!/usr/bin/env python
coding: utf-8
In[64]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
In[65]:
path = 'D:\STUDY\machine learning\homework1\ex1data1.txt'
data = pd.read_csv(path, names = ['Population','Profit'] )
data.head()
In[39]:
data.describe()
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data.plot(kind = 'scatter',x = 'Population',y = 'Profit',figsize = (12,8))
plt.show()
In[66]:
def computeCost(X, y, theta):
j = np.power(((X * theta.T)-y),2)
return np.sum(j)/(2*len(X))
In[42]:
data.insert(0,'Ones',1)
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cols = data.shape[1]#數(shù)據(jù)列數(shù)
X = data.iloc[:,0:cols-1]
y = data.iloc[:,cols-1:cols]
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X.head()
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y.head()
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X = np.matrix(X.values)
y = np.matrix(y.values)
theta = np.zeros([1,2])
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computeCost(X, y, theta)
In[67]:
def gradientDescent(X, y, theta, alpha, iters):
temp = np.matrix(np.zeros(theta.shape))
parameters = int(len(theta.ravel()))
cost = np.zeros(iters)
print(parameters)
for i in range(iters):
error = (X * theta.T) - y
for j in range(parameters):
term = np.multiply(error, X[:,j])
temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term))
theta = temp
cost[i] = computeCost(X, y, theta)
return theta , cost
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alpha = 0.01
iters = 1000
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g ,cost = gradientDescent(X, y, theta, alpha,iters)
In[51]:
computeCost(X, y, g)
In[52]:
x = np.linspace(data.Population.min(), data.Population.max(), 100)
f = g[0, 0] + (g[0, 1] * x)
fig, ax = plt.subplots(figsize=(12,8))
ax.plot(x, f, 'r', label='Prediction')
ax.scatter(data.Population, data.Profit, label='Traning Data')
ax.legend(loc=2)
ax.set_xlabel('Population')
ax.set_ylabel('Profit')
ax.set_title('Predicted Profit vs. Population Size')
plt.show()
In[53]:
fig, ax = plt.subplots(figsize=(12,8))
ax.plot(np.arange(iters), cost, 'r')
ax.set_xlabel('Iterations')
ax.set_ylabel('Cost')
ax.set_title('Error vs. Training Epoch')
plt.show()
In[69]:
path = "D:\STUDY\machine learning\homework1\ex1data2.txt"
In[70]:
data2 = pd.read_csv(path, header = None, names = ['Size', 'Bedrooms', 'Price'])
data2.head()
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data2.describe()
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data2 = (data2-data2.mean())/data2.std()
data2.head()
In[73]:
data2.insert(0, 'Ones', 1)
In[74]:
cols = data2.shape[1]
X2 = data2.iloc[:,0:cols -1]
y2 = data2.iloc[:,cols-1:cols]
X2,y2
In[75]:
X2 = np.matrix(X2.values)
y2 = np.matrix(y2.values)
theta2 = np.zeros([1,3])
In[76]:
g2 , cost2 = gradientDescent(X2, y2, theta2, alpha,iters)
computeCost(X2, y2, g2)
In[77]:
fig, ax = plt.subplots(figsize=(12,8))
ax.plot(np.arange(iters), cost2, 'r')
ax.set_xlabel('Iterations')
ax.set_ylabel('Cost')
ax.set_title('Error vs. Training Epoch')
plt.show()
In[80]:
def normalEqn(X, y):
theta = (np.linalg.inv((X.T)X))(X.T)*y
return theta
In[81]:
final_theta2 = normalEqn(X,y)
final_theta2
