|
|
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'
|
|
|
# 双特征的loss为：0.08517538069974877
|
|
|
x_train = train_data[[input_param_name_1, input_param_name_2]].values
|
|
|
# 全特征的loss为：0.0019415807477718364
|
|
|
# feat_list = list(train_data.columns.drop(['Happiness.Score','Country']))
|
|
|
# x_train = train_data[feat_list].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)
|
