Non-negative least square method is giving fixed values

Question

Arnab Paul 2024-5-27

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https://ww2.mathworks.cn/matlabcentral/answers/2123126-non-negative-least-square-method-is-giving-fixed-values

回答： Nipun 2024-6-11

I am trying the NNLS with my dataset to solve the a problem. The values are for each column remain same and no changes at all in each column. what is the possible exlanation for this?

I have adde the .mat adn .m file with the question. I could use SVD but the the values need to be positive as hey are concentration.

Any help will be appreciated.

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Arnab Paul 2024-5-30

在 MATLAB Online 中打开

%upload the table
A = readtable('Total_kernel_size.xlsx', 'ReadRowNames', true, 'PreserveVariableNames', true);

A_matrix = table2array(A);
A_micro = readtable('interp_kernal_micro.xlsx', 'ReadRowNames', true, 'PreserveVariableNames', true);
A_nano = readtable('interp_kernal_nano.xlsx', 'ReadRowNames', true, 'PreserveVariableNames', true);
A_pico = readtable('interp_kernal_pico.xlsx', 'ReadRowNames', true, 'PreserveVariableNames', true);
%convert the table to array
A_matrix_micro = table2array(A_micro);
A_matrix_nano = table2array(A_nano);
A_matrix_pico = table2array(A_pico);
excel_file_aph = readtable('standardized_aph.xlsx', 'PreserveVariableNames', true);
excel_file_aph(:,1:9) = [];
excel_file_aph = table2array(excel_file_aph);
excel_file_aph = excel_file_aph.';
options = optimset('TolX', 1e-6);
x = zeros(size(A_matrix, 2), size(excel_file_aph, 2));
x_micro = zeros(size(A_matrix_micro, 2), size(excel_file_aph, 2));
x_nano = zeros(size(A_matrix_nano, 2), size(excel_file_aph, 2));
x_pico = zeros(size(A_matrix_pico, 2), size(excel_file_aph, 2));
for j = 1:size(excel_file_aph, 2)
        %x(:, j) = lsqnonneg(A_matrix, excel_file_aph(:, j));
         x_micro(:, j) = lsqnonneg(A_matrix_micro, excel_file_aph(:, j), options);
         x_nano(:, j) = lsqnonneg(A_matrix_nano, excel_file_aph(:, j), options);
         x_pico(:, j) = lsqnonneg(A_matrix_pico, excel_file_aph(:, j), options);
end
f_micro = x_micro./(x_micro+x_nano+x_pico);
f_nano = x_nano./(x_micro+x_nano+x_pico);
f_pico = x_pico./(x_micro+x_nano+x_pico);
disp(f_micro)
  Columns 1 through 18

    0.5506    0.5507    0.5520    0.5542    0.5538    0.5771    0.5689    0.5675    0.5695    0.5697    0.5705    0.5720    0.5647    0.5726    0.5698    0.5779    0.5734    0.5684

  Columns 19 through 36

    0.5633    0.5618    0.5610    0.5566    0.5544    0.5499    0.5676    0.5679    0.5700    0.5656    0.5660    0.5551    0.5601    0.5469    0.5453    0.5431    0.5445    0.5590

  Columns 37 through 54

    0.5539    0.5508    0.5664    0.5813    0.5796    0.5793    0.5767    0.5730    0.5715    0.5611    0.5673    0.5563    0.5718    0.5798    0.5811    0.5816    0.5808    0.5722

  Columns 55 through 72

    0.5662    0.5556    0.5675    0.5672    0.5767    0.5790    0.5755    0.5714    0.5668    0.5740    0.5518    0.5455    0.5408    0.5438    0.5784    0.5707    0.5747    0.5750

  Columns 73 through 90

    0.5682    0.5794    0.5759    0.5797    0.5661    0.5640    0.5545    0.5505    0.5429    0.5389    0.5695    0.5649    0.5740    0.5399    0.5744    0.5683    0.5502    0.5733

  Columns 91 through 108

    0.5686    0.5327    0.5664    0.5709    0.5715    0.5523    0.5738    0.5705    0.5463    0.5458    0.5443    0.5407    0.5444    0.5705    0.5597    0.5407    0.5388    0.5641

  Columns 109 through 126

    0.5385    0.5371    0.5384    0.5682    0.5692    0.5457    0.5345    0.5476    0.5691    0.5617    0.5418    0.5405    0.5435    0.5461    0.5378    0.5420    0.5630    0.5540

  Columns 127 through 144

    0.5522    0.5560    0.5444    0.5436    0.5427    0.5522    0.5442    0.5576    0.5605    0.5568    0.5503    0.5604    0.5493    0.5432    0.5404    0.5446    0.5528    0.5521

  Columns 145 through 162

    0.5502    0.5530    0.5559    0.5495    0.5483    0.5435    0.5429    0.5583    0.5341    0.5379    0.5404    0.5328    0.5401    0.5405    0.5484    0.5744    0.5685    0.5716

  Columns 163 through 180

    0.5727    0.5687    0.5736    0.5640    0.5745    0.5752    0.5726    0.5681    0.5670    0.5667    0.5593    0.5660    0.5657    0.5454    0.5594    0.5725    0.5763    0.5588

  Columns 181 through 198

    0.5690    0.5676    0.5730    0.5681    0.5710    0.5689    0.5758    0.5773    0.5760    0.5745    0.5723    0.5730    0.5712    0.5699    0.5536    0.5440    0.5454    0.5684

  Columns 199 through 205

    0.5666    0.5703    0.5628    0.5641    0.5625    0.5582    0.5768

Hi @Matt J I ran it successfully, the question is why f_micro/nano/pico coming almost same throughout the columns? What is the mathematical explanation for this?

Thanks for your help.

Matt J 2024-5-30

Maybe your input data don't differ very much.

Arnab Paul 2024-5-30

They are actually different. Even though is it possible to have the monotonous values all across the column?

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Answer 1

Nipun 2024-6-11

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2123126-non-negative-least-square-method-is-giving-fixed-values#answer_1470471

Hi Arnab,

I understand that you are experience an issue with NNLS (Non-Negative Least Squares) where the values for each column remain unchanged. This issue might be due to several factors, such as:

Insufficient variability in the data.
Constraints not properly applied.
Issues with the initial guess or convergence criteria.

For more details on NNLS, you can refer to the following MathWorks documentation link: https://www.mathworks.com/help/matlab/ref/lsqnonneg.html

Hope this helps.

Regards,

Nipun

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