Data interpolation -- normalize data of different magnitude

In some cases , Normalization can improve the interpolation results , But in other cases, it may affect the accuracy of the solution . Whether to use normalization needs to be judged according to the nature of interpolation data .

advantage ： Normalized data may improve the interpolation results when the independent variables have different units and different scales . under these circumstances , Scaling the input to a similar magnitude can improve the numerical shape of interpolation .

Be careful ： If each variable has the same unit , Be careful when normalizing the data , Even if the scale of each variable is different . For data of the same unit , Normalization will affect the basic triangulation and eventually reduce the accuracy of interpolation due to adding direction deviation , So that the solution is distorted . for example , If x and y Both represent positions and are represented by “ rice ” In units of , Then normalization is wrong . At this time, it is not recommended to x and y Make inconsistent scaling , Because Zhengdong 10 Meter and true north 10 Meters are the same in space distance .

Create some sample data , among y The value ratio in x The value in is several orders of magnitude larger . hypothesis x and y Have different units .

x = rand(1,1000)/100;

y = 2.*(rand(1,1000)-0.5).*90;

z = x.^2;

Use the above sample data to build a grid data , Interpolate based on the sample data on the grid and draw the results .

x1 = linspace(min(x),max(x),25);

y1= linspace(min(y),max(y),25);

[X, Y] = meshgrid(x1,y1);

Z = griddata(x,y,z,X,Y);

plot3(x,y,z,'co')

hold on

mesh(X,Y,Z)

griddata The result is not very smooth , There seems to be noisy data . This is because the independent variables have different scales , Because a small change in the size of one variable will lead to a huge change in the size of another variable .

because x and y Have different units , Normalize them to a similar order , It should help produce better results . Normalize the sample points , And use griddata Regenerate interpolation .

%  Normalized data

x = mapminmax(x);

y = mapminmax(y);

% Generating grid data

x1 = linspace(min(x),max(x),25);

y1 = linspace(min(y),max(y),25);

[X,Y] = meshgrid(x1,y1);

% Data interpolation

Z= griddata(x,y,z,X,Y);

plot3(x,y,z,'co')

hold on

mesh(X,Y,Z)

under these circumstances , Normalizing the sample points will make griddata  Calculate a smoother solution .

This shows that when the data magnitude varies greatly , Direct interpolation is not a very wise choice , Try to process the data , This is an important skill .

The articles

matlab mapping | Axis axis Some common settings of

matlab mapping | Gradient fill