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Optimal_rank_using_LOOCV_smaller_subset_mfile.m
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Optimal_rank_using_LOOCV_smaller_subset_mfile.m
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%%Initation
clc; clf; rng(1); %clear;
%%Data extraction
%Data_extraction_and_structuring;
functional_groups = table2struct(readtable("GR Hermanus (22796002).xlsx", "Sheet", "Properties"), 'ToScalar', true);
functional_groups.Name = string(functional_groups.Name);
functional_groups.FunctionalGroup = string(functional_groups.FunctionalGroup);
index_smaller_subset = (functional_groups.FunctionalGroup == "Alkane" | ...
functional_groups.FunctionalGroup == "Primary Alcohol" | ...
functional_groups.FunctionalGroup == "Secondary Alcohol" |...
functional_groups.FunctionalGroup == "Diol" | ...
functional_groups.FunctionalGroup == "Branched Alcohol" | ...
functional_groups.FunctionalGroup == "Ether" | ...
functional_groups.FunctionalGroup == "Ester"); %index for the smaller subset of the data
index_smaller_subset = ones(size(index_smaller_subset)) == 1;
%%LOOCV and optimal rank
A_original2 = tensor_4D(index_smaller_subset, index_smaller_subset, 1, 1);
[number_rows, number_columns] = size(A_original2);
size_A = min([number_rows, number_columns]);
options = ["c", "r", "all", "rc", "JR", "ideal"];
%below code runs the LOOCV on the data set ans gives the MSE and MAE of the
%data with size of l j k x; where l = composition, j = rank, k = option for
%centering, x = option for the initial guess
ii = index;
index = 0;
for x = 5:6
option_initial_guess = options(x);
for k = 1:2
option_centering = options(k);
for l = 1: number_composition
A_original2 = tensor_4D(index_smaller_subset, index_smaller_subset,l,:);
for j = 3 : 8
rank = j;
temp = A_original2.*( eye(size_A, size_A) == 0);
known_indices = find(A_original2.*(eye(size_A,size_A)==0) ~= 0);
unknown_indices = (A_original2 == 0);
counter = 0;
for i = 1: numel(known_indices)
if index < ii
index = index + 1;
else
temp = unknown_indices; %temporary variable
temp(known_indices(i)) = 1; %sets element i equals to one, i.e. removing that spesific element of the original matrix
if l == 5
temp = (temp ~= unknown_indices)' + temp;
end
A_original = A_original2.*(temp == 0); %extracts new non-zero elements of the original matrix
if ( (sum(A_original, 1) ~= 0) & (sum(A_original, 2) ~= 0) ) %checks wether the rows and columns has all non-zero entries
counter = counter + 1;
%if both the rows and columns does not have all zero entries repeat
%itterations
%% Intial guess
A = fun_intial_guess(A_original, option_initial_guess, mole_fraction_Component1(l)); %intial guess
%% itterations
sigma = 10; %stopping criterion
itterations = 0; %number of itterations
while sigma > 1
A_new = fun_svd_itterations(A, rank, option_centering, mole_fraction_Component1(l)); %centering, SVD, and reverse centering
A = A_original + A_new.*temp; %replaces the unknown values by the itterated values
%Convergence
itterations = itterations + 1;
%stopping criterion
if itterations == 1
sigma = 10;
else
sigma = sum (abs( ( A_new(temp == 1) - A_prev(temp == 1) ) ));
end %end of stopping criterion
User_input = []; %used for maximum itterations
if rem(itterations,1000000) == 0 %some fancy stuff for insuring the loop does not continue indefinitely
% asks user after every 5000 itterations whether to stop or
% continue itterations
User_input = 'o'; %sets user_input to 'o' used to control while loop
while User_input == 'o'
fprintf('Maximum number itterations exceeded. Program stopped pre-maturely. Results might be incorrect\n\n');
User_input = input('Continue itterations? Y-Yes, N-No: \n\n', "s");
if User_input == 'N' | User_input == 'n'
break;
elseif User_input == 'Y' | User_input == 'y'
else
fprintf('Invalid selection. Please enter valid selection\n\n');
User_input = 'o';
end
end
end %end of fancy stuff
%additional code to exit while loop if user chooses
if User_input == 'N' | User_input == 'n' %exist the itteration loop
break
elseif isempty(User_input)
end %end of additional code
%idx = setdiff(1:numel(known_indices), counter);
%subplot(3, 1, 1);
%plot(itterations, sum( (A_new(known_indices(idx)) - A_original(known_indices(idx))).^2), '.k'); hold on
%subplot(3, 1, 2);
%plot(itterations, sigma, '.r'); hold on;
%subplot(3, 1, 3);
%plot(itterations, abs(A_original2(known_indices(counter))-A(known_indices(counter))), '.b'); hold on
%pause(0.1);
if sigma > 0.5
A_prev = A_new;
end
end %end of itterations
if l == 5 %for composition = 0.5 matrix should be symmetrical
A = (A+A')/2; %makes the matrix symmetrical by taking average;
end
index = index + 1;
LOOCV.Original (index, :) = A_original2(known_indices(i));
LOOCV.Itterations (index, :) = A(known_indices(i));
LOOCV.Initial (index, :) = options(x);
LOOCV.Centering (index, :) = options(k);
LOOCV.Composition (index, :) = l;
LOOCV.Rank (index, :) = rank;
LOOCV.NumberOfItterations (index, :) = itterations;
clc;
if rem(index,100) == 0
save("Results_LOOCV_subset_All");
end
end
end
end
end
end
end
end
function A_guess = fun_intial_guess (A, option, composition)
%this function calculates the intial guesses based on the option type, row
%averages, columns averages and a combination of row and column averages
option = convertCharsToStrings(option); %makes sure that a string is used
A_guess = A;
%[unknown_rows, unknwon_columns] = find(A_guess == 0); %returns the indices of the unknown rows and columns
check = 0; %intilises to zero
[number_rows, number_columns] = size(A);
while check == 0
if ( (option == "r") | (option == "c") | (option == "rc") | (option == "all") | (option == "JR") | (option == "ideal"))
check = 1;
elseif check == 0
option = input('Please enter a valid selection for "option".\nThe options as "r", "c" or "rc"\n', "s");
end
if option == "r"
for i = 1:number_rows
for j = 1:number_columns
n = numel( nonzeros(A(i, :)) ); %number of non-zerp elements in the row
if n == 0
fprintf('Warning! No entries in the row. No calculations were done'); %protective coding
break; % goes to next row
else
average = sum(A(i, :), 2)/n;
if A(i, j) == 0
A_guess(i, j) = average; %assignes zero values to row average
end
end
end % end of assigning one average to row i and column j
end % end of assigning average to row
%end of rows averages
elseif option == "c"
for i = 1:number_rows
for j = 1:number_columns
n = numel( nonzeros(A(:, j)) ); %number of non-zero elements in the column
if n == 0
fprintf('Warning! No entries in the column. No calculations were done'); %protective coding
break; % goes to next column
else
average = sum(A(:, j), 1)/n;
if A(i, j) == 0
A_guess(i, j) = average; %assignes zero values to column average
end
end
end % end of assigning one average to row i and column j
end % end of assigning average to a column
%end of column averages
elseif option == "rc"
for i = 1:number_rows
for j = 1:number_columns
n = numel(nonzeros([A(:,j); A(i,:)'])) - 1 * (A(i,j)~=0); %number of non-zero entries in a row and column
if n == 0
fprintf('Warning! No entries in the row and column. No calculations were done'); %protective coding
break; % goes to next entry
else
average = (sum([A(:,j); A(i,:)']) - A(i, j)) / n; %average of the non-zero rows and columns
if A(i, j) == 0
A_guess(i, j) = average;
end
end
end
end
elseif option == "all"
average = mean(nonzeros(A), "all");
unknown = (A == 0);
A_guess = A_guess + average*unknown;
elseif option == "ideal"
pure_comp = diag(A);
for i = 1 : number_rows
for j = 1: number_columns
if A(i, j) == 0
if (pure_comp(i) == 0) | (pure_comp(j) == 0)
A_guess(i, j) = mean(nonzeros(A(:, j))); %if pure component not known replace with column mean
else
A_guess(i, j) = composition*pure_comp(i) + (1-composition)*pure_comp(j);
end
end
end
end
elseif option == "JR"
T = readtable("GR Hermanus (22796002).xlsx", "Sheet", "Densities and molecular weight");
A_guess = A;
pure_comp = diag(A);
for i = 1:number_rows
for j = 1:number_columns
if A(i,j) == 0
if pure_comp(i) == 0 | pure_comp(j) == 0
A_guess(i,j) = mean( nonzeros(A(i,:)), "all" );
else
A_guess(i,j) = ( composition*T.MolecularWeight_kg_mol_(i)...
/T.Density_kg_m3_(i)+(1-composition)*T.MolecularWeight_kg_mol_(j)/T.Density_kg_m3_(j) )/...
( (composition*T.MolecularWeight_kg_mol_(i))+((1-composition)*T.MolecularWeight_kg_mol_(j)) )^(1/2) ...
* ( ( composition*T.MolecularWeight_kg_mol_(i)/T.Density_kg_m3_(i)+(1-composition)*T.MolecularWeight_kg_mol_(j)/...
T.Density_kg_m3_(j) )/( composition*T.Density_kg_m3_(i)*pure_comp(i)^2+...
(1-composition)*T.Density_kg_m3_(j)*pure_comp(j)^2) )^(-1/2);
end
end
end
end
end
end %end of while loop
end % end of intial guess function
function [Ac, average] = fun_centering(A, option)
%this function calculates the centered matrix based on 3 different methods.
%Centering based on columns means - r, centering based on row means - c,
%centering based on the rows and averages - rc, and centering based on all
%the entries - all
%the entries
option = convertCharsToStrings(option); %converts chars to strings
check = 0;
[number_rows, number_columns] = size(A);
while check == 0
if ( (option == "r") | (option == "c") | (option == "rc") | (option =="all") )
check = 1;
elseif check == 0
option = input('Please enter a valid selection for "option".\nThe options as "r", "c", "rc" or "all"\n', "s");
end
if option == "r"
for i = 1:number_rows
if sum(A(i,:)) == 0
average(i, :) = zeros(1, number_columns);
else
average(i, :) = mean(A(i, :))*ones(1, number_columns);
end
end
Ac = A - average;
elseif option == "c"
for j = 1:number_columns
if sum(A(:,j)) == 0
average(:, j) = zeros(number_rows, 1);
else
average(:, j) = mean(A(:, j))*ones(number_rows, 1);
end
end
Ac = A - average;
elseif option == "rc"
for i = 1:number_rows
for j = 1:number_columns
n = numel(nonzeros([A(:,j); A(i,:)'])) - 1 * (A(i,j)~=0); %number of non-zero entries in a row and column
if n == 0
average(i,j) = 0;
else
average(i,j) = (sum([A(:,j); A(i,:)']) - A(i, j)) / n; %average of the non-zero rows and columns
end
end
end
Ac = A - average;
elseif option == "all"
average = mean(A, "all")*ones(size(A));
Ac = A - average;
end
end
end %end of the centering function
function A_new = fun_svd_itterations(A, rank, option, composition)
%this function calculates the svd itterations
[Ac, average] = fun_centering(A, option); %centering
[U, S, V] = svd(Ac); %svd on centerd date
Ac_recon = U(:,1:rank)*S(1:rank, 1:rank)*V(:,1:rank)'; %reconstructed centered data
A_new = Ac_recon + average; %new martix
if composition == 0.5
A_new = (A_new + A_new')/2;
end
end