Two-step discretization evaluation (TEDIE)

Two-step discretization evaluation (TEDIE) procedure: MATLAB files and example data. 
m files are written using MATLAB 2016a.

Author: yuezheli

Diff for: README.md

@@ -1 +1,29 @@
-# DiscretizationAlgorithms
+This is the two-step discretization evaluation (TEDIE) procedure. This procedure is proposed by T. Jann, Y. Li, and Dr. P. Vera-Licona. 
+
+TEDIE procedure contains two steps: 
+1. Qualification: run Wilcoxon sign rank test; 
+2. Evaluaton: calculate mean area between the curves as a criteria; 
+
+##------ functions ------##
+
+benchmark.m: 
+For evaluation step; 
+Depend on prebenchmark.m;
+!! Each time series should come in as a n*1 vertical vector; 
+This function is able to calculate a matrix with multiple times series when each are coming in a column; 
+
+
+prebenchmark.m: 
+calculate difference of area between lines formed by 4 points: 
+                line 1: (x1, y1) -- (x2, y2)
+				line 2: (x3, y3) -- (x4, y4)
+				A sub-funciton for benchmark.m; 
+Notice that this is NOT mean area between the curves; 
+
+##------ Examples ------##
+
+*.mat: 
+data file for example use; 
+
+main_*.m: example files for TEDIE procedure that uses benchmark.m;
+

Diff for: TEDIEvignette.docx

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+function f = benchmark(data1, data2)
+m = size(data1,1); % number of rows
+n = size(data1, 2); % number of columns
+% replace NaN
+data1(isnan(data1)) = 0.5 ;
+data2(isnan(data2)) = 0.5 ;
+% initialization
+area = 0;
+for i = 1:n
+    for j = 1:m-1
+        x1 = j;
+        x2 = j+1;
+        x3 = x1;
+        x4 = x2; 
+        y1 = data1(j,i);
+        y2 = data1(j+1, i);
+        y3 = data2(j,i);
+        y4 = data2(j+1, i);
+        addarea = prebenchmark(x1,y1,x2,y2,x3,y3,x4,y4);
+        area = area + addarea;
+    end
+end
+f = area/(m*n);

Diff for: benchmark.m

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+clc,clear
+format short
+% load an example data file; keep all the files in the same folder; 
+load('example.mat'); 
+% put the discretization you are interested in here, make sure that your
+% loaded data contains the dataset of interest! 
+test_data = eval( 'meanstd');
+% data normalization
+nouveau = ( test_data-ones(size(test_data))*min(min(test_data)) )/ (max(max(test_data)) - min(min(test_data)));
+clear test_data;
+test_data = nouveau; 
+clear nouveau;
+%% qualification
+for i = 1:length(original)
+    res = original(i,:)-test_data(i,:); 
+    rocile(i,1) = signtest(sort(res));
+    clear res;
+end
+zygote(1) = quantile(rocile, 0.25);
+clear i rocile;
+if zygote <0.01
+    disp('stop here! choose another discretization method!');
+else 
+    disp('qualification passed! move to evaluation')
+    %% evaluation
+    for i = 1:8
+        startt = (i-1)*13+1;
+        endd = i*13;
+        roche(i,1) = benchmark(original(startt:endd,:)', test_data(startt:endd,:)' );    
+        clear startt endd;
+    end
+    zygote(2) = sum(roche)/8;
+    clear i roche;
+    disp('mean area between the curve: ')
+    disp(zygote(2))
+end
+clear test_data;

Diff for: example.mat

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+function f = prebenchmark(x1,y1,x2,y2,x3,y3,x4,y4)
+%% this is written by Yuezhe Li at Oct. 16, 2016
+% this is a benchmark dirretization eavluation proposed by Tiffiny Jann as a REU student
+% this is intend to calculate area between two lines
+% line1 = (x1, y1) -- (x2,y2)
+% line2 = (x3, y3) -- (x4, y4)
+diff1 = y3-y1;
+diff2 = y4-y2;
+dif = diff1*diff2;
+if dif < 0
+    % here 2 line intersects somewhere in the middle
+    m1 = (y2-y1)/(x2-x1);
+    b1 = y1 - m1*x1; 
+    m2 = (y4-y3)/(x4-x3);
+    b2 = y3 - m2*x3;
+    xint = (-1)*(b2 - b1)/(m2-m1);
+    area1 = (y3-y1)*abs(xint-x1)/2; 
+    area2 = abs(y4-y2)*abs(xint-x2)/2;
+    area = area1 + area2; 
+else if dif > 0 
+        area = ( abs(diff1) + abs(diff2) ) * abs(x2-x1)/2;
+    else
+        ydif = max( abs(y4-y2), abs(y3-y1) );
+        xdif = abs(x2 - x1);
+        area = xdif*ydif/2;
+    end
+end
+f = area;