FindGraph: Approximation performed for neural network with non linear fitting

Approximation

Regression line through a series of points

Follow these steps to build the regression line:

1. To select series of points in list, double click on it.
2. The dialog 'Information on points series' appears.
3. Click the <Function...> button.
4. The Wizard of approximation starts.
5. On a step 1 we choose relation Y = f( X ).
6. On a step 2 we choose 'Regression line'.
7. On a step 3 we choose ''Polynomial'.
8. On a step 4 we select polynomial degree 1.
9. Recalculate.
10. Put information string on the Clipboard.
11. On a step 5 we select color and width of line.
12. Regression line was build.
13. Click button and paste information string.

Using the neural network approximation

Follow these steps to use the neural network:

1. To select series of points in list, double click on it.
2. The dialog 'Information on points series' appears.
3. Click the <Function...> button.
4. The Wizard of approximation starts.
5. On a step 1 we choose relation Y = f( X ).
6. On a step 2 we choose 'Neural network'.
7. On a step 3 we choose 300 iterations.
8. On a step 4 we select 20 neurons.
9. Recalculate.
10. If failed, we select 12 neurons.
11. Recalculate.
12. On a step 5 we select color and width of line.
13. Approximation line was build.

Using the non-linear fitting

Follow these steps to use the non-linear fitting:

1. To select series of points in list, double click on it.
2. The dialog 'Information on points series' appears.
3. Click the <Function...> button.
4. The Wizard of approximation starts.
5. On a step 1 we choose relation Y = f( X ).
6. On a step 2 we choose 'Non-linear'.
7. On a step 3 we input desirable formula with parameter (a) Y( u ) = u + a*sin(u).
8. Define initial values of the fitting parameters and click the <Preview> button.
9. New graph appears. See how fit curve conforms your data.
10. On a step 4 recalculate. It may take a lot of time for slow computers.
11. On a step 5 we select color and width of line.
12. Approximation line was build.

Important: The expression must be composed from internal functions (see formula for more details), operators and only following parameters: a, b, c, d. The result of your fitting session critically depends on initial values of parameters.

Examples:

Y( u ) = a + b*u^2.5 + c*u^4;
Y( u ) = a + b/u + c * exp( u/10 );
Y( u ) = 5+ a*besselj0( u );
Y( u ) = 5+ a*normal( u, c);

Trick: View Log Fitting Window to discover the best model to describe your data.

Best curve fit

Follow these steps to find the best curve fit:

1. To select series of points in list, click on it.
2. Select menu item <Fit><Best Function> or click on button .
3. The Wizard starts.
4. On a step 1 we choose X and Y ranges.
5. On a step 2 we check groups of functions.
6. On a step 3 we click on button Start. Fitting process runs. It may take a lot of time for slow computers.
7. New graphs appear. See how fit curves conform your data.
8. Results are sorted by Std. error value or by Ra-square (Adjusted coefficient of Multiple Determination) value.
9. Select the number of best fit functions to plot. Only this functions are saved.
10. Several approximation lines were build.

B-spline through all points inside area

Follow these steps to build the B-spline:

1. Select and create area around points.
2. Select editor mode
3. Click left inside the rectangle area.
4. The dialog 'Information on selected area' appears.
5. Click the <Function...> button
6. The Wizard of approximation starts
7. On a step 1 we choose relation Y = f( X ).
8. On a step 2 we choose 'B-spline'.
9. On a step 4 we select the power and the number of control points of B-spline.
10. On a step 5 we select color and width of line.
11. Spline was build.

Sections through all red points inside selected area

Follow these steps to build the sections:

1. Select and create area around points.
2. Use to select area.
3. Select the current color - red
4. Click right button on area. Popup menu appears.
5. Select item <Function through red selected points>.
6. The Wizard of approximation starts.
7. On a step 1 we choose relation Y = f( X ).
8. On a step 2 we choose 'Sections'.
9. On a step 4 we select nodes of net 50.
10. On a step 5 we select color and width of line.
11. Sections were build.