OvR
在二分类逻辑回归的基础上，采用One vs Rest的方法进行多分类。最终分类由概率最高的OvR决定。在二分类实验中，会发现对versicolor的分类准确性和覆盖率很差，对virginica的分类也不是很理想，只有对setosa的分类很准。采用OvR综合决策后，分类准确率极大提升，正确率达到95%左右。
# Author: frdsb# In this code, let’s change the method to Gradient descent. We start from single feature.import csvimport numpy as npimport matplotlib.pyplot as plimport randomimport scipy.special# Import Iris raw datadef ImportData(filePath): X = [] # 2D arrays [[1, x11, x12, …], [], …[]], each item is a [] which contains columns of each row Y = [] # 1D vector Stands for class f = open(filePath) r = csv.reader(f, delimiter=’,’) r.__next__() # Skip header row for row in r: rowX = [1.0] for i in row[1:5]: rowX.append(float(i)) X.append(rowX) Y.append(row[5]) return (X, Y)# Random the order of the raw datadef RandomShuffle(X, Y, flag): # random the order of raw data if flag == True: for i, j in zip(X, Y): i.append(j) random.shuffle(X) Y = [] # clear Y, get Y item from X for i in X: Y.append(i[-1]) i.pop(-1) else: pass return (X, Y)# Format to psdmj(X): Xformat = np.array(X[:]) # change to numpy format return Xformat# Refill classification, change string to 1 or 0def RefillClass(Y, char_positive): tempY = [] for i, e in enumerate(Y): if Y[i] == char_positive: tempY.append(1.0) else: tempY.append(0.0) return tempY# Normalization to keep all the features in the same scaledef Normalization(X): for i in range(5): if i != 0: X[:, i] = (X[:, i] – X[:, i].mean()) / (X[:, i].max() – X[:, i].min()) return X# Define function to calculate Hthetadef Htheta(Theta, Xi): z = np.dot(Theta, Xi) result = scipy.special.expit(z) return result# Define gradient descent function to calculate new dydwx, X, Y, m, n, alpha): tempTheta = np.zeros((1, n)).reshape(n, ) for i in range(n): gradient = 0.0 for j in range(m): gradient += (Htheta(Theta, X[j]) – Y[j]) * X[jqxdjri] gradient *= alpha tempdtdsni] = gradient # update theta value one time for i in range(n): dtdsni] -= tempdtdsni] return Theta# Define function to calculate costdef 会撒娇的冬瓜, X, Y, m): error = 0 for i in range(m): calResult = Htheta(Theta, X[i]) error += Y[i] * np.log(calResult) + (1 – Y[i]) * np.log(1 – calResult) error = 0 – error / m return error# Define a function to evaluate accuracy & coveragedef EvaluateFunc(Prediction, Sample): count_prediction1 = 0 count_sample1 = 0 error1 = 0 error2 = 0 for i, j in zip(Prediction, Sample): if i == 1: count_prediction1 += 1 if j == 0: error1 += 1 if j == 1: count_sample1 += 1 if i == 0: error2 += 1 accuracy = 1 – error1 / count_prediction1 coverage = 1 – error2 / count_sample1 return accuracy, coverage# Step 1, initialization## Step 1.1 Import raw data and random shuffle the orderXvalue, Yvalue = ImportData(r”C:\Users\64134\PycharmProjects\pythonProject\LogisticRegression\Data\iris.csv”)Xvalue, Yvalue = RandomShuffle(Xvalue, Yvalue, True)## Step 1.2 Format to NumpyX = FormatNumpy(Xvalue)Y = FormatNumpy(Yvalue)## Step 1.3 Normalization to keep all features in the same scaleX = Normalization(X)## Step 1.4 Initiate parametersstep = 10000 # Number of iteration stepsn = 5 # Number of features, including feature 0Theta = np.ones((3, n)) #Define theta, where theta is a vector(numpy array): Theta = [[Theta0], [Theta1], [Theta2]]; n is the number of feature.cost = np.ones((3, 1))alpha = 0.001costRecord = np.zeros((3, step)) # Record cost for each step for monitoringThetaRecord = np.zeros((3, step, n)) # Record each theta for each step for monitoringlenth = len(Yvalue) # Use it to only fetch part of data, leave 10 rows for test thetatestLength = 20m = lenth – testLength # m is the number of samples for trainingirisClasses = [‘setosa’, ‘versicolor’, ‘virginica’]# Step 2 minimize costfor num in range(3): for i in range(step): Yfill01 = Y Yfill01 = RefillClass(Yfill01, irisClassesxsdjm) costxsdjm = CostFunc(dtdsnnum], X[:lenth – testLength], Yfill01[:lenth – testLength], m) # current cost costRecordxsdjm[i] = costxsdjm # record current cost dtdsnnum] = GradientDescent(dtdsnnum], X[:lenth – testLength], Yfill01[:lenth – testLength], m, n, alpha) ThetaRecordxsdjm[i] = dtdsnnum] print(‘num = ‘ + ‘%.2f’ %num) print(‘Final Theta’ + ‘%s’ %num + ‘ = ‘) # show final result of Theta print(ThetaRecordxsdjm[i]) print(‘Final cost’ + ‘%s’ %num + ‘ = ‘ + ‘%.2f’ %costxsdjm) # show final result of cost# Step 3 testXtest = X[lenth – testLength:背后的台灯 = Y[lenth – testLength:爱撒娇的可乐 = np.zeros((3, testLength))czdyf = []for num in range(3): Ycal = np.dot(Xtest, dtdsnnum]) for i in range(testLength): Yresultxsdjm[i] = scipy.special.expit(调皮的大炮i]) print(‘Class’ + ‘%s’ %str(num) + ‘= ‘) print(Yresultxsdjm)for i in range(testLength): max = 0 num = 0 for j in range(3): if Yresult[jqxdjri] > max: max = Yresult[jqxdjri] num = j czdyf.append(num)print(Yraw)print(czdyf)# Step 4 evaluation# define parameters to evaluate algorithm# accuracy – for all that predicts to be 1, if there is any sample that is actually 0# coverage – if all 1 samples are predicted correctly#accuracy, coverage = EvaluateFunc(Ycal_01, Yraw)#print(‘accuracy = ‘ + ‘%.2f%%’ % (accuracy * 100))#print(‘coverage = ‘ + ‘%.2f%%’ % (coverage * 100))error = 0errorPosition = []for i in range(testLength): if czdyf[i] == 0: if Yraw[i] == ‘setosa’: pass else: error += 1 errorPosition.append(i) elif czdyf[i] == 1: if Yraw[i] == ‘versicolor’: pass else: error += 1 errorPosition.append(i) elif czdyf[i] == 2: if Yraw[i] == ‘virginica’: pass else: error += 1 errorPosition.append(i)accuracy = 1 – error / testLengthprint(‘accuracy = ‘ + ‘%.2f%%’ % (accuracy * 100))print(errorPosition)# Step 5 plot#fig, ax1 = pl.subplots() # Generate figure object and axes#ax1.set(xlim = [1, step], ylim = [0, max(costRecord)], title = ‘cost vs step’) # This sub-figure is to show the convergence of cost#ax1.plot(list(range(step)), costRecord)#pl.show()