differ in the model formulation ("smoothed code" versus standard code) with respect to the FD method and in the population size and number of possibilities with respect to the μGA method. The FD method fails to estimate optimal parameters due to the ill-shaped nature of the cost function caused by the strong non-linearity of the system, whereas the genetic algorithms can effectively estimate near optimal parameters. The results of the study indicate that the sophisticated stochastic approach (μGA) is of practical use for parameter optimization of a coupled ocean–sea ice model with a medium-sized horizontal resolution of 50 km × 50 km as used in this study.

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