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"content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Perceptron Tutorial\\n\",\n \"\\n\",\n \"The perceptron algorithm is a supervised algorithm for binary classification. This linear classifier was introduced by Frank Rosenblatt in 1957 in his paper, 'The Perceptron--a perceiving and recognizing automaton.' The perceptron makes predictions based on a linear combination of it's weights with the feature vector. It also allows for online learning, which means that it can process each element in a training set one at a time. \\n\",\n \"\\n\",\n \"The perceptron is trained with the 'perceptron learning rule' which is defined as follows:\\n\",\n \"\\n\",\n \"1. Initialize the weight vector (Wo), either to 0 or small random numbers. \\n\",\n \"2. Calculate the initial 'guess' as a linear combination of that weight vector and the first input.\\n\",\n \"3. Compare the perceptron output to the target output (error). Since this is a binary classification algorithm the outputs and targets will either be values of 0 or 1.\\n\",\n \"4. Update the new weight vector (Wn) depending on how the target compares to the perceptron output. If the target is less than the output than the weights will be decreased and if the target is greater than the output the weights will be increased. \\n\",\n \"5. Steps 1-4 are repeated until every output matches the target value for each training example.\\n\",\n \"\\n\",\n \"Here we are going to code up a perceptron and train it with the perceptron learning rule using a hard limit as the activation function. I am using numpy here because it is readible and optimized for linear algebra operations. I am defining the perceptron rule as:\\n\",\n \"\\n\",\n \"```\\n\",\n \"Wn = Wo + alpha * error * input.T\\n\",\n \"error = true - predicted\\n\",\n \"```\\n\",\n \"\\n\",\n \"The complete code for the perceptron is below.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 316,\n \"metadata\": {\n \"collapsed\": false\n },\n \"outputs\": [],\n \"source\": [\n \"import random\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"%matplotlib inline\\n\",\n \"plt.style.use('ggplot')\\n\",\n \"\\n\",\n \"def hardlim(a):\\n\",\n \" if a > 0.0:\\n\",\n \" return 1.\\n\",\n \" else:\\n\",\n \" return 0.\\n\",\n \"\\n\",\n \"class Perceptron(object):\\n\",\n \" '''\\n\",\n \" simple feed forward perceptron with a hard limit activation\\n\",\n \" trained with the perceptron learning rule\\n\",\n \" '''\\n\",\n \" def __init__(self):\\n\",\n \" self.alpha = None\\n\",\n \" self.w = None\\n\",\n \"\\n\",\n \" def response(self, X):\\n\",\n \" '''\\n\",\n \" perceptron response\\n\",\n \" :param X: input vector\\n\",\n \" :return: perceptron out\\n\",\n \" '''\\n\",\n \" a = hardlim(np.dot(self.w.T, X))\\n\",\n \" return a\\n\",\n \"\\n\",\n \" def updateWeight(self, X, error):\\n\",\n \" '''\\n\",\n \" update the vector of input weights\\n\",\n \" :param X: input data\\n\",\n \" :param error: prediction != true\\n\",\n \" :return: updated weight vector\\n\",\n \" '''\\n\",\n \" self.w += self.alpha * error * X\\n\",\n \"\\n\",\n \" def train(self, X, y, alpha, iterations):\\n\",\n \" '''\\n\",\n \" trains perceptron on vector data by looping each row and updating the weight vector\\n\",\n \" :param X: input data\\n\",\n \" :param y: correct y value\\n\",\n \" :return: updated parameters\\n\",\n \" '''\\n\",\n \" # initialize the learning rate and count data size\\n\",\n \" self.alpha = alpha\\n\",\n \" num_examples, num_features = np.shape(X)\\n\",\n \"\\n\",\n \" # set up bias\\n\",\n \" bias = np.ones(shape=(num_examples,1))\\n\",\n \" X = np.hstack((X, bias))\\n\",\n \"\\n\",\n \" # initialize weight vector\\n\",\n \" self.w = np.random.rand(num_features + 1)\\n\",\n \" \\n\",\n \" error_count = []\\n\",\n \" for i in range(iterations):\\n\",\n \" for j in range(num_examples):\\n\",\n \" prediction = self.response(X[j])\\n\",\n \" error = int(y[j]) - prediction \\n\",\n \" self.updateWeight(X[j], error)\\n\",\n \" error_count.append(error)\\n\",\n \" \\n\",\n \" error_count = np.array(error_count)\\n\",\n \" plt.plot(error_count)\\n\",\n \" plt.ylim([-1,1])\\n\",\n \" plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The perceptron is contained in a python class. Within the class there are functions to create the output, update the weights based on the error and a function to contain the training loop. \\n\",\n \"\\n\",\n \"* **Response** - This simply calcualtes the linear combination of the weights and input vectors. Then pushes that output through the hard limit function which will generate either a 0 or 1 for the class prediction. \\n\",\n \"* **UpdateWeight** - This function will take the error term and update the perceptron weights as defined by the perceptron learning rule.\\n\",\n \"* **Train** - The train function first initializes some of the parameters of the perceptron. It will take an 'alpha' which should be any number between 0 and 1. Then it will determine the proper size of the weight vector by setting it to the corresponding size of the input vectors. Finally before training it will initialize that weight vector to small random numbers and tack on a bias. During training the loop will run for a predetermined number of iterations. On each iteration the perceptron will; generate it's prediciton, compare that prediction to the target (error), then update the weights as necessary based on the error term.\\n\",\n \"\\n\",\n \"At the end of training the perceptron will generate a plot which shows the error generated by each training example. When the plot flatlines at 0 it may be safe to assume that the perceptron converged to a good solution.\\n\",\n \"\\n\",\n \"Now we will come up with some data for the perceptron to solve. Let's take the data from [Neural Network Design](http://hagan.okstate.edu/NNDesign.pdf) page 4-7 and plot the points below.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 309,\n \"metadata\": {\n \"collapsed\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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hUWFi56u+NlnA8//FDPPfecfvazn+nzzz+POa6vr0+NjY169tln1d3d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\\nA4AB/gcNkeLUhiCmDAAAAABJRU5ErkJggg==\\n\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# generate training data\\n\",\n \"X = np.array([[-1,-1],\\n\",\n \" [-1,1],\\n\",\n \" [1,-1],\\n\",\n \" [1,1]])\\n\",\n \"\\n\",\n \"y = np.array([[0],\\n\",\n \" [0],\\n\",\n \" [0],\\n\",\n \" [1]])\\n\",\n \"\\n\",\n \"# plot the points\\n\",\n \"plt.plot(X[0][0],X[0][1], 'ro', markersize=15)\\n\",\n \"plt.plot(X[1][0],X[1][1], 'ro', markersize=15)\\n\",\n \"plt.plot(X[2][0],X[2][1], 'ro', markersize=15)\\n\",\n \"plt.plot(X[3][0],X[3][1], 'bo', markersize=15)\\n\",\n \"plt.axis([-1.1,1.1,-1.1,1.1])\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So we are trying to draw a decision boundary to seperate the blue from the red circles. \\n\",\n \"\\n\",\n \"Lets train the network and see how it does. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 321,\n \"metadata\": {\n \"collapsed\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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zCe9VyqKnIzQE5hhK1rrwCXgozCPBHwGonpWgv3PBMIOPq1LG1tNNxW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\\niwW/1gAAAABJRU5ErkJggg==\\n\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"model = Perceptron()\\n\",\n \"model.train(X, y, alpha=0.1, iterations=10) \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This plot allows us to see how many examples the perceptron needed to see in order to converge to a solution. Anytime the error shows -1 the true prediction was 0 and our perceptron predicted 1. Anytime the error shows 1 the true was 1 and the perceptron predicted 0. When the error is 0 that's when the perceptron got that training case correct.\\n\",\n \"\\n\",\n \"\\n\",\n \"### Decision Boundaries\\n\",\n \"\\n\",\n \"Now lets plot the final decision boundary from the perceptron.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 320,\n \"metadata\": {\n \"collapsed\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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se9MH36/X2sM+UZSFi41dGIPIoreyIA0rM31LIiQAR6xQKYw59aHYnI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\\nEQWA/w9XO744BVYhkQAAAABJRU5ErkJggg==\\n\",\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"n = np.linalg.norm(model.w[0:2])\\n\",\n \"ww = (model.w[0:2]) / n\\n\",\n \"ww1 = [float(ww[1])* 2., -1.0*float(ww[0])* 2.] \\n\",\n \"ww2 = [-1.0*float(ww[1]) * 2., float(ww[0]) * 2.]\\n\",\n \"plt.plot([ww1[0]-model.w[2],ww2[0]-model.w[2]], [ww1[1]-model.w[2],ww2[1]-model.w[2]])\\n\",\n \"plt.plot(X[0][0],X[0][1], 'ro', markersize=15)\\n\",\n \"plt.plot(X[1][0],X[1][1], 'ro', markersize=15)\\n\",\n \"plt.plot(X[2][0],X[2][1], 'ro', markersize=15)\\n\",\n \"plt.plot(X[3][0],X[3][1], 'bo', markersize=15)\\n\",\n \"plt.axis([-1.1,1.1,-1.1,1.1])\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"collapsed\": false\n },\n \"source\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"Here is a cool animation of the how the decision boundary updates after every full iteration through the training data. This animation was created on a different run of the algorithm so the final boundary is not the same as the one above. It is worth noting that the decision boundary may not always be the same.\\n\",\n \"\\n\",\n \"\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": false\n },\n \"outputs\": [],\n \"source\": []\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"collapsed\": true\n },\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 2\",\n \"language\": \"python\",\n \"name\": \"python2\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 2\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython2\",\n \"version\": \"2.7.8\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n"
},
{
"path": "Data/denver.csv",
"content": "6.9,1.8,30.2,58.3,27.3,84.9,-14.2\r8.4,28.5,38.8,87.5,39.8,172.6,-34.1\r5.7,7.8,31.7,83.5,26,154.2,-15.8\r7.4,2.3,24.2,14.2,29.4,35.2,-13.9\r8.5,-0.7,28.1,46.7,26.6,69.2,-13.9\r13.8,7.2,10.4,57.9,26.2,111,-22.6\r1.7,32.2,7.5,73.8,50.5,704.1,-40.9\r3.6,7.4,30,61.3,26.4,69.9,4\r8.2,10.2,12.1,41,11.7,65.4,-32.5\r5,10.5,13.6,17.4,14.7,132.1,-8.1\r2.1,0.3,18.3,34.4,24.2,179.9,12.3\r4.2,8.1,21.3,64.9,21.7,139.9,-35\r3.9,2,33.1,82,26.3,108.7,-2\r4.1,10.8,38.3,83.3,32.6,123.2,-2.2\r4.2,1.9,36.9,61.8,21.6,104.7,-14.2\r9.4,-1.5,22.4,22.2,33.5,61.5,-32.7\r3.6,-0.3,19.6,8.6,27,68.2,-13.4\r7.6,5.5,29.1,62.8,32.2,96.9,-8.7\r8.5,4.8,32.8,86.2,16,258,0.5\r7.5,2.3,26.5,18.7,23.7,32,-0.6\r4.1,17.3,41.5,78.6,23.5,127,-12.5\r4.6,68.6,39,14.6,38.2,27.1,45.4\r7.2,3,20.2,41.4,27.6,70.7,-38.2\r13.4,7.1,20.4,13.9,22.5,38.3,-33.6\r10.3,1.4,29.8,43.7,29.4,54,-10\r9.4,4.6,36,78.2,29.9,101.5,-14.6\r2.5,-3.3,37.6,88.5,27.5,185.9,-7.6\r10.3,-0.5,31.8,57.2,27.2,61.2,-17.6\r7.5,22.3,28.6,5.7,31.3,38.6,27.2\r18.7,6.2,39.7,55.8,28.7,52.6,-2.9\r5.1,-2,23.8,29,29.3,62.6,-10.3\r3.7,19.6,12.3,77.3,32,207.7,-45.6\r10.3,3,31.1,51.7,26.2,42.4,-31.9\r7.3,19.2,32.9,68.1,25.2,105.2,-35.7\r4.2,7,22.1,41.2,21.4,68.6,-8.8\r2.1,5.4,27.1,60,23.5,157.3,6.2\r2.5,2.8,20.3,29.8,24.1,58.5,-27.5\r8.1,8.5,30,66.4,26,63.1,-37.4\r10.3,-1.9,15.9,39.9,38.5,86.4,-13.5\r10.5,2.8,36.4,72.3,26,77.5,-21.6\r5.8,2,24.2,19.5,28.3,63.5,2.2\r6.9,2.9,20.7,6.6,25.8,68.9,-2.4\r9.3,4.9,34.9,82.4,18.4,102.8,-12\r11.4,2.6,38.7,78.2,18.4,86.6,-12.8"
},
{
"path": "Data/denver_data_description.txt",
"content": "X1 = total population (in thousands)\nX2 = % change in population over past several years\nX3 = % of children (under 18) in population\nX4 = % free school lunch participation\nX5 = % change in household income over past several years\nX6 = crime rate (per 1000 population)\nX7 = % change in crime rate over past "
},
{
"path": "Data/ex1data1.txt",
"content": "6.1101,17.592\n5.5277,9.1302\n8.5186,13.662\n7.0032,11.854\n5.8598,6.8233\n8.3829,11.886\n7.4764,4.3483\n8.5781,12\n6.4862,6.5987\n5.0546,3.8166\n5.7107,3.2522\n14.164,15.505\n5.734,3.1551\n8.4084,7.2258\n5.6407,0.71618\n5.3794,3.5129\n6.3654,5.3048\n5.1301,0.56077\n6.4296,3.6518\n7.0708,5.3893\n6.1891,3.1386\n20.27,21.767\n5.4901,4.263\n6.3261,5.1875\n5.5649,3.0825\n18.945,22.638\n12.828,13.501\n10.957,7.0467\n13.176,14.692\n22.203,24.147\n5.2524,-1.22\n6.5894,5.9966\n9.2482,12.134\n5.8918,1.8495\n8.2111,6.5426\n7.9334,4.5623\n8.0959,4.1164\n5.6063,3.3928\n12.836,10.117\n6.3534,5.4974\n5.4069,0.55657\n6.8825,3.9115\n11.708,5.3854\n5.7737,2.4406\n7.8247,6.7318\n7.0931,1.0463\n5.0702,5.1337\n5.8014,1.844\n11.7,8.0043\n5.5416,1.0179\n7.5402,6.7504\n5.3077,1.8396\n7.4239,4.2885\n7.6031,4.9981\n6.3328,1.4233\n6.3589,-1.4211\n6.2742,2.4756\n5.6397,4.6042\n9.3102,3.9624\n9.4536,5.4141\n8.8254,5.1694\n5.1793,-0.74279\n21.279,17.929\n14.908,12.054\n18.959,17.054\n7.2182,4.8852\n8.2951,5.7442\n10.236,7.7754\n5.4994,1.0173\n20.341,20.992\n10.136,6.6799\n7.3345,4.0259\n6.0062,1.2784\n7.2259,3.3411\n5.0269,-2.6807\n6.5479,0.29678\n7.5386,3.8845\n5.0365,5.7014\n10.274,6.7526\n5.1077,2.0576\n5.7292,0.47953\n5.1884,0.20421\n6.3557,0.67861\n9.7687,7.5435\n6.5159,5.3436\n8.5172,4.2415\n9.1802,6.7981\n6.002,0.92695\n5.5204,0.152\n5.0594,2.8214\n5.7077,1.8451\n7.6366,4.2959\n5.8707,7.2029\n5.3054,1.9869\n8.2934,0.14454\n13.394,9.0551\n5.4369,0.61705\n"
},
{
"path": "Data/ex1data2.txt",
"content": "2104,3,399900\n1600,3,329900\n2400,3,369000\n1416,2,232000\n3000,4,539900\n1985,4,299900\n1534,3,314900\n1427,3,198999\n1380,3,212000\n1494,3,242500\n1940,4,239999\n2000,3,347000\n1890,3,329999\n4478,5,699900\n1268,3,259900\n2300,4,449900\n1320,2,299900\n1236,3,199900\n2609,4,499998\n3031,4,599000\n1767,3,252900\n1888,2,255000\n1604,3,242900\n1962,4,259900\n3890,3,573900\n1100,3,249900\n1458,3,464500\n2526,3,469000\n2200,3,475000\n2637,3,299900\n1839,2,349900\n1000,1,169900\n2040,4,314900\n3137,3,579900\n1811,4,285900\n1437,3,249900\n1239,3,229900\n2132,4,345000\n4215,4,549000\n2162,4,287000\n1664,2,368500\n2238,3,329900\n2567,4,314000\n1200,3,299000\n852,2,179900\n1852,4,299900\n1203,3,239500\n"
},
{
"path": "Data/heart.txt",
"content": 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76,68,74,56,59,73,76,54,48,75,78,47,53,25,19,60,56,56,54,80,79,47,53,19,14,58,50,67,71,63,54,49,48,66,65,62,58,57,72,31,30,15,11\n1,68,76,79,78,63,73,68,78,64,71,73,77,67,71,58,57,61,63,52,64,64,74,53,72,36,44,52,54,49,56,73,81,65,80,53,60,63,70,58,64,52,57,49,50\n1,68,64,65,68,63,64,77,73,75,72,80,77,70,71,61,61,73,68,63,62,76,73,69,69,48,59,62,44,66,59,75,74,64,64,63,61,70,69,74,67,51,48,45,45\n0,62,67,64,70,59,58,67,74,60,66,68,68,73,71,60,63,64,74,64,65,74,77,69,73,59,58,58,67,65,69,78,76,61,62,64,67,72,74,71,71,71,69,66,61\n0,62,67,68,70,65,70,73,77,69,70,69,73,71,74,71,71,76,75,66,67,73,73,70,74,63,67,58,68,66,69,78,79,69,70,71,73,72,71,73,77,72,76,64,66\n0,59,68,69,67,69,59,78,73,66,65,77,73,74,66,66,55,71,66,69,68,75,73,80,79,69,65,69,66,68,65,75,71,59,61,65,64,73,71,81,75,74,65,69,66\n0,75,75,70,77,67,75,75,75,67,66,74,73,68,72,64,70,76,70,67,63,74,75,72,68,69,68,75,69,71,74,75,76,63,70,71,69,66,63,70,73,66,68,58,59\n0,77,79,79,77,74,76,76,81,65,68,66,66,74,73,72,68,67,73,63,62,72,67,76,69,68,64,64,61,69,68,73,75,70,66,64,70,70,70,73,76,79,73,65,63\n0,68,64,74,80,76,72,78,75,67,64,75,80,78,77,66,64,67,67,70,60,78,82,70,68,63,60,64,60,54,56,70,73,59,65,55,58,50,51,73,70,69,65,42,41\n0,76,73,74,76,60,69,76,76,68,69,78,79,57,62,69,69,67,66,73,69,80,81,58,68,75,69,73,70,58,65,79,76,74,71,66,64,65,62,78,68,75,68,62,60\n0,61,76,71,68,77,69,77,69,64,75,71,81,75,72,71,69,70,73,61,71,69,79,64,65,62,66,61,65,71,68,67,71,59,64,66,65,60,68,74,71,69,68,63,59\n0,67,65,77,74,67,66,67,70,65,64,75,78,66,74,62,60,65,65,73,72,75,76,74,81,66,65,65,63,63,67,76,80,63,64,63,64,73,72,76,75,72,74,65,64\n0,71,61,74,74,76,74,69,56,68,78,71,78,58,64,70,72,71,68,72,71,79,78,67,68,63,60,67,67,76,74,67,79,67,71,71,64,70,74,83,76,74,73,54,54\n0,64,70,71,69,72,70,75,78,61,66,69,68,68,70,71,70,75,76,73,72,80,78,79,81,74,70,72,79,73,75,77,73,65,64,72,72,59,62,71,74,68,67,58,57\n0,76,75,68,78,71,72,72,75,61,65,67,70,67,75,60,58,63,67,59,63,67,72,74,73,56,56,52,52,67,68,73,78,65,68,61,67,69,74,77,75,74,70,63,61\n0,74,73,72,75,63,62,67,67,73,74,75,79,70,71,64,67,65,69,79,78,81,80,71,73,60,62,69,67,69,69,75,75,66,67,67,66,71,73,66,69,62,65,55,56\n0,65,67,69,76,62,68,65,66,65,64,74,73,60,75,66,63,64,62,73,65,77,74,69,69,66,59,68,59,69,69,76,79,65,63,60,60,69,64,69,74,69,70,62,57\n0,59,75,70,76,62,70,65,74,65,67,75,76,70,73,63,61,74,67,78,69,75,73,70,68,67,64,79,68,70,75,76,77,59,63,72,69,64,64,65,72,61,61,51,55\n0,76,72,73,69,67,73,74,72,60,65,73,66,66,73,68,67,69,70,60,58,66,76,69,75,65,64,63,60,74,71,77,79,61,68,71,70,62,63,73,76,62,69,52,59\n0,71,75,78,78,68,67,75,72,67,68,72,75,74,74,67,66,66,67,66,66,78,80,73,75,67,72,67,67,67,65,77,78,61,64,63,66,51,57,77,67,78,76,60,59\n0,80,76,75,75,69,68,74,75,77,77,76,78,74,70,66,65,67,75,74,73,74,77,68,67,61,58,60,67,61,63,75,75,66,62,59,61,77,74,69,67,65,66,61,58\n0,68,70,66,72,63,71,77,82,61,63,61,62,61,65,65,62,72,77,69,73,72,78,74,77,69,69,77,74,64,63,66,70,58,60,65,69,75,77,77,77,69,77,65,64\n0,67,57,73,78,63,68,72,73,61,59,59,76,71,72,69,66,70,68,65,77,79,68,71,75,62,66,70,78,68,69,70,76,65,65,66,67,62,72,69,72,70,68,60,59\n0,72,74,67,69,69,70,74,81,66,70,73,78,69,80,65,65,70,77,69,70,73,79,64,68,56,58,67,64,68,68,69,74,62,67,66,70,73,77,74,77,71,72,63,65\n0,62,71,78,84,64,68,72,74,53,57,71,70,71,72,54,53,63,67,54,57,71,71,70,74,54,57,54,57,62,64,75,72,62,65,60,64,64,67,72,77,62,62,61,65\n0,69,78,74,76,70,67,69,73,68,75,75,76,71,77,58,61,66,70,67,72,76,72,56,62,56,61,57,62,67,73,76,74,58,63,64,68,66,76,70,72,64,68,60,56\n0,59,65,53,60,72,74,67,69,64,67,64,65,71,70,68,71,72,70,70,70,75,78,72,71,71,71,67,64,67,71,71,74,62,66,72,73,57,57,64,71,70,69,53,49\n0,66,67,63,70,69,70,73,72,61,62,68,68,70,71,71,67,71,69,65,65,76,78,71,70,65,64,68,71,70,71,73,74,58,63,68,71,70,72,77,79,79,79,66,66\n0,62,66,66,68,73,76,68,71,62,62,63,68,74,75,63,68,71,68,58,58,65,66,65,76,64,70,63,60,70,72,71,77,67,69,72,71,63,63,70,72,75,79,62,59\n0,71,71,69,71,65,65,76,73,67,66,69,79,76,76,63,62,74,71,58,66,76,78,78,74,68,66,69,68,68,68,71,74,59,57,65,66,73,71,78,74,68,70,57,55\n0,63,61,75,72,68,71,69,70,64,56,70,75,76,73,70,72,76,73,68,68,79,76,68,76,66,73,58,68,72,75,72,75,65,61,66,67,58,57,72,72,68,71,57,58\n0,74,81,80,78,70,69,74,77,69,71,73,76,68,68,62,61,68,68,67,70,74,80,68,74,57,62,57,65,61,65,71,76,63,65,67,67,70,74,63,72,68,70,61,64\n0,69,64,73,72,49,70,66,71,57,56,64,62,76,74,65,62,63,58,63,63,75,76,78,80,75,77,51,62,74,68,77,77,70,68,68,64,59,58,69,66,74,75,62,59\n0,70,64,68,67,76,68,76,69,67,64,69,65,62,65,70,67,74,68,65,65,74,75,64,69,63,63,64,64,56,61,62,68,66,66,62,58,57,48,75,64,79,74,59,58\n0,65,68,70,78,65,72,72,74,64,69,71,73,72,68,62,62,65,62,72,75,79,78,72,76,66,67,62,61,68,76,72,78,65,64,67,63,64,67,67,77,66,66,59,57\n0,64,53,74,70,65,63,70,70,57,57,64,64,73,74,65,59,65,63,63,62,72,73,79,76,75,68,60,58,69,66,72,76,64,65,63,65,63,65,75,80,74,67,71,67\n0,70,71,71,74,68,66,72,70,66,69,74,72,70,69,64,66,73,72,75,73,81,81,76,75,71,70,74,82,69,72,76,74,60,56,66,66,64,64,73,72,66,63,54,58\n0,72,70,75,80,73,70,76,73,66,56,72,70,73,75,67,65,69,69,73,72,81,77,80,79,67,64,64,66,69,68,70,75,63,59,66,63,74,77,81,78,79,75,65,66\n0,70,75,72,72,67,71,71,78,63,67,73,76,71,74,59,61,67,64,74,71,77,77,70,72,61,61,62,58,63,69,76,75,64,65,66,67,68,70,70,71,64,67,56,54\n0,59,57,67,71,66,68,68,70,56,62,77,61,67,71,75,71,67,64,62,54,64,75,71,72,76,79,75,70,71,77,71,69,56,54,62,64,56,53,71,68,64,63,56,56\n0,67,64,73,75,77,77,74,70,65,62,74,75,65,67,68,70,66,69,67,60,74,75,62,64,66,71,62,61,64,69,73,76,64,66,61,64,65,60,68,75,74,80,67,68\n0,68,65,72,72,47,74,76,74,67,66,71,69,69,67,63,64,68,68,70,74,77,77,73,60,49,48,42,69,70,69,76,79,63,66,64,69,71,73,73,75,68,56,58,44\n0,66,54,69,66,69,69,75,72,63,62,68,66,68,70,71,68,70,69,66,68,73,72,65,73,67,63,60,57,70,68,75,75,65,67,69,65,65,64,67,69,71,68,59,59"
},
{
"path": "Data/heart_test.txt",
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{
"path": "Data/stackloss.csv",
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{
"path": "LinearRegression.py",
"content": "import numpy as np\n\nclass LinReg(object):\n \"\"\"\n multivariate linear regression using gradient descent\n \"\"\"\n def __init__(self, learning_rate = 0.01, iterations = 50, verbose = True, l2 = 0, \n tolerance = 0, intercept = True):\n \"\"\"\n :param learning_rate: learning rate constant\n :param iterations: how many epochs\n :param tolerance: the error value in which to stop training\n :param intercept: whether to fit an intercept\n :param verbose: whether to spit out error rates while training\n :param l2: L2 regularization term\n \"\"\"\n self.learning_rate = learning_rate\n self.iterations = iterations\n self.tolerance = tolerance\n self.intercept = intercept\n self.verbose = verbose\n self.l2 = l2\n self.theta = None\n self.mean = []\n self.std = []\n\n def fit(self, X, y):\n \"\"\"\n Gradient descent, loops over theta and updates to\n take steps in direction of steepest decrease of J.\n :return: value of theta that minimizes J(theta) and J_history\n \"\"\"\n if self.intercept:\n intercept = np.ones((np.shape(X)[0],1))\n X = np.concatenate((intercept, X), 1)\n \n num_examples, num_features = np.shape(X)\n\n # initialize theta to 1\n self.theta = np.ones(num_features)\n\n for i in range(self.iterations):\n # make prediction\n predicted = np.dot(X, self.theta.T)\n # update theta with gradient descent\n self.theta = (self.theta * (1 - (self.learning_rate * self.l2))) - self.learning_rate / num_examples * np.dot((predicted - y).T, X)\n # sum of squares cost\n error = predicted - y\n cost = np.sum(error**2) / (2 * num_examples)\n \n if i % 10 == 0 and self.verbose == True:\n print 'iteration:', i\n print 'theta:', self.theta\n print 'cost:', cost\n \n if cost < self.tolerance:\n return self.theta\n break\n\n return self.theta\n\n def predict(self, X):\n \"\"\"\n Make linear prediction based on cost and gradient descent\n :param X: new data to make predictions on\n :return: return prediction\n \"\"\"\n if self.intercept:\n intercept = np.ones((np.shape(X)[0],1))\n X = np.concatenate((intercept, X), 1)\n \n num_examples, num_features = np.shape(X)\n prediction = []\n for sample in range(num_examples):\n yhat = 0\n for value in range(num_features):\n yhat += X[sample, value] * self.theta[value]\n prediction.append(yhat)\n \n return prediction\n\ndef demo():\n # initialize linear regression parameters\n iterations = 2000\n learning_rate = 0.1\n l2 = 0.0001\n\n linearReg = LinReg(learning_rate = learning_rate, iterations = iterations, verbose = 1, l2 = l2)\n\n data = np.genfromtxt('Data/blood_pressure.csv', delimiter = ',', skip_header = 1)\n X = data[:, 1:]\n y = data[:, 0]\n \n # scale data\n max = np.amax(X)\n X /= max\n print X\n print y\n\n # fit the linear reg\n linearReg.fit(X = X, y = y)\n\n # load testing dataset\n test = np.genfromtxt('Data/blood_pressure.csv', delimiter = ',', skip_header = 1)\n X_test = test[:, 1:]\n y_test = test[:, 0]\n \n max = np.amax(X_test)\n X_test /= max\n print X_test\n\n predictions = np.array(linearReg.predict(X_test))\n\n print 'correct: ', y_test\n print 'prediction: ', predictions\n\nif __name__ == '__main__':\n demo()"
},
{
"path": "LogisticClassifier.py",
"content": "import math\nimport numpy as np\n\n\nclass Logit(object):\n \"\"\"\n logistic regression using gradient descent\n \"\"\"\n def __init__(self, learning_rate = 0.01, iterations = 100, verbose = True, \n tolerance = 0, l2 = 0, intercept = True):\n \"\"\"\n :param learning_rate: learning rate constant\n :param iterations: how many epochs\n :param tolerance: the error value in which to stop training\n :param intercept: whether to fit an intercept\n :param verbose: whether to spit out error rates while training\n :param l2: L2 regularization term\n \"\"\"\n self.learning_rate = learning_rate\n self.iterations = iterations\n self.tolerance = tolerance\n self.intercept = intercept\n self.verbose = verbose\n self.l2 = l2\n self.theta = None\n self.mean = []\n self.std = []\n\n def sigmoid(self, x):\n \"\"\"\n Typical sigmoid function created from input vector x\n\n :param x: input vector\n :return: sigmoided vector\n \"\"\"\n return 1 / (1 + np.exp(-x))\n\n def fit(self, X, y):\n \"\"\"\n Gradient descent, loops over theta and updates to\n take steps in direction of steepest decrease of J.\n :input x: must be numpy array\n :input y: must be numpy vector of 0 and 1\n :return: value of theta that minimizes J(theta) and J_history\n \"\"\"\n if self.intercept:\n intercept = np.ones((np.shape(X)[0],1))\n X = np.concatenate((intercept, X), 1)\n \n num_examples, num_features = np.shape(X)\n\n # initialize theta to 1\n self.theta = np.ones(num_features)\n\n for i in range(self.iterations):\n # make predictions\n predicted = self.sigmoid(np.dot(X, self.theta.T))\n # update theta with gradient descent\n self.theta = (self.theta * (1 - (self.learning_rate * self.l2))) - self.learning_rate * np.dot((predicted - y).T, X)\n # sum of squares cost\n error = predicted - y\n cost = np.sum(error**2) / (2 * num_examples)\n\n if i % (self.iterations/10) == 0 and self.verbose == True:\n print 'iteration:', i\n print 'theta:', self.theta\n print 'cost:', cost\n\n if cost < self.tolerance:\n return self.theta\n break\n\n return self.theta\n\n def predict(self, X, labels):\n \"\"\"\n Make linear prediction based on cost and gradient descent\n\n :param X: new data to make predictions on\n :param labels: boolean\n :return: return prediction\n \"\"\"\n if self.intercept:\n intercept = np.ones((np.shape(X)[0],1))\n X = np.concatenate((intercept, X), 1)\n \n num_examples, num_features = np.shape(X)\n prediction = []\n for sample in range(num_examples):\n yhat = 0\n for value in range(num_features):\n yhat += X[sample, value] * self.theta[value]\n \n pred = self.sigmoid(yhat)\n \n if labels:\n if pred > 0.5:\n prediction.append(int(1))\n else:\n prediction.append(int(0))\n else:\n prediction.append(yhat) \n \n return prediction\n \n\ndef demo():\n from sklearn.cross_validation import train_test_split\n from sklearn.metrics import confusion_matrix, classification_report \n # initialize linear regression parameters\n max_iterations = 50000\n learning_rate = 0.0001\n l2 = 1.0\n\n lgit = Logit(learning_rate = learning_rate, iterations = max_iterations, \n verbose = True, tolerance = 0.001, l2 = l2)\n\n data = np.loadtxt('Data/ionosphere.csv', delimiter = ',')\n X = data[:, 1:]\n y = data[:, 0]\n \n # scale data\n max = np.amax(X)\n X /= max\n \n prediction = []\n correct = []\n for i in range(0,10):\n \n X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.1)\n\n # fit the reg\n lgit.fit(X = X_train, y = y_train)\n \n # make a predictions\n prediction.append(lgit.predict(X_test, labels = True))\n correct.append(y_test.tolist())\n \n print classification_report(np.array(correct), np.array(prediction))\n \nif __name__ == '__main__':\n demo()"
},
{
"path": "MultiLayerPerceptron.py",
"content": "import time\nimport random\nimport numpy as np\nnp.seterr(all = 'ignore')\n\n# transfer functions\ndef sigmoid(x):\n return 1 / (1 + np.exp(-x))\n\n# derivative of sigmoid\ndef dsigmoid(y):\n return y * (1.0 - y)\n\n# using softmax as output layer is recommended for classification where outputs are mutually exclusive\ndef softmax(w):\n e = np.exp(w - np.amax(w))\n dist = e / np.sum(e)\n return dist\n\n# using tanh over logistic sigmoid for the hidden layer is recommended \ndef tanh(x):\n return np.tanh(x)\n \n# derivative for tanh sigmoid\ndef dtanh(y):\n return 1 - y*y\n\nclass MLP_Classifier(object):\n \"\"\"\n Basic MultiLayer Perceptron (MLP) neural network with regularization and learning rate decay\n Consists of three layers: input, hidden and output. The sizes of input and output must match data\n the size of hidden is user defined when initializing the network.\n The algorithm can be used on any dataset.\n As long as the data is in this format: [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]],\n [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]],\n ...\n [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]]]\n An example is provided below with the digit recognition dataset provided by sklearn\n Fully pypy compatible.\n \"\"\"\n def __init__(self, input, hidden, output, iterations = 50, learning_rate = 0.01, \n l2_in = 0, l2_out = 0, momentum = 0, rate_decay = 0, \n output_layer = 'logistic', verbose = True):\n \"\"\"\n :param input: number of input neurons\n :param hidden: number of hidden neurons\n :param output: number of output neurons\n :param iterations: how many epochs\n :param learning_rate: initial learning rate\n :param l2: L2 regularization term\n :param momentum: momentum\n :param rate_decay: how much to decrease learning rate by on each iteration (epoch)\n :param output_layer: activation (transfer) function of the output layer\n :param verbose: whether to spit out error rates while training\n \"\"\"\n # initialize parameters\n self.iterations = iterations\n self.learning_rate = learning_rate\n self.l2_in = l2_in\n self.l2_out = l2_out\n self.momentum = momentum\n self.rate_decay = rate_decay\n self.verbose = verbose\n self.output_activation = output_layer\n \n # initialize arrays\n self.input = input + 1 # add 1 for bias node\n self.hidden = hidden \n self.output = output\n\n # set up array of 1s for activations\n self.ai = np.ones(self.input)\n self.ah = np.ones(self.hidden)\n self.ao = np.ones(self.output)\n\n # create randomized weights\n # use scheme from Efficient Backprop by LeCun 1998 to initialize weights for hidden layer\n input_range = 1.0 / self.input ** (1/2)\n self.wi = np.random.normal(loc = 0, scale = input_range, size = (self.input, self.hidden))\n self.wo = np.random.uniform(size = (self.hidden, self.output)) / np.sqrt(self.hidden)\n \n # create arrays of 0 for changes\n # this is essentially an array of temporary values that gets updated at each iteration\n # based on how much the weights need to change in the following iteration\n self.ci = np.zeros((self.input, self.hidden))\n self.co = np.zeros((self.hidden, self.output))\n\n def feedForward(self, inputs):\n \"\"\"\n The feedforward algorithm loops over all the nodes in the hidden layer and\n adds together all the outputs from the input layer * their weights\n the output of each node is the sigmoid function of the sum of all inputs\n which is then passed on to the next layer.\n :param inputs: input data\n :return: updated activation output vector\n \"\"\"\n if len(inputs) != self.input-1:\n raise ValueError('Wrong number of inputs you silly goose!')\n\n # input activations\n self.ai[0:self.input -1] = inputs\n\n # hidden activations\n sum = np.dot(self.wi.T, self.ai)\n self.ah = tanh(sum)\n \n # output activations\n sum = np.dot(self.wo.T, self.ah)\n if self.output_activation == 'logistic':\n self.ao = sigmoid(sum)\n elif self.output_activation == 'softmax':\n self.ao = softmax(sum)\n else:\n raise ValueError('Choose a compatible output layer activation or check your spelling ;-p') \n \n \n return self.ao\n\n def backPropagate(self, targets):\n \"\"\"\n For the output layer\n 1. Calculates the difference between output value and target value\n 2. Get the derivative (slope) of the sigmoid function in order to determine how much the weights need to change\n 3. update the weights for every node based on the learning rate and sig derivative\n\n For the hidden layer\n 1. calculate the sum of the strength of each output link multiplied by how much the target node has to change\n 2. get derivative to determine how much weights need to change\n 3. change the weights based on learning rate and derivative\n :param targets: y values\n :param N: learning rate\n :return: updated weights\n \"\"\"\n if len(targets) != self.output:\n raise ValueError('Wrong number of targets you silly goose!')\n\n # calculate error terms for output\n # the delta (theta) tell you which direction to change the weights\n if self.output_activation == 'logistic':\n output_deltas = dsigmoid(self.ao) * -(targets - self.ao)\n elif self.output_activation == 'softmax':\n output_deltas = -(targets - self.ao)\n else:\n raise ValueError('Choose a compatible output layer activation or check your spelling ;-p') \n \n # calculate error terms for hidden\n # delta (theta) tells you which direction to change the weights\n error = np.dot(self.wo, output_deltas)\n hidden_deltas = dtanh(self.ah) * error\n \n # update the weights connecting hidden to output, change == partial derivative\n change = output_deltas * np.reshape(self.ah, (self.ah.shape[0],1))\n regularization = self.l2_out * self.wo\n self.wo -= self.learning_rate * (change + regularization) + self.co * self.momentum \n self.co = change \n\n # update the weights connecting input to hidden, change == partial derivative\n change = hidden_deltas * np.reshape(self.ai, (self.ai.shape[0], 1))\n regularization = self.l2_in * self.wi\n self.wi -= self.learning_rate * (change + regularization) + self.ci * self.momentum \n self.ci = change\n\n # calculate error\n if self.output_activation == 'softmax':\n error = -sum(targets * np.log(self.ao))\n elif self.output_activation == 'logistic':\n error = sum(0.5 * (targets - self.ao)**2)\n \n return error\n\n def test(self, patterns):\n \"\"\"\n Currently this will print out the targets next to the predictions.\n Not useful for actual ML, just for visual inspection.\n \"\"\"\n for p in patterns:\n print(p[1], '->', self.feedForward(p[0]))\n\n def fit(self, patterns):\n if self.verbose == True:\n if self.output_activation == 'softmax':\n print 'Using softmax activation in output layer'\n elif self.output_activation == 'logistic':\n print 'Using logistic sigmoid activation in output layer'\n \n num_example = np.shape(patterns)[0]\n \n for i in range(self.iterations):\n error = 0.0\n random.shuffle(patterns)\n for p in patterns:\n inputs = p[0]\n targets = p[1]\n self.feedForward(inputs)\n error += self.backPropagate(targets)\n \n with open('error.txt', 'a') as errorfile:\n errorfile.write(str(error) + '\\n')\n errorfile.close()\n \n if i % 10 == 0 and self.verbose == True:\n error = error/num_example\n print('Training error %-.5f' % error)\n \n # learning rate decay\n self.learning_rate = self.learning_rate * (self.learning_rate / (self.learning_rate + (self.learning_rate * self.rate_decay)))\n \n def predict(self, X):\n \"\"\"\n return list of predictions after training algorithm\n \"\"\"\n predictions = []\n for p in X:\n predictions.append(self.feedForward(p))\n return predictions\n\ndef demo():\n from sklearn.preprocessing import scale\n \"\"\"\n run NN demo on the digit recognition dataset from sklearn\n \"\"\"\n def load_data():\n data = np.loadtxt('Data/sklearn_digits.csv', delimiter = ',')\n\n # first ten values are the one hot encoded y (target) values\n y = data[:,0:10]\n \n data = data[:,10:] # x data\n data = scale(data)\n \n out = []\n #print data.shape\n\n # populate the tuple list with the data\n for i in range(data.shape[0]):\n tupledata = list((data[i,:].tolist(), y[i].tolist())) # don't mind this variable name\n out.append(tupledata)\n\n return out\n \n start = time.time()\n \n X = load_data()\n\n #print X[9] # make sure the data looks right\n\n NN = MLP_Classifier(64, 4000, 10, iterations = 50, learning_rate = 0.01, \n momentum = 0.5, rate_decay = 0.0001, \n output_layer = 'logistic')\n\n NN.fit(X)\n \n end = time.time()\n print end - start\n \n #NN.test(X)\n\nif __name__ == '__main__':\n demo()\n"
},
{
"path": "Old/BackPropagationNN.py",
"content": "import math\nimport random\nimport numpy as np\nnp.seterr(all = 'ignore')\n\n# sigmoid transfer function\n# IMPORTANT: when using the logit (sigmoid) transfer function for the output layer make sure y values are scaled from 0 to 1\n# if you use the tanh for the output then you should scale between -1 and 1\n# we will use sigmoid for the output layer and tanh for the hidden layer\ndef sigmoid(x):\n return 1 / (1 + np.exp(-x))\n\n# derivative of sigmoid\ndef dsigmoid(y):\n return y * (1.0 - y)\n\n# using tanh over logistic sigmoid is recommended \ndef tanh(x):\n return math.tanh(x)\n \n# derivative for tanh sigmoid\ndef dtanh(y):\n return 1 - y*y\n\nclass MLP_NeuralNetwork(object):\n \"\"\"\n Basic MultiLayer Perceptron (MLP) network, adapted and from the book 'Programming Collective Intelligence' (http://shop.oreilly.com/product/9780596529321.do)\n Consists of three layers: input, hidden and output. The sizes of input and output must match data\n the size of hidden is user defined when initializing the network.\n The algorithm has been generalized to be used on any dataset.\n As long as the data is in this format: [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]],\n [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]],\n ...\n [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]]]\n An example is provided below with the digit recognition dataset provided by sklearn\n Fully pypy compatible.\n \"\"\"\n def __init__(self, input, hidden, output, iterations, learning_rate, momentum, rate_decay):\n \"\"\"\n :param input: number of input neurons\n :param hidden: number of hidden neurons\n :param output: number of output neurons\n \"\"\"\n # initialize parameters\n self.iterations = iterations\n self.learning_rate = learning_rate\n self.momentum = momentum\n self.rate_decay = rate_decay\n \n # initialize arrays\n self.input = input + 1 # add 1 for bias node\n self.hidden = hidden\n self.output = output\n\n # set up array of 1s for activations\n self.ai = [1.0] * self.input\n self.ah = [1.0] * self.hidden\n self.ao = [1.0] * self.output\n\n # create randomized weights\n # use scheme from 'efficient backprop to initialize weights\n input_range = 1.0 / self.input ** (1/2)\n output_range = 1.0 / self.hidden ** (1/2)\n self.wi = np.random.normal(loc = 0, scale = input_range, size = (self.input, self.hidden))\n self.wo = np.random.normal(loc = 0, scale = output_range, size = (self.hidden, self.output))\n \n # create arrays of 0 for changes\n # this is essentially an array of temporary values that gets updated at each iteration\n # based on how much the weights need to change in the following iteration\n self.ci = np.zeros((self.input, self.hidden))\n self.co = np.zeros((self.hidden, self.output))\n\n def feedForward(self, inputs):\n \"\"\"\n The feedforward algorithm loops over all the nodes in the hidden layer and\n adds together all the outputs from the input layer * their weights\n the output of each node is the sigmoid function of the sum of all inputs\n which is then passed on to the next layer.\n :param inputs: input data\n :return: updated activation output vector\n \"\"\"\n if len(inputs) != self.input-1:\n raise ValueError('Wrong number of inputs you silly goose!')\n\n # input activations\n for i in range(self.input -1): # -1 is to avoid the bias\n self.ai[i] = inputs[i]\n\n # hidden activations\n for j in range(self.hidden):\n sum = 0.0\n for i in range(self.input):\n sum += self.ai[i] * self.wi[i][j]\n self.ah[j] = tanh(sum)\n\n # output activations\n for k in range(self.output):\n sum = 0.0\n for j in range(self.hidden):\n sum += self.ah[j] * self.wo[j][k]\n self.ao[k] = sigmoid(sum)\n\n return self.ao[:]\n\n def backPropagate(self, targets):\n \"\"\"\n For the output layer\n 1. Calculates the difference between output value and target value\n 2. Get the derivative (slope) of the sigmoid function in order to determine how much the weights need to change\n 3. update the weights for every node based on the learning rate and sig derivative\n\n For the hidden layer\n 1. calculate the sum of the strength of each output link multiplied by how much the target node has to change\n 2. get derivative to determine how much weights need to change\n 3. change the weights based on learning rate and derivative\n :param targets: y values\n :param N: learning rate\n :return: updated weights\n \"\"\"\n if len(targets) != self.output:\n raise ValueError('Wrong number of targets you silly goose!')\n\n # calculate error terms for output\n # the delta tell you which direction to change the weights\n output_deltas = [0.0] * self.output\n for k in range(self.output):\n error = -(targets[k] - self.ao[k])\n output_deltas[k] = dsigmoid(self.ao[k]) * error\n\n # calculate error terms for hidden\n # delta tells you which direction to change the weights\n hidden_deltas = [0.0] * self.hidden\n for j in range(self.hidden):\n error = 0.0\n for k in range(self.output):\n error += output_deltas[k] * self.wo[j][k]\n hidden_deltas[j] = dtanh(self.ah[j]) * error\n\n # update the weights connecting hidden to output\n for j in range(self.hidden):\n for k in range(self.output):\n change = output_deltas[k] * self.ah[j]\n self.wo[j][k] -= self.learning_rate * change + self.co[j][k] * self.momentum\n self.co[j][k] = change\n\n # update the weights connecting input to hidden\n for i in range(self.input):\n for j in range(self.hidden):\n change = hidden_deltas[j] * self.ai[i]\n self.wi[i][j] -= self.learning_rate * change + self.ci[i][j] * self.momentum\n self.ci[i][j] = change\n\n # calculate error\n error = 0.0\n for k in range(len(targets)):\n error += 0.5 * (targets[k] - self.ao[k]) ** 2\n return error\n\n def test(self, patterns):\n \"\"\"\n Currently this will print out the targets next to the predictions.\n Not useful for actual ML, just for visual inspection.\n \"\"\"\n for p in patterns:\n print(p[1], '->', self.feedForward(p[0]))\n\n def train(self, patterns):\n # N: learning rate\n for i in range(self.iterations):\n error = 0.0\n random.shuffle(patterns)\n for p in patterns:\n inputs = p[0]\n targets = p[1]\n self.feedForward(inputs)\n error += self.backPropagate(targets)\n with open('error.txt', 'a') as errorfile:\n errorfile.write(str(error) + '\\n')\n errorfile.close()\n if i % 10 == 0:\n print('error %-.5f' % error)\n # learning rate decay\n self.learning_rate = self.learning_rate * (self.learning_rate / (self.learning_rate + (self.learning_rate * self.rate_decay)))\n \n def predict(self, X):\n \"\"\"\n return list of predictions after training algorithm\n \"\"\"\n predictions = []\n for p in X:\n predictions.append(self.feedForward(p))\n return predictions\n\ndef demo():\n \"\"\"\n run NN demo on the digit recognition dataset from sklearn\n \"\"\"\n def load_data():\n data = np.loadtxt('Data/sklearn_digits.csv', delimiter = ',')\n\n # first ten values are the one hot encoded y (target) values\n y = data[:,0:10]\n #y[y == 0] = -1 # if you are using a tanh transfer function make the 0 into -1\n #y[y == 1] = .90 # try values that won't saturate tanh\n \n data = data[:,10:] # x data\n #data = data - data.mean(axis = 1)\n data -= data.min() # scale the data so values are between 0 and 1\n data /= data.max() # scale\n \n out = []\n print data.shape\n\n # populate the tuple list with the data\n for i in range(data.shape[0]):\n fart = list((data[i,:].tolist(), y[i].tolist())) # don't mind this variable name\n out.append(fart)\n\n return out\n\n X = load_data()\n\n print X[9] # make sure the data looks right\n\n NN = MLP_NeuralNetwork(64, 100, 10, iterations = 50, learning_rate = 0.5, momentum = 0.5, rate_decay = 0.01)\n\n NN.train(X)\n\n NN.test(X)\n\nif __name__ == '__main__':\n demo()\n"
},
{
"path": "Old/README.md",
"content": "* BackPropagationNN.py - Basic MultiLayer Perceptron (MLP) network, adapted and from the book ['Programming Collective Intelligence'](http://shop.oreilly.com/product/9780596529321.do) Consists of three layers: input, hidden and output. The sizes of input and output must match data the size of hidden is user defined when initializing the network. The algorithm has been generalized to be used on any dataset. Write up on my [blog](http://databoys.github.io/Feedforward/)"
},
{
"path": "README.md",
"content": "# Machine-Learning\nVarious machine learning algorithms broken down in basic and readable python code. Useful for studying and learning how the algorithms function.\n\n* MultiLayerPerceptron.py - Basic multilayer perceptron neural network written with numpy. With weight decay regularization, learning rate decay, softmax or logistic sigmoid output layer, and tanh hidden layer.\n\n* LinearRegression.py - Gradient descent linear regression with l2 regularization.\n\n* LogisticRegression.py - Gradient descent logistic regression with l2 regularization. \n\n\n# Usage\n\n### MultiLayerPerceptron ###\n#### Parameters ####\n-**input (int)**: Size of input layer, must match the number of features in the input dataset.\n\n-**hidden (int)**: Size of hidden layer, more hidden neurons can model more complex data at the cost of potentially overfitting.\n\n-**output (int)**: Size of output layers, must match the number of possible classes. Can use 1 for binary classification.\n\n-**iterations (int)**: controls the number of passes over the traning data (aka epochs). Defaults to 50\n\n-**learning_rate (float)**: The learning rate constant controls how much weights are updated on each iteration. Defaults to 0.01.\n\n-**l2_in (float)**: Weight decay regularization term for the input layer weights, keeps weights low to avoid overfitting. Useful when hidden layer is large. Defaults to 0 (off).\n\n-**l2_out (float)**: Weight decay regularization term for the hidden layer weights, keeps weights low to avoid overfitting. Useful when hidden layer is large. Defaults to 0 (off).\n\n-**momentum (float)**: Adds a fraction of the previous weight update to the current weight update. Is used to help system from converging at a local minimum. A high value can increase the learning speed but risks overshooting the minimum. A low momentum can get stuck in a local minimum and decreases the speed of learning. Defaults to 0 (off).\n\n-**rate_decay (float)**: How much to decrease learning rate on each iteration. The idea is to start with a high learning rate to avoid local minima and then slow down as the global minimum is approached. Defaults to 0 (off).\n\n-**output_layer (string)**: Which activation function to use for the output layer. Currently accepts 'logistic' for logistic sigmoid or 'softmax' for softmax. Use softmax when the outputs are mutually exclusive. Defaults to 'logistic'.\n\n-**verbose (bool)**: Whether to print current error rate while training. Defaults to True.\n\n#### Fitting and predicting ####\n\n1) Initialize the network and setting up the size of each layer.\n```python\nNN = MLP_Classifier(64, 100, 10)\n```\n\n2) Train the network with the training dataset. The training dataset must be in the following format with y values one hot encoded. There is an example in the demo function of the MLP on how to import data with numpy and get it into the appropriate format. \n```\t\n\t[[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]],\n [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]],\n ...\n [[[x1, x2, x3, ..., xn], [y1, y2, ..., yn]]]\n```\n\t\n```python\nNN.fit(train)\n```\n\n3) Make predictions on testing dataset. Same format as training dataset without the list of y values. Will return a list of predictions.\n```python\nNN.predict(X_test)\n```\n\n### Linear and Logistic Regression ###\n#### Parameters ####\n-**learning_rate (float)**: The learning rate constant controls how much weights are updated on each iteration. Defaults to 0.01.\n\n-**iterations (int)**: controls the number of passes over the traning data (aka epochs). Defaults to 50.\n\n-**intercept (bool)**: Whether or not to fit an intercept. Defaults to True.\n\n-**L2 (float)**: Weight decay regularization term for the weights, keeps weights low to avoid overfitting. Defaults to 0 (off).\n\n-**tolerance (float)**: The error value in which to stop training. Defaults to 0 (off).\n\n-**verbose (bool)**: Whether to print current error rate while training. Defaults to True.\n\n#### Fitting and predicting ####\n\n1) Initialize the linear model.\n```python\nlinearReg = LinReg(learning_rate = 0.1, iterations = 500, verbose = True, l2 = 0.001)\n```\n\n2) Train the model with the training dataset. The training dataset has to be a numpy array, the X and y values must be seperated into two different arrays. \n\t\n```python\nlinearReg.fit(X = X_train, y = y_train)\n```\n\n3) Make predictions on testing dataset. Same format as training dataset without the array of y values. Will return a list of predictions.\n```python\nlinearReg.predict(X_test)\n```\nLogistic regression has one extra parameter for .predict. If labels is set to 'True' the predicted class is returned, otherwise the probability of the class being label 1 is returned.\n``` python\nlogit.predict(X_test, labels = True)\n```"
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