% Autocorrelation for Points based on the distance between those points
% data is the sensor data. one point per row. 
% lag_size is the number of required lags
function [corr, lag] = distCorr(data, lag_size)
    
    n = length(data);
    
    %if lag size is bigger as data, then use data length - 1
    % -1 because the max. lag is -1 of the data length.. 
    if(lag_size >= n)
        lag_size = n - 1; %
    end

    %init 
    corr = zeros(lag_size + 1, 1); % +1, because the first index is lag 0.
    lag = (-lag_size:1:lag_size)';
    
    %mean shift and l2 normalization
    %data = data - mean(data);
    %data = data / norm(data);
    
    for j = 1:lag_size + 1 % +1, because the first index is lag 0.
        dist = zeros(n - abs(j), 1);
        idx = 1;
        
        for i = j:n
            %x_i * x_i-(j-1)
            dist(idx) = norm(data(i, :) - data(i-(j-1), :));
            idx = idx + 1;
        end
        
        corr(j) = geomean(dist);
    end
    
    %mirror corr(2:512) and put it infront 
    corr = [flipud(corr(2:end)); corr];
    
    %to [0, 1]
    corr = ((corr .* -1) / max(corr)) + 1;
    
end