Is there a way to identify which dataset a value belongs to for overlapping datasets?

I have three types of datasets. These data sets visually shows that `data a` has comparatively lower values compared to `data b` and `data c`. I used a box plot to make a comparison and it shows that they have differences but there are overlaps. I will demonstrate them in the code below:

clc; clear all; close all
load("dataset.mat")
figure
hold on
xlabel('index of points')
ylabel('data value')
plot(a,'.',DisplayName='data1')
plot(b,'.',DisplayName='data2')
plot(c,'.',DisplayName='data3')

figure;
boxplot([a b c],'Notch','on','Labels',{'data1','data2','data3'})
 grid on

Now considering these data sets, I have a set of values, say [4 7 40 8 4], I want to predict which dataset these value may belong to. Is there a way to do that? Having a very basic knowledge of statistics, I cannot come up with a solution. I found one solution based on which Kernel density estimate (kde) was used for comparison. However, the data was distinctly separable. In my case, the datasets are more overlapped, is there a way to predict in this case? Forgive my very basic knowledge and suggest a solution. Will appreciate it.

Thanks in advance.

 figure
hold on
[fn,xfn,bwn] = kde(a);
plot(xfn,fn)
[fn,xfn,bwn] = kde(b);
plot(xfn,fn)
[fn,xfn,bwn] = kde(c);
plot(xfn,fn)

[Jeff Miller]

You might look into logistic regression and discriminant function analysis. These are both techniques for predicting category membership.

[UH]

Thank you for the idea. I am looking into these.

Answer 1

[Chunru]

websave("dataset.mat", "https://www.mathworks.com/matlabcentral/answers/uploaded_files/1650591/dataset.mat")

ans = '/users/mss.system.pbnsl/dataset.mat'

load("dataset.mat")
figure
hold on
xlabel('index of points')
ylabel('data value')
plot(a,'.',DisplayName='data1')
plot(b,'.',DisplayName='data2')
plot(c,'.',DisplayName='data3')

whos

  Name               Size            Bytes  Class             Attributes

  a                 90x1               720  double                      
  ans                1x35               70  char                        
  b                 90x1               720  double                      
  c                 90x1               720  double                      
  cmdout             1x33               66  char                        
  gdsCacheDir        1x14               28  char                        
  gdsCacheFlag       1x1                 8  double                      
  i                  0x0                 0  double                      
  managers           1x0                 0  cell                        
  managersMap        0x1                 8  containers.Map              

figure;
boxplot([a b c],'Notch','on','Labels',{'data1','data2','data3'})
 grid on

 x =  [4 7 40 8 4]';
 
 % K Nearest neighbour (KNN) classification
 data = [a; b; c];
 label = [ones(size(a)); 2*ones(size(b)); 3*ones(size(b)) ];
 Mdl = fitcknn(data, label, "NumNeighbors", 80);    % larger number of neighbours
 predictedClass = predict(Mdl, x)                   % predicted class

predictedClass = 5x1

1 1 3 2 1

[UH]

Thank you for your answer. I will further check with whether the most occuring prediction leads to the predicted class or I have to perform some additional analysis. This probably works. Thank you. Good day.