exponential_smoothing.m

function [accumulator] = exponential_smoothing(post_probabilities, feedback_starts, alpha)
% [accumulator] = exponential_smoothing(post_probabilities, feedback_starts, alpha)
%
%   The function returns the smoothed posterior probabilities with respect
%   to the exponential smoothing algorithm
%            
%  	Note: the function will only consider the first class' posterior
%  	probabilities 
%
% 	First class: values tending to 1
% 	Second class: values tending to 0
% 	Undecided: in the middle
%
% Input arguments:
%   -post_probabilities [samples x num_classes] post probabilities of the
%   classes from the classifier
% 	-feedback_starts    [num_feedback x 1]: associates each sample to
%  	a trial, contains   starting time of each trial
%  	-alpha              smoothing value of the algorithm
%
% Output arguments:
%	-accumulator [samples x 1]: smoothed posterior probabilities in
% 	according to the smoothing algorithm

    num_samples = length(post_probabilities);
    %reset accumulation to the base probability of this class = 1/2
    reset_accumulation = 1./2;
    %contains the accumulation evidence for the sample_i of the training set
    accumulator = nan(num_samples, 1);
    
    % init accumulator
    accumulator(1) = reset_accumulation;
    % actual evidence accumulation
    for sample_i = 2:num_samples
        %if the sample is a start of a feedbck period
        if  ismember(sample_i, feedback_starts)
            % reset accumulation
            accumulator(sample_i) = reset_accumulation;
        else
            new_evidence  = post_probabilities(sample_i, 1);% (,1) for selecting both feet
            state = accumulator(sample_i - 1);
            accumulator(sample_i) = state.*alpha + new_evidence.*(1-alpha);
        end
    end
end