- 追加された行はこの色です。
- 削除された行はこの色です。
#author("2019-11-20T04:35:55+00:00","","")
#author("2019-11-20T07:32:38+00:00","","")
#mynavi(機械学習の為の数学の基礎)
#setlinebreak(on);
* 目次 [#d8db4f2c]
#contents
- 関連
-- [[機械学習の為の数学の基礎]]
-- [[Python覚え書き]]
-- [[IPythonの使い方メモ]]
-- [[numpy入門]]
-- [[pandas入門]]
-- [[matplotlibでグラフ作成]]
* 概要 [#g644cbdc]
#html(<div style="padding-left: 10px;">)
#TODO
#html(</div>)
* 実装 [#b1b871c1]
#html(<div style="padding-left: 10px;">)
データ: &ref(sample_rent1.csv);
sample_rent1.py
#mycode2(python){{
"""
重回帰分析.
"""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# データ読み込み
data = np.loadtxt("sample.csv", delimiter=",", skiprows=1)
def normalize(X, data=None):
"""正規化(Z-score normalization)."""
data = X if data is None else data
m = data.shape[0]
X_norm = np.zeros((data.shape[0], data.shape[1]))
for i in range(data.shape[1]):
X_norm[:, i] = (data[:, i] - float(np.mean(X[:, i]))) / float(np.std(X[:, i]))
x = data[:, :3]
y = data[:, 3]
#y = np.transpose([data[:, 3]])
m = len(y)
# x0を追加
X_norm = np.column_stack([np.ones([m,1]), X_norm])
# 正規化(Z-score normalization)
def norm(X):
X_norm = np.zeros((X.shape[0], X.shape[1]))
X_mean = np.zeros((1, X.shape[1]))
X_std = np.zeros((1, X.shape[1]))
for i in range(X.shape[1]):
X_mean[:, i] = np.mean(X[:, i])
X_std[:, i] = np.std(X[:, i])
X_norm[:, i] = (X[:, i] - float(X_mean[:, i])) / float(X_std[:, i])
return X_norm, X_mean, X_std
return X_norm
weight_int = np.zeros((4, 1))
# コスト関数
def cost(x, y, weight):
m = len(y)
J = 0
y_hut = x.dot(weight)
diff = np.power((y_hut - np.transpose([y])), 2)
#diff = np.power((y_hut - y), 2)
J = (1.0 / (2 * m)) * diff.sum(axis=0)
def cost(x, y, w):
"""コスト関数."""
diff = np.power((x.dot(w) - y), 2)
J = diff.sum(axis=0) / (2 * len(y))
return J
# コスト関数(ベクトル化版)
def cost2(x, y, weight):
def gradient_descent(x, y, w, alpha, iter_num):
"""最急降下法."""
m = len(y)
y_shaped = np.transpose([y])
xw = x.dot(weight)
result = np.dot((xw - y_shaped).T, (xw - y_shaped)) / (2*m)
#J = (1.0 / (2 * m)) * result
return result
costs = np.zeros((iter_num, 1))
for i in range(iter_num):
w = w - alpha * (1.0/m) * np.transpose(x).dot(x.dot(w) - y)
costs[i] = cost(x, y, w)
return w, costs
def gradient_descent(x, y, weight, alpha, iter_num):
if __name__ == "__main__":
# データ読み込み
data = np.loadtxt("data/sample_rent1.csv", delimiter=",", skiprows=1)
x = data[:, 1:3] # N行3列の行列
y = data[:, 3:4] # N行1列の行列
# データサイズ
m = len(y)
j_hist = np.zeros((iter_num, 1))
for i in range(iter_num):
weight = weight - alpha * (1.0/m) * np.transpose(x).dot(x.dot(weight) - np.transpose([y]))
j_hist[i] = cost(x, y, weight)
return weight, j_hist
# 正規化し、x0を追加
X_norm = normalize(x)
if __name__ == "__main__":
# 初期値
w_int = np.zeros((3, 1))
# 学習率、学習回数
alpha = 0.01
iter_num = 500
iter_num = 1000
# 最急降下法による重回帰分析
w, costs = gradient_descent(X_norm, y, w_int, alpha, iter_num)
# 訓練データを正規化して、x0の列を追加する
x_padded = np.column_stack([np.ones([m,1]), X_norm])
# 3Dグラフを表示
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(data[:,1], data[:,2], data[:,3], color="#ef1234")
ax.set_xlabel("Size")
ax.set_ylabel("Age")
ax.set_zlabel("Rent")
plt.show()
# 正規化したデータを使用して最急降下法で W を求める
weight, j_hist = gradient_descent(x_padded, y, weight_int, alpha, iter_num)
# 学習毎のコストをグラフ表示
plt.plot(range(costs.size), costs[:, 0], "r")
plt.xlabel("iterations")
plt.ylabel("cost")
plt.grid(True)
plt.show()
print("weight: ", weight)
#print("weight:")
#print(w)
# 学習毎のコストの可視化
plt.plot(range(j_hist.size), j_hist[:, 0], "r")
plt.xlabel("number of iterations")
plt.ylabel("cost J")
plt.grid(True)
plt.show()
# 作成したモデルを使用して別のデータを予測してみる
z = np.array([[60, 10]])
result = normalize(x, z).dot(w)
print("広さ: {}��, 築年数: {}年 ≒ {:0.1f}万円".format(z[0,0], z[0,1], result[0,0]))
}}
#html(</div>)
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