In a logical array find how the density of TRUE values increases

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Giorgos Papakonstantinou 2013-8-6

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编辑： Spencer Talbot 2023-2-23

Supposedly we have a logical array:

t=[1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0];

The true values at the beginning are very few but the true values become more and more at the end of the array. Is there any way to identify the increasing density of the true values?

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Azzi Abdelmalek 2013-8-7

在 MATLAB Online 中打开

[Giorgos commented]

I still can not solve my actual problem. So I will post it here. I have a set of data in which fluctuate until a point after which the fluctuation fades out.

To be more specific you can see below my data plotted.

I have multiple datasets that are similar to the first plot of the figure. In the figure I have plotted only one case from my dataset. As you can see in the beginning of the plot the fluctuation is less and as we move to the right the fluctuation is significant. The magenta points are the extreme points. I have stored in a logical array the extreme values (the pink) indicated by TRUE and all the others (the blue) indicated by FALSE.

In every case I would like to spot the *point *after which the fluctuation becomes significant.

The method that Azzi provided in his last comment, to indicate the FALSE values in the logical array with -1 and then cumsum the array resulted in the second plot that you see.

The point that I want to pick lies in the local minima of the second plot. In the best case scenario if the magenta points are monotonously increasing then the point would be the global minimum of the second plot.

I am able to find the local minima of the second plot, but I am not able to find a rule on how to locate that point. To find the local minima I use the following function

function minima = findminima(x)
%FINDMINIMA  Find location of local minima
%  From David Sampson
%  See also FINDMAXIMA
minima = findmaxima(-x);
function maxima = findmaxima(x)
%FINDMAXIMA  Find location of local maxima
%  From David Sampson
%  See also FINDMINIMA
% Unwrap to vector
x = x(:);
% Identify whether signal is rising or falling
upordown = sign(diff(x));
% Find points where signal is rising before, falling after
maxflags = [upordown(1)<0; diff(upordown)<0; upordown(end)>0];
maxima   = find(maxflags);

Below I have zoomed in the right area of both plots, so you can visualize better the problem.

I would appreciate if take a look my problem. You can also download the data of both plots from this link

Azzi Abdelmalek 2013-8-7

编辑：Azzi Abdelmalek 2013-8-7

Giorgos, please, do not answer your question when you want to add a comment. Click on comment on this answer if you want to add a comment to any answer

Giorgos Papakonstantinou 2013-8-7

Ok Azzi! Thank you!

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Answer 1

Image Analyst 2013-8-6

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You have to define density over some area (number of elements) because, obviously, the density changes depending on how many elements it's calculated over. For example, to calculate the density over a window size of 5, try this code:

t=[1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0];
density = conv(t, ones(1, 5)/5, 'valid')
plot(density, 'b-', 'LineWidth', 3);
grid on;
xlabel('Element', 'FontSize', 30);
ylabel('Density', 'FontSize', 30);

conv() is a function that will give the sum in the window and then divide by 5 so it gives the average value within the window of length 5.

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Image Analyst 2013-8-6

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You can do that if you want.

% densityThreshold is some value you define.
aboveDensityThreshold = density > densityThreshold;  
% Assign original data to false in those locations.
t(aboveDensityThreshold) = false;

Giorgos Papakonstantinou 2013-8-10

Thank you Image Analyst for your suggestion but I haven't solved yet my original problem neither with the "density" nor with the cumsum. I posted in the beginning of this thread my original question.

I would appreciate if you could take a look at it. And if there is something unclear I would be happy to explain it further.

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Answer 2

Azzi Abdelmalek 2013-8-6

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What you did in your previous comment is

sort(t)

I do not think this is what you want. Can you explain mathematically what is density?

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Azzi Abdelmalek 2013-8-6

编辑：Azzi Abdelmalek 2013-8-6

在 MATLAB Online 中打开

Edit

t=[1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 ];
s=num2str(t)
s1=strrep(s,' ','')
n1=cellfun(@numel,regexp(s1,'1+','match'))
n2=cellfun(@numel,regexp(s1,'0+','match'))
stairs(cumsum(n1))
hold all
stairs(cumsum(n2))

Azzi Abdelmalek 2013-8-6

Look at edit

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Answer 3

Azzi Abdelmalek 2013-8-6

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编辑：Azzi Abdelmalek 2013-8-6

在 MATLAB Online 中打开

%or maybe

t=[1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 ];
s=num2str(t)
s1=strrep(s,' ','')
n1=cellfun(@numel,regexp(s1,'1+','match'))
n2=-cellfun(@numel,regexp(s1,'0+','match'))
out=zeros(1,numel([n1 n2]))
out(1:2:2*numel(n1)-1)=n1
out(2:2:2*numel(n2))=n2
stairs(cumsum(out))

%or maybe

close
t=[1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 ];
t(t==0)=-1
stairs(cumsum(t))

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Giorgos Papakonstantinou 2013-8-6

I like the last one a lot! Seems very tidy and fast.

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Answer 4

Spencer Talbot 2023-2-23

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编辑：Spencer Talbot 2023-2-23

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I know this question is old, but I recently had a similar question. Here's what I came up with:

    t=[1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0];
    density = zeros(length(t),2); % initialize the density matrix (1st column is # of consecutive TRUE instances, 2nd column is the index where that streak occurs)
    k = 1; % initialize the index for keeping track of density
    for i = 1:length(t)
        if t(i)
            density(k) = density(k,1) + 1; % if the current value is true, plus one count for density
            if density(k,1) == 1
                density(k,2) = i; % If it's the start of a new streak, record the index
            end
        else
            k = k + 1; % if a streak ends, move on to the next index to prepare for a new streak
        end
    end
    
    [max_density, idx] = max(density(:,1)); % find the value and starting index for the longest streak
    range_idx = density(idx,2):density(idx,2) + max_density - 1; % compute the range of indices for which the max density streak lasts