Theme: calculation of spectral coefficients of signals using the machine learning method based on xaar bases

piece-quadratic
	Signal number	64		128		64		128		64		128
№		Kс	Nk %	Kc	Nk %	Kс	Nk %	Kс	Nk %	Кс	Nk %	Kс	Nk %
1.	Y= ex	1	0	1	0	1.7	70	4.1	75.7	5.3	81	8.5	88.2
2.	Y=e2x сос(4x)	1	0	1	0	1.6	37.2	2.8	55.1	1.7	40	2.8	64.3
3.	th(x)	1	0	1	0	1.1	65	2.3	70.5	6.4	85	9.1	89.2

Kc - compression coefficient in the table, Nk-number of zero coefficients. 

IMPROVEMENT OF HAAR BASES BASED ON MACHINE LEARNING.

• Machine Learning – is a new branch of computer programming in which software can read data, learn from that data, and allow computers to learn without being directly programmed. There are also different categories of machine learning. Based on how data is used, we can divide machine learning into the following categories:
• supervised learning;
• unsupervised learning;
• reinforcement learning;
• Supervised learning – the most common method of this type of training is to train a computer program using specified data. Supervised learning itself is divided into 2 categories:
• Regression;
• Classification.

We use univariate linear regression to solve the fitted mass. One of the main tasks when working with linear regression is to find the best regression line that represents the data. If the regression line is determined based on the following formula , we need to find the coefficients wi and bi

• We use univariate linear regression to solve the fitted mass. One of the main tasks when working with linear regression is to find the best regression line that represents the data. If the regression line is determined based on the following formula , we need to find the coefficients wi and bi
• Yi = wixi+bi
• In this case, the result predicted by these constants must be close to the actual value presented in the data set.

•  

Figure. Finding values closest to actual values using predicted values.

The 1st line in the graph is the predicted values. Line 2 is the closest value to the actual value based on the predicted values. The difference between the predicted value and the actual value should be as small as possible. This difference is taken as an error and a value function is generated. The main task of the value function is to detect this error. Based on this function, we can determine how correctly the regression coefficients (w i and b i ) are found, that is, through these coefficients, we can find the error between the predicted and the actual value. For this we use the mean squared error function as the value function. Medium quadratic error is expressed in the form of a graph

Mean squared error count graph

The farther the predicted value is from the true value, the larger the root mean square error function. Depending on the error calculated by the root mean square error function, we need to update the regression coefficients (wi and bi ) to get better predictions and reduce the error. For this, we use the gradient descent method. Gradient descent allows us to reduce the error by updating the regression coefficients. Usually, at the beginning of the training process, the coefficients (wi and bi) are assigned a random value. Then the error is found by calculating the value function (r). Our main goal is to minimize the value function(r), and in the case of linear regression, the mean square function, depending on the value of the error. For this, we perform gradient descent.

Here is the 𝑎 -learning rate.

Using the mentioned sequences, we will perform improvement on the bases of existing algorithms and machine learning method, observing the conditions of interpolation of Haar's second-order partial polynomial base. In this case, we determine the bi-coefficient in the formula using the machine controlled learning method. For this, let's integrate between two points

• Using the mentioned sequences, we will perform improvement on the bases of existing algorithms and machine learning method, observing the conditions of interpolation of Haar's second-order partial polynomial base. In this case, we determine the bi-coefficient in the formula using the machine controlled learning method. For this, let's integrate between two points

spread is formed in the form of the following formula.
– a function formed on the bases of integration. As a result of integration if we pay attention to this formula wi – an unknown coefficient appears.