From 824024810c9d9bdd0e5719e6ff360705ef6f33a8 Mon Sep 17 00:00:00 2001
From: benjas <909336740@qq.com>
Date: Wed, 24 Feb 2021 14:55:16 +0800
Subject: [PATCH] Add. MultivariateLinearRegression

---
 .../MultivariateLinearRegression.py           | 131 ++++++++++++++++++
 .../UnivariateLinearRegression.py             |  15 ++
 2 files changed, 146 insertions(+)
 create mode 100644 机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/MultivariateLinearRegression.py

diff --git a/机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/MultivariateLinearRegression.py b/机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/MultivariateLinearRegression.py
new file mode 100644
index 0000000..1a0f16b
--- /dev/null
+++ b/机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/MultivariateLinearRegression.py
@@ -0,0 +1,131 @@
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+import plotly
+import plotly.graph_objs as go
+
+from linear_regression import LinearRegression
+plotly.offline.init_notebook_mode()  # 在线显示图标，更多功能
+
+data = pd.read_csv('../data/world-happiness-report-2017.csv')
+
+train_data = data.sample(frac=0.8)
+test_data = data.drop(train_data.index)
+
+# 与单特征模型相比，只是多了一个特征列
+input_param_name_1 = 'Economy..GDP.per.Capita.'
+input_param_name_2 = 'Freedom'
+output_param_name = 'Happiness.Score'
+
+x_train = train_data[[input_param_name_1, input_param_name_2]].values
+y_train = train_data[[output_param_name]].values
+
+x_test = test_data[[input_param_name_1, input_param_name_2]].values
+y_test = test_data[[output_param_name]].values
+
+# Configure the plot with training dataset.
+plot_training_trace = go.Scatter3d(
+    x=x_train[:, 0].flatten(),
+    y=x_train[:, 1].flatten(),
+    z=y_train.flatten(),
+    name='Training Set',
+    mode='markers',
+    marker={
+        'size': 10,
+        'opacity': 1,
+        'line': {
+            'color': 'rgb(255, 255, 255)',
+            'width': 1
+        },
+    }
+)
+
+plot_test_trace = go.Scatter3d(
+    x=x_test[:, 0].flatten(),
+    y=x_test[:, 1].flatten(),
+    z=y_test.flatten(),
+    name='Test Set',
+    mode='markers',
+    marker={
+        'size': 10,
+        'opacity': 1,
+        'line': {
+            'color': 'rgb(255, 255, 255)',
+            'width': 1
+        },
+    }
+)
+
+plot_layout = go.Layout(
+    title='Date Sets',
+    scene={
+        'xaxis': {'title': input_param_name_1},
+        'yaxis': {'title': input_param_name_2},
+        'zaxis': {'title': output_param_name}
+    },
+    margin={'l': 0, 'r': 0, 'b': 0, 't': 0}
+)
+
+plot_data = [plot_training_trace, plot_test_trace]
+
+plot_figure = go.Figure(data=plot_data, layout=plot_layout)
+
+plotly.offline.plot(plot_figure)
+
+num_iterations = 500
+learning_rate = 0.01
+polynomial_degree = 0
+sinusoid_degree = 0
+
+linear_regression = LinearRegression(x_train, y_train, polynomial_degree, sinusoid_degree)
+
+(theta, cost_history) = linear_regression.train(learning_rate, num_iterations)
+
+print('开始时的损失：', cost_history[0])
+print('训练后的损失：', cost_history[-1])
+
+plt.plot(range(num_iterations), cost_history)
+plt.xlabel('Iterations')
+plt.ylabel('Cost')
+plt.title('Gradient Descent')
+plt.show()
+
+predictions_num = 10
+
+x_min = x_train[:, 0].min()
+x_max = x_train[:, 0].max()
+
+y_min = x_train[:, 1].min()
+y_max = x_train[:, 1].max()
+
+x_axis = np.linspace(x_min, x_max, predictions_num)
+y_axis = np.linspace(y_min, y_max, predictions_num)
+
+x_predictions = np.zeros((predictions_num * predictions_num, 1))
+y_predictions = np.zeros((predictions_num * predictions_num, 1))
+
+x_y_index = 0
+for x_index, x_value in enumerate(x_axis):
+    for y_index, y_value in enumerate(y_axis):
+        x_predictions[x_y_index] = x_value
+        y_predictions[x_y_index] = y_value
+        x_y_index += 1
+
+z_predictions = linear_regression.predict(np.hstack((x_predictions, y_predictions)))
+
+plot_predictions_trace = go.Scatter3d(
+    x=x_predictions.flatten(),
+    y=y_predictions.flatten(),
+    z=z_predictions.flatten(),
+    name='Prediction Plane',
+    mode='markers',
+    marker={
+        'size': 1,
+    },
+    opacity=0.8,
+    surfaceaxis=2,
+)
+
+plot_data = [plot_training_trace, plot_test_trace, plot_predictions_trace]
+plot_figure = go.Figure(data=plot_data, layout=plot_layout)
+plotly.offline.plot(plot_figure)
diff --git a/机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/UnivariateLinearRegression.py b/机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/UnivariateLinearRegression.py
index 6aa6db2..8a42c5c 100644
--- a/机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/UnivariateLinearRegression.py
+++ b/机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/UnivariateLinearRegression.py
@@ -41,3 +41,18 @@ plt.xlabel('Iteration')
 plt.ylabel('Cost')
 plt.title('GD')
 plt.show()
+
+# 测试线性回归模型
+predictions_num = 100  # 预测100个
+# 拿最大和最小值画一条线
+x_predictions = np.linspace(x_train.min(), x_train.max(), predictions_num).reshape(predictions_num, 1)
+y_predictions = linear_regression.predict(x_predictions)
+
+plt.scatter(x_train, y_train, label='Train data')
+plt.scatter(x_test, y_test, label='Test data')
+plt.plot(x_predictions, y_predictions, 'r', label='Prediction')
+plt.xlabel(input_param_name)
+plt.ylabel(output_param_name)
+plt.title('Happy')
+plt.legend()
+plt.show()