import pandas as pd
import seaborn as sns
sns.set(context="notebook", style="whitegrid", palette="dark")
import matplotlib.pyplot as plt
import tensorflow as tf
import numpy as np
df = pd.read_csv('ex1data1.txt', names=['population', 'profit'])#讀取資料並賦予列名
df.head()#看前五行
df.info()
sns.lmplot('population', 'profit', df, size=6, fit_reg=false)
plt.show()
def get_x(df):#讀取特徵
ones = pd.dataframe()#ones是m行1列的dataframe
data = pd.concat([ones, df], axis=1) # 合併資料，根據列合併
return data.iloc[:, :-1].as_matrix() # 這個操作返回 ndarray,不是矩陣
def get_y(df):#讀取標籤
return np.array(df.iloc[:, -1])
def linear_regression(x_data, y_data, alpha, epoch, optimizer=tf.train.gradientdescentoptimizer):# 這個函式是舊金山的乙個大神lucas shen寫的
# placeholder for graph input
x = tf.placeholder(tf.float32, shape=x_data.shape)
y = tf.placeholder(tf.float32, shape=y_data.shape)
# construct the graph
with tf.variable_scope('linear-regression'):
w = tf.get_variable("weights",
(x_data.shape[1], 1),
initializer=tf.constant_initializer()) # n*1
y_pred = tf.matmul(x, w) # m*n @ n*1 -> m*1
loss = 1 / (2 * len(x_data)) * tf.matmul((y_pred - y), (y_pred - y), transpose_a=true) # (m*1).t @ m*1 = 1*1
opt = optimizer(learning_rate=alpha)
opt_operation = opt.minimize(loss)
# run the session
with tf.session() as sess:
sess.run(tf.global_variables_initializer())
loss_data =
if len(loss_data) > 1 and np.abs(loss_data[-1] - loss_data[-2]) < 10 ** -9: # early break when it's converged
# print('converged at epoch {}'.format(i))
break
# clear the graph
tf.reset_default_graph()
return # just want to return in row vector format
data = pd.read_csv('ex1data1.txt', names=['population', 'profit'])#讀取資料，並賦予列名
data.head()#看下資料前5行
x = get_x(data)
print(x.shape, type(x))
y = get_y(data)
print(y.shape, type(y))
#看下資料維度
theta = np.zeros(x.shape[1])#x.shape[1]=2,代表特徵數n
def lr_cost(theta, x, y):
# """
# x: r(m*n), m 樣本數, n 特徵數
# y: r(m)
# theta : r(n), 線性回歸的引數
# """
m = x.shape[0]#m為樣本數
inner = x @ theta - y # r(m*1)，x @ theta等價於x.dot(theta)
# 1*m @ m*1 = 1*1 in matrix multiplication
# but you know numpy didn't do transpose in 1d array, so here is just a
# vector inner product to itselves
square_sum = inner.t @ inner
cost = square_sum / (2 * m)
return cost
lr_cost(theta, x, y)#返回theta的值
def gradient(theta, x, y):
m = x.shape[0]
inner = x.t @ (x @ theta - y) # (m,n).t @ (m, 1) -> (n, 1)，x @ theta等價於x.dot(theta)
return inner / m
def batch_gradient_decent(theta, x, y, epoch, alpha=0.01):
# 擬合線性回歸，返回引數和代價
# epoch: 批處理的輪數
# """
cost_data = [lr_cost(theta, x, y)]
_theta = theta.copy() # 拷貝乙份，不和原來的theta混淆
return _theta, cost_data
#批量梯度下降函式
epoch = 500
final_theta, cost_data = batch_gradient_decent(theta, x, y, epoch)
final_theta
#最終的theta
cost_data
# 看下代價資料
# 計算最終的代價
lr_cost(final_theta, x, y)
ax = sns.tsplot(cost_data, time=np.arange(epoch+1))
ax.set_xlabel('epoch')
ax.set_ylabel('cost')
plt.show()
#可以看到從第二輪代價資料變換很大，接下來平穩了
b = final_theta[0] # intercept，y軸上的截距
m = final_theta[1] # slope，斜率
plt.scatter(data.population, data.profit, label="training data")
plt.plot(data.population, data.population*m + b, label="prediction")
plt.legend(loc=2)
plt.show()
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