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analysis8_v2018.m
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clear all
load('EC1','-mat')
load('CA1','-mat')
count=ones(6,3);
percent=99;
total_cells=0;
for index=1:length(data)
if isempty(data{index})~=1
for j=1:length(data{index})
total_cells=total_cells+1;
cell_name(total_cells,:)=data{index}{j}.name;
for aspect=1:6
test=sort(data{index}{j}.TEST.I(aspect,:));
information(aspect,total_cells)=data{index}{j}.I(aspect);
information_delta(aspect,total_cells)=data{index}{j}.I_delta(aspect);
information_theta(aspect,total_cells)=data{index}{j}.I_theta(aspect);
I(aspect,total_cells)=0;
I_delta(aspect,total_cells)=0;
I_theta(aspect,total_cells)=0;
if data{index}{j}.I(aspect)>test(percent)
I(aspect,total_cells)=1;
end
test=sort(data{index}{j}.TEST.I_delta(aspect,:));
if data{index}{j}.I_delta(aspect)>test(99)
I_delta(aspect,total_cells)=1;
end
test=sort(data{index}{j}.TEST.I_theta(aspect,:));
if data{index}{j}.I_theta(aspect)>test(99)
I_theta(aspect,total_cells)=1;
end
end
end
end
end
matrix1=information.*I;
matrix2=information_delta.*I_delta;
matrix3=information_theta.*I_theta;
%al possible combinations
vector=[1,1,1,1,1,1,0,0,0,0,0,0];
matrix=nchoosek(vector,6);
number=2;
element(1,:)=matrix(1,:);
for i=1:length(matrix)
index=0;
for j=1:size(element,1)
if ~isequal(matrix(i,:),element(j,:))
index=index+1;
end
end
if index==size(element,1)
element(number,:)=matrix(i,:);
number=number+1;
end
end
new_element(1,:)=element(1,:);
number2=2;
for k=1:size(element)
permutations=perms(element(k,:));
for i=1:length(permutations)
index=0;
for j=1:size(new_element,1)
if ~isequal(permutations(i,:),new_element(j,:))
index=index+1;
end
end
if index==size(new_element,1)
new_element(number2,:)=permutations(i,:);
number2=number2+1;
end
end
end
%compute the data matrix
%compare with I
probability1=zeros(size(new_element,1),1);
for i=1:length(matrix1)
for j=1:size(new_element,1)
if isequal(I(:,i),new_element(j,:)')
probability1(j)=probability1(j)+1;
end
end
end
probability1=probability1/length(I);
%compare with I_delta
probability=zeros(size(new_element,1),1);
for i=1:length(matrix1)
for j=1:size(new_element,1)
if isequal(I_delta(:,i),new_element(j,:)')
probability(j)=probability(j)+1;
end
end
end
probability2=probability/length(I_delta);
%compare with I_theta
probability=zeros(size(new_element,1),1);
for i=1:length(matrix1)
for j=1:size(new_element,1)
if isequal(I_theta(:,i),new_element(j,:)')
probability(j)=probability(j)+1;
end
end
end
probability3=probability/length(I_theta);
h1=-sum((probability1+eps).*log((probability1+eps)));
h2=-sum((probability2+eps).*log((probability2+eps)));
h3=-sum((probability3+eps).*log((probability3+eps)));
for k=1:200
% generate a 6d random vector from a uniform distribution
random_vector1=zeros(6,length(I));
random_vector2=zeros(6,length(I));
random_vector3=zeros(6,length(I));
for l=1:6
x=randperm(length(I));
random_vector1(l,:)=I(l,x);
random_vector2(l,:)=I_delta(l,x);
random_vector3(l,:)=I_theta(l,x);
end
%generate random data
probability_random1=zeros(size(new_element,1),1);
probability_random2=zeros(size(new_element,1),1);
probability_random3=zeros(size(new_element,1),1);
for i=1:length(I)
for j=1:size(new_element,1)
if isequal(random_vector1(:,i),new_element(j,:)')
probability_random1(j)=probability_random1(j)+1;
end
if isequal(random_vector2(:,i),new_element(j,:)')
probability_random2(j)=probability_random2(j)+1;
end
if isequal(random_vector3(:,i),new_element(j,:)')
probability_random3(j)=probability_random3(j)+1;
end
end
end
probability_random1=probability_random1/length(I);
probability_random2=probability_random2/length(I_delta);
probability_random3=probability_random3/length(I_theta);
h1_r=-sum((probability_random1+eps).*log((probability_random1+eps)));
h2_r=-sum((probability_random2+eps).*log((probability_random2+eps)));
h3_r=-sum((probability_random3+eps).*log((probability_random3+eps)));
h_random=-sum((matrix_random+eps)'.*log(matrix_random+eps)');
dkl_atributes(1,k)=KLDivergence_v2018(probability1,probability_random1);
dkl_atributes(2,k)=KLDivergence_v2018(probability2,probability_random2);
dkl_atributes(3,k)=KLDivergence_v2018(probability3,probability_random3);
end
figure(1)
histogram(dkl_atributes(1,:),'Binwidth',0.1,'Normalization','probability')
hold on
histogram(dkl_atributes(2,:),'Binwidth',0.1,'Normalization','probability')
histogram(dkl_atributes(3,:),'Binwidth',0.1,'Normalization','probability')
legend('Firing','Delta','Theta')
number=1;
for i=1:3
for j=i+1:3
[h p]=ttest(dkl_atributes(1,:),dkl_atributes(2,:));
prob(number)=p;
number=number+1;
end
end
%example
matrix_random1=zeros(7,20);
matrix_random1(1,1)=probability_random1(1);%/sum(probability_random(1));
matrix_random1(2,1:6)=probability_random1(2:7);%/sum(probability_random(2:7));
matrix_random1(3,1:15)=probability_random1(8:22);%/sum(probability_random(8:22));
matrix_random1(4,1:20)=probability_random1(23:42);%/sum(probability_random(23:42));
matrix_random1(5,1:15)=probability_random1(43:57);%/sum(probability_random(43:57));
matrix_random1(6,1:6)=probability_random1(58:63);%/sum(probability_random(58:63));
matrix_random1(7,1)=probability_random1(64);%/sum(probability_random(64));
matrix_random2=zeros(7,20);
matrix_random2(1,1)=probability_random2(1);%/sum(probability_random(1));
matrix_random2(2,1:6)=probability_random2(2:7);%/sum(probability_random(2:7));
matrix_random2(3,1:15)=probability_random2(8:22);%/sum(probability_random(8:22));
matrix_random2(4,1:20)=probability_random2(23:42);%/sum(probability_random(23:42));
matrix_random2(5,1:15)=probability_random2(43:57);%/sum(probability_random(43:57));
matrix_random2(6,1:6)=probability_random2(58:63);%/sum(probability_random(58:63));
matrix_random2(7,1)=probability_random2(64);%/sum(probability_random(64));
matrix_random3=zeros(7,20);
matrix_random3(1,1)=probability_random3(1);%/sum(probability_random(1));
matrix_random3(2,1:6)=probability_random3(2:7);%/sum(probability_random(2:7));
matrix_random3(3,1:15)=probability_random3(8:22);%/sum(probability_random(8:22));
matrix_random3(4,1:20)=probability_random3(23:42);%/sum(probability_random(23:42));
matrix_random3(5,1:15)=probability_random3(43:57);%/sum(probability_random(43:57));
matrix_random3(6,1:6)=probability_random3(58:63);%/sum(probability_random(58:63));
matrix_random3(7,1)=probability_random3(64);%/sum(probability_random(64));
matrix_z1=zeros(7,20);
matrix_z1(1,1)=(probability1(1)+eps);
matrix_z1(2,1:6)=(probability1(2:7)+eps);
matrix_z1(3,1:15)=(probability1(8:22)+eps);
matrix_z1(4,1:20)=(probability1(23:42)+eps);
matrix_z1(5,1:15)=(probability1(43:57)+eps);
matrix_z1(6,1:1:6)=(probability1(58:63)+eps);
matrix_z1(7,1)=(probability1(64)+eps);
matrix_z2=zeros(7,20);
matrix_z2(1,1)=(probability2(1)+eps);
matrix_z2(2,1:6)=(probability2(2:7)+eps);
matrix_z2(3,1:15)=(probability2(8:22)+eps);
matrix_z2(4,1:20)=(probability2(23:42)+eps);
matrix_z2(5,1:15)=(probability2(43:57)+eps);
matrix_z2(6,1:6)=(probability2(58:63)+eps);
matrix_z2(7,1)=(probability2(64)+eps);
matrix_z3=zeros(7,20);
matrix_z3(1,1)=(probability3(1)+eps);
matrix_z3(2,1:6)=(probability3(2:7)+eps);
matrix_z3(3,1:15)=(probability3(8:22)+eps);
matrix_z3(4,1:20)=(probability3(23:42)+eps);
matrix_z3(5,1:15)=(probability3(43:57)+eps);
matrix_z3(6,1:6)=(probability3(58:63)+eps);
matrix_z3(7,1)=(probability3(64)+eps);
subplot(2,3,1)
bar3(matrix_random1')
ylim([0 20])
subplot(2,3,4)
bar3(matrix_z1')
ylim([0 20])
subplot(2,3,2)
bar3(matrix_random1')
ylim([0 20])
subplot(2,3,5)
bar3(matrix_z2')
ylim([0 20])
subplot(2,3,3)
bar3(matrix_random3')
ylim([0 20])
subplot(2,3,6)
bar3(matrix_z3')
ylim([0 20])
%% the same but for conditioned encoded atributes
p_marg1=sum(matrix_z1,2)/sum(sum(matrix_z1,2));
p_marg2=sum(matrix_z2,2)/sum(sum(matrix_z2,2));
p_marg3=sum(matrix_z3,2)/sum(sum(matrix_z3,2));
%plot marginls! code this!
matrix_z1=zeros(7,20);
matrix_z1(1,1)=(probability1(1)+eps)/sum(probability1(1)+eps);
matrix_z1(2,1:6)=(probability1(2:7)+eps)/sum(probability1(2:7)+eps);
matrix_z1(3,1:15)=(probability1(8:22)+eps)/sum(probability1(8:22)+eps);
matrix_z1(4,1:20)=(probability1(23:42)+eps)/sum(probability1(23:42)+eps);
matrix_z1(5,1:15)=(probability1(43:57)+eps)/sum(probability1(43:57)+eps);
matrix_z1(6,1:6)=(probability1(58:63)+eps)/sum(probability1(58:63)+eps);
matrix_z1(7,1)=(probability1(64)+eps)/sum(probability1(64)+eps);
matrix_z2=zeros(7,20);
matrix_z2(1,1)=(probability2(1)+eps)/sum(probability2(1)+eps);
matrix_z2(2,1:6)=(probability2(2:7)+eps)/sum(probability2(2:7)+eps);
matrix_z2(3,1:15)=(probability2(8:22)+eps)/sum(probability2(8:22)+eps);
matrix_z2(4,1:20)=(probability2(23:42)+eps)/sum(probability2(23:42)+eps);
matrix_z2(5,1:15)=(probability2(43:57)+eps)/sum(probability2(43:57)+eps);
matrix_z2(6,1:6)=(probability2(58:63)+eps)/sum(probability2(58:63)+eps);
matrix_z2(7,1)=(probability2(64)+eps)/sum(probability2(64)+eps);
matrix_z3=zeros(7,20);
matrix_z3(1,1)=(probability3(1)+eps)/sum(probability3(1)+eps);
matrix_z3(2,1:6)=(probability3(2:7)+eps)/sum(probability3(2:7)+eps);
matrix_z3(3,1:15)=(probability3(8:22)+eps)/sum(probability3(8:22)+eps);
matrix_z3(4,1:20)=(probability3(23:42)+eps)/sum(probability3(23:42)+eps);
matrix_z3(5,1:15)=(probability3(43:57)+eps)/sum(probability3(43:57)+eps);
matrix_z3(6,1:6)=(probability3(58:63)+eps)/sum(probability3(58:63)+eps);
matrix_z3(7,1)=(probability3(64)+eps)/sum(probability3(64)+eps);
for k=1:200
% generate a 6d random vector from a uniform distribution
random_vector1=zeros(6,length(I));
random_vector2=zeros(6,length(I));
random_vector3=zeros(6,length(I));
for l=1:6
x=randperm(length(I));
random_vector1(l,:)=I(l,x);
random_vector2(l,:)=I_delta(l,x);
random_vector3(l,:)=I_theta(l,x);
end
%generate random data
probability_random1=zeros(size(new_element,1),1);
probability_random2=zeros(size(new_element,1),1);
probability_random3=zeros(size(new_element,1),1);
for i=1:length(I)
for j=1:size(new_element,1)
if isequal(random_vector1(:,i),new_element(j,:)')
probability_random1(j)=probability_random1(j)+1;
end
if isequal(random_vector2(:,i),new_element(j,:)')
probability_random2(j)=probability_random2(j)+1;
end
if isequal(random_vector3(:,i),new_element(j,:)')
probability_random3(j)=probability_random3(j)+1;
end
end
end
probability_random1=probability_random1/length(I);
probability_random2=probability_random2/length(I_delta);
probability_random3=probability_random3/length(I_theta);
matrix_random1=zeros(7,20);
matrix_random1(1,1)=probability_random1(1)/sum(probability_random1(1)+eps);
matrix_random1(2,1:6)=probability_random1(2:7)/sum(probability_random1(2:7)+eps);
matrix_random1(3,1:15)=probability_random1(8:22)/sum(probability_random1(8:22)+eps);
matrix_random1(4,1:20)=probability_random1(23:42)/sum(probability_random1(23:42)+eps);
matrix_random1(5,1:15)=probability_random1(43:57)/sum(probability_random1(43:57)+eps);
matrix_random1(6,1:6)=probability_random1(58:63)/sum(probability_random1(58:63)+eps);
matrix_random1(7,1)=probability_random1(64)/sum(probability_random1(64)+eps);
matrix_random2=zeros(7,20);
matrix_random2(1,1)=probability_random2(1)/sum(probability_random2(1)+eps);
matrix_random2(2,1:6)=probability_random2(2:7)/sum(probability_random2(2:7)+eps);
matrix_random2(3,1:15)=probability_random2(8:22)/sum(probability_random2(8:22)+eps);
matrix_random2(4,1:20)=probability_random2(23:42)/sum(probability_random2(23:42)+eps);
matrix_random2(5,1:15)=probability_random2(43:57)/sum(probability_random2(43:57)+eps);
matrix_random2(6,1:6)=probability_random2(58:63)/sum(probability_random2(58:63)+eps);
matrix_random2(7,1)=probability_random2(64)/sum(probability_random2(64)+eps);
matrix_random3=zeros(7,20);
matrix_random3(1,1)=probability_random3(1)/sum(probability_random3(1)+eps);
matrix_random3(2,1:6)=probability_random3(2:7)/sum(probability_random3(2:7)+eps);
matrix_random3(3,1:15)=probability_random3(8:22)/sum(probability_random3(8:22)+eps);
matrix_random3(4,1:20)=probability_random3(23:42)/sum(probability_random3(23:42)+eps);
matrix_random3(5,1:15)=probability_random3(43:57)/sum(probability_random3(43:57)+eps);
matrix_random3(6,1:6)=probability_random3(58:63)/sum(probability_random3(58:63)+eps);
matrix_random3(7,1)=probability_random3(64)/sum(probability_random3(64)+eps);
for condition=1:7
dkl(condition,1,k)=p_marg1(condition)*KLDivergence_v2018(matrix_z1(condition,:),matrix_random1(condition,:));
dkl(condition,2,k)=p_marg2(condition)*KLDivergence_v2018(matrix_z2(condition,:),matrix_random2(condition,:));
dkl(condition,3,k)=p_marg3(condition)*KLDivergence_v2018(matrix_z3(condition,:),matrix_random3(condition,:));
end
end
dkl_mean=mean(dkl,3)
bar3(dkl_mean')
%examples plot
subplot(2,3,1)
bar3(matrix_random1')
ylim([0 20])
subplot(2,3,4)
bar3(matrix_z1')
ylim([0 20])
subplot(2,3,2)
bar3(matrix_random1')
ylim([0 20])
subplot(2,3,5)
bar3(matrix_z2')
ylim([0 20])
subplot(2,3,3)
bar3(matrix_random3')
ylim([0 20])
subplot(2,3,6)
bar3(matrix_z3')
ylim([0 20])
figure(2)
number=1;
for i=1:3
for condition=1:7
subplot(3,7,number)
number=number+1;
histogram(dkl(condition,i,:),20,'Normalization','probability')
end
end