import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
path = 'ex2data1.txt'
data = pd.read_csv(path, header=None, names=['Exam 1', 'Exam 2', 'Admitted'])
data.head()
## Exam 1 Exam 2 Admitted
## 0 34.623660 78.024693 0
## 1 30.286711 43.894998 0
## 2 35.847409 72.902198 0
## 3 60.182599 86.308552 1
## 4 79.032736 75.344376 1
positive = data[data['Admitted'].isin([1])]
negative = data[data['Admitted'].isin([0])]
fig, ax = plt.subplots(figsize=(12,8))
ax.scatter(positive['Exam 1'], positive['Exam 2'], s=50, c='b', marker='o', label='Admitted')
ax.scatter(negative['Exam 1'], negative['Exam 2'], s=50, c='r', marker='x', label='Not Admitted')
ax.legend()
ax.set_xlabel('Exam 1 Score')
ax.set_ylabel('Exam 2 Score')
plt.show()
def sigmoid(z):
return 1 / (1 + np.exp(-z))
nums = np.arange(-10, 10, step=1)
fig, ax = plt.subplots(figsize=(12,8))
ax.plot(nums, sigmoid(nums), 'r')
plt.show()
def cost(theta, X, y):
theta = np.matrix(theta)
X = np.matrix(X)
y = np.matrix(y)
first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
return np.sum(first - second) / (len(X))
# add a ones column - this makes the matrix multiplication work out easier
data.insert(0, 'Ones', 1)
# set X (training data) and y (target variable)
cols = data.shape[1]
X = data.iloc[:,0:cols-1]
y = data.iloc[:,cols-1:cols]
# convert to numpy arrays and initalize the parameter array theta
X = np.array(X.values)
y = np.array(y.values)
theta = np.zeros(3)
theta
## array([0., 0., 0.])
X.shape, y.shape, theta.shape
## ((100, 3), (100, 1), (3,))
cost(theta, X, y)
## 0.6931471805599453
def gradient(theta, X, y):
theta = np.matrix(theta)
X = np.matrix(X)
y = np.matrix(y)
parameters = int(theta.ravel().shape[1])
grad = np.zeros(parameters)
error = sigmoid(X * theta.T) - y
for i in range(parameters):
term = np.multiply(error, X[:,i])
grad[i] = np.sum(term) / len(X)
return grad
gradient(theta, X, y)
## array([ -0.1 , -12.00921659, -11.26284221])
import scipy.optimize as opt
result = opt.fmin_tnc(func=cost, x0=theta, fprime=gradient, args=(X, y))
result
## (array([-25.16131863, 0.20623159, 0.20147149]), 36, 0)
cost(result[0], X, y)
## 0.20349770158947458
def predict(theta, X):
probability = sigmoid(X * theta.T)
return [1 if x >= 0.5 else 0 for x in probability]
theta_min = np.matrix(result[0])
predictions = predict(theta_min, X)
correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y)]
accuracy = (sum(map(int, correct)) % len(correct))
print ('accuracy = {0}%'.format(accuracy))
## accuracy = 89%
path = 'ex2data2.txt'
data2 = pd.read_csv(path, header=None, names=['Test 1', 'Test 2', 'Accepted'])
data2.head()
## Test 1 Test 2 Accepted
## 0 0.051267 0.69956 1
## 1 -0.092742 0.68494 1
## 2 -0.213710 0.69225 1
## 3 -0.375000 0.50219 1
## 4 -0.513250 0.46564 1
positive = data2[data2['Accepted'].isin([1])]
negative = data2[data2['Accepted'].isin([0])]
fig, ax = plt.subplots(figsize=(12,8))
ax.scatter(positive['Test 1'], positive['Test 2'], s=50, c='b', marker='o', label='Accepted')
ax.scatter(negative['Test 1'], negative['Test 2'], s=50, c='r', marker='x', label='Rejected')
ax.legend()
ax.set_xlabel('Test 1 Score')
ax.set_ylabel('Test 2 Score')
plt.show()
degree = 5
x1 = data2['Test 1']
x2 = data2['Test 2']
data2.insert(3, 'Ones', 1)
for i in range(1, degree):
for j in range(0, i):
data2['F' + str(i) + str(j)] = np.power(x1, i-j) * np.power(x2, j)
data2.drop('Test 1', axis=1, inplace=True)
data2.drop('Test 2', axis=1, inplace=True)
data2.head()
## Accepted Ones F10 F20 ... F40 F41 F42 F43
## 0 1 1 0.051267 0.002628 ... 0.000007 0.000094 0.001286 0.017551
## 1 1 1 -0.092742 0.008601 ... 0.000074 -0.000546 0.004035 -0.029801
## 2 1 1 -0.213710 0.045672 ... 0.002086 -0.006757 0.021886 -0.070895
## 3 1 1 -0.375000 0.140625 ... 0.019775 -0.026483 0.035465 -0.047494
## 4 1 1 -0.513250 0.263426 ... 0.069393 -0.062956 0.057116 -0.051818
##
## [5 rows x 12 columns]
def costReg(theta, X, y, learningRate):
theta = np.matrix(theta)
X = np.matrix(X)
y = np.matrix(y)
first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
reg = (learningRate / (2 * len(X))) * np.sum(np.power(theta[:,1:theta.shape[1]], 2))
return np.sum(first - second) / len(X) + reg
def gradientReg(theta, X, y, learningRate):
theta = np.matrix(theta)
X = np.matrix(X)
y = np.matrix(y)
parameters = int(theta.ravel().shape[1])
grad = np.zeros(parameters)
error = sigmoid(X * theta.T) - y
for i in range(parameters):
term = np.multiply(error, X[:,i])
if (i == 0):
grad[i] = np.sum(term) / len(X)
else:
grad[i] = (np.sum(term) / len(X)) + ((learningRate / len(X)) * theta[:,i])
return grad
# set X and y (remember from above that we moved the label to column 0)
cols = data2.shape[1]
X2 = data2.iloc[:,1:cols]
y2 = data2.iloc[:,0:1]
# convert to numpy arrays and initalize the parameter array theta
X2 = np.array(X2.values)
y2 = np.array(y2.values)
theta2 = np.zeros(11)
learningRate = 1
costReg(theta2, X2, y2, learningRate)
## 0.6931471805599454
gradientReg(theta2, X2, y2, learningRate)
## array([0.00847458, 0.01878809, 0.05034464, 0.01150133, 0.01835599,
## 0.00732393, 0.00819244, 0.03934862, 0.00223924, 0.01286005,
## 0.00309594])
result2 = opt.fmin_tnc(func=costReg, x0=theta2, fprime=gradientReg, args=(X2, y2, learningRate))
result2
## (array([ 0.53010246, 0.29075567, -1.60725764, -0.58213819, 0.01781027,
## -0.21329507, -0.40024142, -1.3714414 , 0.02264304, -0.95033581,
## 0.0344085 ]), 22, 1)
theta_min = np.matrix(result2[0])
predictions = predict(theta_min, X2)
correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y2)]
accuracy = (sum(map(int, correct)) / len(correct))
print ('accuracy = {0}%'.format(accuracy))
## accuracy = 0.6610169491525424%
from sklearn import linear_model#调用sklearn的线性回归包
model = linear_model.LogisticRegression(penalty='l2', C=1.0)
model.fit(X2, y2.ravel())
## LogisticRegression()
model.score(X2, y2)
## 0.6610169491525424