所以我能够解决这个问题。问题是：
- 我正在绘制数据的空间。我之前的网格网格范围是 -3 到 3，增量为 0.1。我更改了它以使用我的训练数据范围限制。 （x_最小值、x_最大值、y_最小值、y_最大值）
- 在绘制决策边界时，我还对训练数据进行了标准化。我删除了它并绘制了原始数据点。 （不确定这是否导致了问题）
- 我使用的 z 值是类值。我将其更改为使用从 sigmoid 函数获得的概率值，以便我可以使用级别参数。
下面是工作代码：
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(style="white")
def map_features(x, degree):
x_old = x.copy()
x = pd.DataFrame({"intercept" : [1]*x.shape[0]})
column_index = 1
for i in range(1, degree+1):
for j in range(0, i+1):
x.insert(column_index, str(x_old.columns[1]) + "^" + str(i-j) + str(x_old.columns[2]) + "^" + str(j), np.multiply(x_old.iloc[:,1]**(i-j), x_old.iloc[:,2]**(j)))
column_index+=1
return x
def normalize_features(x):
global mean_values
global std_values
for column_name in x.columns[1:]:
mean = x[column_name].mean()
std = x[column_name].std()
x[column_name] = (x[column_name] - mean) / std
mean_values[column_name] = mean
std_values[column_name] = std
return x
def sigmoid(z):
return 1/(1+np.exp(-z))
def cost(x, y, theta):
m = x.shape[0]
h_theta = pd.DataFrame(sigmoid(np.dot(x,theta)))
cost = 1/m * ((-np.multiply(y,h_theta.apply(np.log)) - np.multiply(1-y, (1-h_theta).apply(np.log))).sum())
return np.asscalar(cost)
def gradient_descent(x, y, theta):
global cost_values
m = x.shape[0]
iterations = 1000
alpha = 0.03
cost_values = pd.DataFrame({'iteration' : [0], 'cost' : [cost(x,y,theta)]})
for iteration in range(0,iterations):
theta_old = theta.copy()
theta.iloc[0,0] = theta.iloc[0,0] - (alpha/m) * np.asscalar((sigmoid(np.dot(x,theta_old)) - y).sum())
for i in range(1,theta.shape[0]):
theta.iloc[i,0] = theta.iloc[i,0] - (alpha/m) * np.asscalar(np.multiply((sigmoid(np.dot(x,theta_old)) - y), pd.DataFrame(x.iloc[:,i])).sum())
c = cost(x,y,theta)
cost_values = cost_values.append({"iteration" : iteration, "cost" : c}, ignore_index=True)
def predict(x):
global theta
probability = np.asscalar(sigmoid(np.dot(x.T,theta)))
return probability
if(probability >= 0.5):
return 1
else:
return 0
### Read train data
train_data = pd.read_csv("ex2data1.csv", names = ["exam1", "exam2", "admit"])
### Create input data
x = train_data.loc[:,"exam1":"exam2"]
### Add intercept column
x.insert(0, "intercept", 1)
mean_values = {}
std_values = {}
mapping_degree = 2
x = normalize_features(x) #normalize features
x = map_features(x, mapping_degree) #map polynomial features
y = pd.DataFrame(train_data.loc[:,"admit"])
theta = pd.DataFrame({"theta" : [0] * len(x.columns)})
### Test cost of initial theta
# print(cost(x,y,theta))
### Perform Gradient Descent
gradient_descent(x, y, theta)
# print(theta)
# print("Cost: " + str(cost(x,y,theta)))
### Plot iteration vs Cost
plt.scatter(cost_values["iteration"], cost_values["cost"])
plt.show()
### Predict an example
student = pd.DataFrame({"exam1": [52], "exam2":[63]})
student.insert(0, "intercept", 1)
#normalizing
for column_name in student.columns[1:]:
student[column_name] = (student[column_name] - mean_values[column_name]) / std_values[column_name]
student = map_features(student, mapping_degree)
print("probability of admission: " + str(predict(student.T)))
### Calculate Accuracy
acc = 0
for i in range(0,x.shape[0]):
p = predict(pd.DataFrame(x.iloc[i,:]))
actual = y.iloc[i,0]
if(p >= 0.5):
p = 1
else:
p = 0
if(p == actual):
acc+=1
print("Accuracy : " + str((acc/x.shape[0]) * 100))
### Plot decision boundary
x_min = train_data["exam1"].min()
x_max = train_data["exam1"].max()
y_min = train_data["exam2"].min()
y_max = train_data["exam2"].max()
x_grid, y_grid = np.meshgrid(np.arange(x_min, x_max, 1), np.arange(y_min, y_max, 1))
xx = pd.DataFrame(x_grid.ravel(), columns=["exam1"])
yy = pd.DataFrame(y_grid.ravel(), columns=["exam2"])
z = pd.DataFrame({"intercept" : [1]*xx.shape[0]})
z["exam1"] = xx
z["exam2"] = yy
z = normalize_features(z)
z = map_features(z,mapping_degree)
p = z.apply(lambda row: predict(pd.DataFrame(row)), axis=1)
p = np.array(p.values)
p = p.reshape(x_grid.shape)
plt.scatter(train_data[train_data["admit"] == 0]["exam1"], train_data[train_data["admit"] == 0]["exam2"],marker="o")
plt.scatter(train_data[train_data["admit"] == 1]["exam1"], train_data[train_data["admit"] == 1]["exam2"],marker="x")
plt.contour(x_grid, y_grid, p, levels = [0.5]) #displays only decision boundary
# plt.contour(x_grid, y_grid, p, 50, cmap="RdBu") #display a colored contour
# plt.colorbar()
plt.show()
以下是我获得的与我的发现相对应的边界
This blog https://jakevdp.github.io/PythonDataScienceHandbook/04.04-density-and-contour-plots.html解释轮廓函数可能会有所帮助。
