Added Logistic Regression

algorithms/machine_learning/Logistic-Regression/Predict.m

@@ -0,0 +1,17 @@
+function P = Predict(Theta, X)
+
+n = size(X, 1); 
+
+P = zeros(n, 1);
+
+for i = 1 : n,
+
+    if Sigmoid(X * Theta)(i) >= 0.5
+
+        P(i) = 1; 
+
+    end
+
+end
+
+end

algorithms/machine_learning/Logistic-Regression/Sigmoid.m

@@ -0,0 +1,17 @@
+function G = Sigmoid(Z)
+
+G = zeros(size(Z));
+
+a = size(Z);
+
+for i = 1 : a(1, 1),
+
+    for j = 1 : a(1, 2),
+
+        G(i, j) = 1 / (1 + e.^-Z(i, j));
+
+    end
+
+end
+
+end

algorithms/machine_learning/Logistic-Regression/costfunction.m

@@ -0,0 +1,15 @@
+function [j, Grad] = costfunction(Theta, X, Y)
+
+n = length(Y); 
+
+j = 0;
+
+j = (1/n)*(-Y'* log(Sigmoid(X * Theta)) - (1 - Y)'* log(1 - Sigmoid(X * Theta))); % See the sigmoid function. 
+
+Grad = zeros(size(Theta));
+
+Grad_ = (1 / n) * ((Sigmoid(X * Theta) - Y)' * X);
+
+Grad = Grad_';
+
+end

algorithms/machine_learning/Logistic-Regression/data.txt

@@ -0,0 +1,100 @@
+34.62365962451697,78.0246928153624,0
+30.28671076822607,43.89499752400101,0
+35.84740876993872,72.90219802708364,0
+60.18259938620976,86.30855209546826,1
+79.0327360507101,75.3443764369103,1
+45.08327747668339,56.3163717815305,0
+61.10666453684766,96.51142588489624,1
+75.02474556738889,46.55401354116538,1
+76.09878670226257,87.42056971926803,1
+84.43281996120035,43.53339331072109,1
+95.86155507093572,38.22527805795094,0
+75.01365838958247,30.60326323428011,0
+82.30705337399482,76.48196330235604,1
+69.36458875970939,97.71869196188608,1
+39.53833914367223,76.03681085115882,0
+53.9710521485623,89.20735013750205,1
+69.07014406283025,52.74046973016765,1
+67.94685547711617,46.67857410673128,0
+70.66150955499435,92.92713789364831,1
+76.97878372747498,47.57596364975532,1
+67.37202754570876,42.83843832029179,0
+89.67677575072079,65.79936592745237,1
+50.534788289883,48.85581152764205,0
+34.21206097786789,44.20952859866288,0
+77.9240914545704,68.9723599933059,1
+62.27101367004632,69.95445795447587,1
+80.1901807509566,44.82162893218353,1
+93.114388797442,38.80067033713209,0
+61.83020602312595,50.25610789244621,0
+38.78580379679423,64.99568095539578,0
+61.379289447425,72.80788731317097,1
+85.40451939411645,57.05198397627122,1
+52.10797973193984,63.12762376881715,0
+52.04540476831827,69.43286012045222,1
+40.23689373545111,71.16774802184875,0
+54.63510555424817,52.21388588061123,0
+33.91550010906887,98.86943574220611,0
+64.17698887494485,80.90806058670817,1
+74.78925295941542,41.57341522824434,0
+34.1836400264419,75.2377203360134,0
+83.90239366249155,56.30804621605327,1
+51.54772026906181,46.85629026349976,0
+94.44336776917852,65.56892160559052,1
+82.36875375713919,40.61825515970618,0
+51.04775177128865,45.82270145776001,0
+62.22267576120188,52.06099194836679,0
+77.19303492601364,70.45820000180959,1
+97.77159928000232,86.7278223300282,1
+62.07306379667647,96.76882412413983,1
+91.56497449807442,88.69629254546599,1
+79.94481794066932,74.16311935043758,1
+99.2725269292572,60.99903099844988,1
+90.54671411399852,43.39060180650027,1
+34.52451385320009,60.39634245837173,0
+50.2864961189907,49.80453881323059,0
+49.58667721632031,59.80895099453265,0
+97.64563396007767,68.86157272420604,1
+32.57720016809309,95.59854761387875,0
+74.24869136721598,69.82457122657193,1
+71.79646205863379,78.45356224515052,1
+75.3956114656803,85.75993667331619,1
+35.28611281526193,47.02051394723416,0
+56.25381749711624,39.26147251058019,0
+30.05882244669796,49.59297386723685,0
+44.66826172480893,66.45008614558913,0
+66.56089447242954,41.09209807936973,0
+40.45755098375164,97.53518548909936,1
+49.07256321908844,51.88321182073966,0
+80.27957401466998,92.11606081344084,1
+66.74671856944039,60.99139402740988,1
+32.72283304060323,43.30717306430063,0
+64.0393204150601,78.03168802018232,1
+72.34649422579923,96.22759296761404,1
+60.45788573918959,73.09499809758037,1
+58.84095621726802,75.85844831279042,1
+99.82785779692128,72.36925193383885,1
+47.26426910848174,88.47586499559782,1
+50.45815980285988,75.80985952982456,1
+60.45555629271532,42.50840943572217,0
+82.22666157785568,42.71987853716458,0
+88.9138964166533,69.80378889835472,1
+94.83450672430196,45.69430680250754,1
+67.31925746917527,66.58935317747915,1
+57.23870631569862,59.51428198012956,1
+80.36675600171273,90.96014789746954,1
+68.46852178591112,85.59430710452014,1
+42.0754545384731,78.84478600148043,0
+75.47770200533905,90.42453899753964,1
+78.63542434898018,96.64742716885644,1
+52.34800398794107,60.76950525602592,0
+94.09433112516793,77.15910509073893,1
+90.44855097096364,87.50879176484702,1
+55.48216114069585,35.57070347228866,0
+74.49269241843041,84.84513684930135,1
+89.84580670720979,45.35828361091658,1
+83.48916274498238,48.38028579728175,1
+42.2617008099817,87.10385094025457,1
+99.31500880510394,68.77540947206617,1
+55.34001756003703,64.9319380069486,1
+74.77589300092767,89.52981289513276,1

algorithms/machine_learning/Logistic-Regression/plotdata.m

@@ -0,0 +1,19 @@
+function plotdata(x, Y)
+
+figure;
+
+hold on;
+
+Pos = find(Y == 1);
+
+Neg = find(Y == 0);
+
+plot(x(Pos, 1), x(Pos, 2), 'k+','LineWidth', 2, ...
+    'MarkerSize', 7);
+
+plot(x(Neg, 1), x(Neg, 2), 'ko', 'MarkerFaceColor', 'y', ...
+    'MarkerSize', 7);
+
+hold off;
+
+end

algorithms/machine_learning/Logistic-Regression/plotdecisionboundary.m

@@ -0,0 +1,43 @@
+function plotdecisionboundary(Theta, X, Y)
+
+plotdata(X(:,2:3), Y);
+
+hold on;
+
+if size(X, 2) <= 3
+
+    plot_X = [min(X(:,2))-2,  max(X(:,2))+2];
+
+    plot_Y = (-1./Theta(3)).*(Theta(2).*plot_X + Theta(1));
+
+    plot(plot_X, plot_Y);
+
+    legend('Admitted', 'Not admitted', 'Decision Boundary');
+
+    axis([30, 100, 30, 100]);
+
+else
+
+    U = linspace(-1, 1.5, 50);
+
+    V = linspace(-1, 1.5, 50);
+
+    Z = zeros(length(U), length(V));
+
+    for i = 1:length(U)
+
+        for j = 1:length(V)
+
+            Z(i,j) = mapFeature(U(i), V(j))*Theta;
+
+        end
+
+    end
+
+    Z = Z'; 
+
+end
+
+hold off;
+
+end

algorithms/machine_learning/Logistic-Regression/runLogisticRegression.m

@@ -0,0 +1,82 @@
+clear; close all; clc;
+
+Data = load('data.txt');
+x = Data(:, [1, 2]); Y = Data(:, 3);
+
+fprintf(['Plotting data with + indicating (Y = 1) examples and o ' ...
+         'indicating (Y = 0) examples.\n']);
+
+plotdata(x, Y);
+
+hold on;
+
+xlabel('Exam 1 score');
+ylabel('Exam 2 score');
+
+legend('Admitted', 'Not admitted');
+hold off;
+
+fprintf('\nProgram paused, press enter to continue.\n');
+pause;
+
+[m, n] = size(x);
+
+X = [ones(m, 1) x];
+
+Initial_Theta = zeros(n + 1, 1);
+
+[Cost, Grad] = costfunction(Initial_Theta, X, Y);
+
+fprintf('Cost at initial theta (zeros): %f\n', Cost);
+fprintf('Expected cost (approx): 0.693\n');
+fprintf('Gradient at initial theta (zeros): \n');
+fprintf(' %f \n', Grad);
+fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');
+
+Test_Theta = [-24; 0.2; 0.2];
+[Cost, Grad] = costfunction(Test_Theta, X, Y);
+
+fprintf('\nCost at test theta: %f\n', Cost);
+fprintf('Expected cost (approx): 0.218\n');
+fprintf('Gradient at test theta: \n');
+fprintf(' %f \n', Grad);
+fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');
+
+fprintf('\nProgram paused, press enter to continue.\n');
+pause;
+
+Options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+[Theta, Cost] = ...
+	fminunc(@(t)(costfunction(t, X, Y)), Initial_Theta, Options);
+
+fprintf('Cost at theta found by fminunc: %f\n', Cost);
+fprintf('Expected cost (approx): 0.203\n');
+fprintf('theta: \n');
+fprintf(' %f \n', Theta);
+fprintf('Expected theta (approx):\n');
+fprintf(' -25.161\n 0.206\n 0.201\n');
+
+plotdecisionboundary(Theta, X, Y);
+
+hold on;
+
+xlabel('Exam 1 score');
+ylabel('Exam 2 score');
+
+legend('Admitted', 'Not admitted');
+hold off;
+
+fprintf('\nProgram paused, press enter to continue.\n');
+pause; 
+
+Prob = Sigmoid([1 45 85] * Theta);
+fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
+         'probability of %f\n'], Prob);
+fprintf('Expected value: 0.775 +/- 0.002\n\n');
+
+P = Predict(Theta, X);
+
+fprintf('Train accuracy: %f\n', mean(double(P == Y)) * 100);
+fprintf('Expected accuracy (approx): 89.0\n');
+fprintf('\n');