如何绘制支持向量回归的支持向量？
How to plot support vectors for support vector regression?
我正在尝试解决硬边距支持向量回归并绘制数据集的超平面和支持向量。
如您所知，硬边距可通过以下假设求解：
我解决了这个问题，但是当我想绘制决策边界和支持向量时，我遇到了以下问题。所有点应位于两个决策边界之间，支持向量应绘制在决策边界上。你能帮我找出问题吗？
完整代码如下：
import pandas as pd
import numpy as np
from pandas import DataFrame
from sklearn import metrics
Data = pd.read_csv("Data.txt",delimiter="\t")
X=Data['waterlevel(x)'].values
y=Data['Area(y)'].values
# Plot Data
import matplotlib.pyplot as plt
fig,ax = plt.subplots(1, 1,constrained_layout=True,figsize=(8, 4))
ax.plot(X, y,'k.')
ax.set_title('Urmia lake Area versus Level')
ax.set_xlabel('Water level (M)',fontsize=15)
ax.set_ylabel('Area (km^2)',fontsize=15)
#plt.axis([0, 25, 0, 25])
plt.grid(True)
plt.show()
# find max and min values of predictor variables (here X) to use it to specify initial values of w and b
max_feature_value=np.amax(X)
min_feature_value=np.amin(X)
w_optimum = max_feature_value*0.5
w = [w_optimum for i in range(1)] # w shoulb be a vector with dimension of the independent features (here:1)
wt_b=w
b_sum=0
for i in range(X.shape[0]):
b_sum+=y[i]-np.dot(wt_b,X[i])
b_ini=b_sum/len(X)
b_step_size_lower = 0.9
b_step_size_upper = 0.2
b_multiple = 500 # step size for b
b_range = np.arange((b_ini*b_step_size_lower), -b_ini*b_step_size_upper, b_multiple)
print(len(b_range))
# Estimate w and b using stochastic gradient descent and trial and error
l_rate=0.1
n_epoch = 250
epsilon=150 # acceptable error
length_Wvector_list=[]
for i in range (len(b_range)):
correctly_regressed = True
for j in range(X.shape[0]):
print(i,j,wt_b,b_range[i])
if (y[j]-(np.dot(wt_b,X[j])+b_range[i]) > epsilon) or (y[j]-(np.dot(wt_b,X[j])+b_range[i]) < -epsilon)==True:
correctly_regressed = False
wt_b = np.asarray(wt_b) - l_rate
if correctly_regressed==True:
length_Wvector_list.append([wt_b[0],wt_b,b_range[i]])
if wt_b[0] < 0:
wt_b=w
break
norms = sorted([n for n in length_Wvector_list])
wt_b=norms[0][1]
b=norms[0][2]
# Predict using the optimized values of w and b
y_predict=[]
for i in range (X.shape[0]):
y_hat=np.dot(wt_b,X[i])+b
y_predict.append(y_hat)
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y, y_predict)))
print('Coefficient of determination (R2):', metrics.r2_score(y, y_predict))
# plot
fig,ax = plt.subplots(1, 1,figsize=(8, 5.2))
ax.scatter(y, y_predict, cmap='K', edgecolor='b',linewidth='0.5',alpha=1, label='testing points',marker='o', s=12)
ax.set_xlabel('Observed Area(km $^{2}$)',fontsize=14)
ax.set_ylabel('Simulated Area(km $^{2}$)',fontsize=14)
# find support vectors
positive_instances=[]
negative_instances=[]
for i in range(X.shape[0]):
y_pre=(np.dot(wt_b,X[i]))+b
if y[i]-y_pre<=epsilon:
positive_instances.append([y[i]-y_pre,[X[i],y[i]]])
elif y[i]-y_pre>=-epsilon:
negative_instances.append([y[i]-y_pre,[X[i],y[i]]])
len(positive_instances)+len(negative_instances)
sort_positive=sorted([n for n in positive_instances])
sort_negative=sorted([n for n in negative_instances])
positive_support_vector=sort_positive[0][1]
negative_support_vector=sort_negative[-1][1]
model_support_vectors=np.stack((positive_support_vector,negative_support_vector),axis=-1)
# visualize the data-set
colors = {1:'r',-1:'b'}
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
plt.scatter(X,y,marker='o',c=y)
# plot support vectors
ax.scatter(model_support_vectors[0, :],model_support_vectors[1, :],s=200, linewidth=1,facecolors='none', edgecolors='b')
# hyperplane = x.w+b
# 0 = x.w+b
# psv = epsilon
# nsv = -epsilon
# dec = 0
def hyperplane_value(x,w,b,e):
return (np.dot(w,x)+b+e)
datarange = (min_feature_value*1.,max_feature_value*1.)
hyp_x_min = datarange[0]
hyp_x_max = datarange[1]
# (w.x+b) = epsilon
# positive support vector hyperplane
psv1 = hyperplane_value(hyp_x_min, wt_b, b, epsilon)
psv2 = hyperplane_value(hyp_x_max, wt_b, b, epsilon)
ax.plot([hyp_x_min,hyp_x_max],[psv1,psv2], 'k')
# (w.x+b) = -epsilon
# negative support vector hyperplane
nsv1 = hyperplane_value(hyp_x_min, wt_b, b, -epsilon)
nsv2 = hyperplane_value(hyp_x_max, wt_b, b, -epsilon)
ax.plot([hyp_x_min,hyp_x_max],[nsv1,nsv2], 'k')
# (w.x+b) = 0
# positive support vector hyperplane
db1 = hyperplane_value(hyp_x_min, wt_b, b, 0)
db2 = hyperplane_value(hyp_x_max, wt_b, b, 0)
ax.plot([hyp_x_min,hyp_x_max],[db1,db2], 'y--')
#plt.axis([-5,10,-12,-1])
plt.show()
我改进了程序，问题解决了。如您所见，决策边界和支持向量绘制在正确的位置。
完整代码如下：
import pandas as pd
import numpy as np
from pandas import DataFrame
from sklearn import metrics
Data = pd.read_csv("Data.txt",delimiter="\t")
X=Data['waterlevel(x)'].values
y=Data['Area(y)'].values
# Plot Data
import matplotlib.pyplot as plt
fig,ax = plt.subplots(1, 1,constrained_layout=True,figsize=(8, 4))
ax.plot(X, y,'k.')
ax.set_title('Urmia lake Area versus Level')
ax.set_xlabel('Water level (M)',fontsize=15)
ax.set_ylabel('Area (km^2)',fontsize=15)
#plt.axis([0, 25, 0, 25])
plt.grid(True)
plt.show()
# find max and min values of predictor variables (here X) to use it to specify initial values of w and b
max_feature_value=np.amax(X)
min_feature_value=np.amin(X)
w_optimum = max_feature_value*0.5
w = [w_optimum for i in range(1)] # w shoulb be a vector with dimension of the independent features (here:1)
wt_b=w
b_sum=0
for i in range(X.shape[0]):
b_sum+=y[i]-np.dot(wt_b,X[i])
b_ini=b_sum/len(X)
b_step_size_lower = 0.9
b_step_size_upper = 0.1
b_multiple = 500 # step size for b
b_range = np.arange((b_ini*b_step_size_lower), -b_ini*b_step_size_upper, b_multiple)
print(len(b_range))
# Estimate w and b using stochastic gradient descent and trial and error
l_rate=0.1
n_epoch = 250
epsilon=500 # acceptable error
length_Wvector_list=[]
for i in range (len(b_range)):
print(i)
optimized = False
while not optimized:
correctly_regressed = True
for j in range(X.shape[0]):
# every data point should be satisfies the constraint yi-(np.dot(w_t,xi)+b) <=epsilon or yi-(np.dot(w_t,xi)+b)>=-epsilon
if (y[j]-(np.dot(wt_b,X[j])+b_range[i]) > epsilon) or (y[j]-(np.dot(wt_b,X[j])+b_range[i]) < -epsilon)==True:
correctly_regressed = False
wt_b = np.asarray(wt_b) - l_rate
if correctly_regressed==True:
length_Wvector_list.append([wt_b[0],wt_b,b_range[i]]) #store w, b for minimum magnitude , magnitude or length of a vector w_t is called the norm
optimized = True
if wt_b[0] < 0:
optimized = True
wt_b_temp=wt_b
wt_b=w
norms = sorted([n for n in length_Wvector_list])
wt_b=norms[0][1]
b=norms[0][2]
# Predict using the optimized values of w and b
y_predict=[]
for i in range (X.shape[0]):
y_hat=np.dot(wt_b,X[i])+b
y_predict.append(y_hat)
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y, y_predict)))
print('Coefficient of determination (R2):', metrics.r2_score(y, y_predict))
# plot
fig,ax = plt.subplots(1, 1,figsize=(8, 5.2))
ax.scatter(y, y_predict, cmap='K', edgecolor='b',linewidth='0.5',alpha=1, label='testing points',marker='o', s=12)
ax.set_xlabel('Observed Area(km $^{2}$)',fontsize=14)
ax.set_ylabel('Simulated Area(km $^{2}$)',fontsize=14)
ax.set_xlim([min(y)-100, max(y)+100])
ax.set_ylim([min(y)-100, max(y)+100])
# find support vectors
positive_instances=[]
negative_instances=[]
for i in range(X.shape[0]):
y_pre=(np.dot(wt_b,X[i]))+b
if ((y[i]-y_pre>0) and (y[i]-y_pre<=epsilon))==True:
positive_instances.append([y[i]-y_pre,[X[i],y[i]]])
elif ((y[i]-y_pre<0) and (y[i]-y_pre>=-epsilon))==True:
negative_instances.append([y[i]-y_pre,[X[i],y[i]]])
len(positive_instances)+len(negative_instances)
sort_positive=sorted([n for n in positive_instances])
sort_negative=sorted([n for n in negative_instances])
positive_support_vector=sort_positive[-1][1]
negative_support_vector=sort_negative[0][1]
model_support_vectors=np.stack((positive_support_vector,negative_support_vector),axis=-1)
# visualize the data-set
colors = {1:'r',-1:'b'}
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
plt.scatter(X,y,marker='o',c=y)
# plot support vectors
ax.scatter(model_support_vectors[0, :],model_support_vectors[1, :],s=200, linewidth=1,facecolors='none', edgecolors='b')
# hyperplane = x.w+b
# 0 = x.w+b
# psv = epsilon
# nsv = -epsilon
# dec = 0
def hyperplane_value(x,w,b,e):
return (np.dot(w,x)+b+e)
datarange = (min_feature_value*1.,max_feature_value*1.)
hyp_x_min = datarange[0]
hyp_x_max = datarange[1]
# (w.x+b) = epsilon
# positive support vector hyperplane
psv1 = hyperplane_value(hyp_x_min, wt_b, b, epsilon)
psv2 = hyperplane_value(hyp_x_max, wt_b, b, epsilon)
ax.plot([hyp_x_min,hyp_x_max],[psv1,psv2], 'k')
# (w.x+b) = -epsilon
# negative support vector hyperplane
nsv1 = hyperplane_value(hyp_x_min, wt_b, b, -epsilon)
nsv2 = hyperplane_value(hyp_x_max, wt_b, b, -epsilon)
ax.plot([hyp_x_min,hyp_x_max],[nsv1,nsv2], 'k')
# (w.x+b) = 0
# positive support vector hyperplane
db1 = hyperplane_value(hyp_x_min, wt_b, b, 0)
db2 = hyperplane_value(hyp_x_max, wt_b, b, 0)
ax.plot([hyp_x_min,hyp_x_max],[db1,db2], 'y--')
#plt.axis([-5,10,-12,-1])
plt.show()
我正在尝试解决硬边距支持向量回归并绘制数据集的超平面和支持向量。
如您所知，硬边距可通过以下假设求解：
我解决了这个问题，但是当我想绘制决策边界和支持向量时，我遇到了以下问题。所有点应位于两个决策边界之间，支持向量应绘制在决策边界上。你能帮我找出问题吗？
完整代码如下：
import pandas as pd
import numpy as np
from pandas import DataFrame
from sklearn import metrics
Data = pd.read_csv("Data.txt",delimiter="\t")
X=Data['waterlevel(x)'].values
y=Data['Area(y)'].values
# Plot Data
import matplotlib.pyplot as plt
fig,ax = plt.subplots(1, 1,constrained_layout=True,figsize=(8, 4))
ax.plot(X, y,'k.')
ax.set_title('Urmia lake Area versus Level')
ax.set_xlabel('Water level (M)',fontsize=15)
ax.set_ylabel('Area (km^2)',fontsize=15)
#plt.axis([0, 25, 0, 25])
plt.grid(True)
plt.show()
# find max and min values of predictor variables (here X) to use it to specify initial values of w and b
max_feature_value=np.amax(X)
min_feature_value=np.amin(X)
w_optimum = max_feature_value*0.5
w = [w_optimum for i in range(1)] # w shoulb be a vector with dimension of the independent features (here:1)
wt_b=w
b_sum=0
for i in range(X.shape[0]):
b_sum+=y[i]-np.dot(wt_b,X[i])
b_ini=b_sum/len(X)
b_step_size_lower = 0.9
b_step_size_upper = 0.2
b_multiple = 500 # step size for b
b_range = np.arange((b_ini*b_step_size_lower), -b_ini*b_step_size_upper, b_multiple)
print(len(b_range))
# Estimate w and b using stochastic gradient descent and trial and error
l_rate=0.1
n_epoch = 250
epsilon=150 # acceptable error
length_Wvector_list=[]
for i in range (len(b_range)):
correctly_regressed = True
for j in range(X.shape[0]):
print(i,j,wt_b,b_range[i])
if (y[j]-(np.dot(wt_b,X[j])+b_range[i]) > epsilon) or (y[j]-(np.dot(wt_b,X[j])+b_range[i]) < -epsilon)==True:
correctly_regressed = False
wt_b = np.asarray(wt_b) - l_rate
if correctly_regressed==True:
length_Wvector_list.append([wt_b[0],wt_b,b_range[i]])
if wt_b[0] < 0:
wt_b=w
break
norms = sorted([n for n in length_Wvector_list])
wt_b=norms[0][1]
b=norms[0][2]
# Predict using the optimized values of w and b
y_predict=[]
for i in range (X.shape[0]):
y_hat=np.dot(wt_b,X[i])+b
y_predict.append(y_hat)
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y, y_predict)))
print('Coefficient of determination (R2):', metrics.r2_score(y, y_predict))
# plot
fig,ax = plt.subplots(1, 1,figsize=(8, 5.2))
ax.scatter(y, y_predict, cmap='K', edgecolor='b',linewidth='0.5',alpha=1, label='testing points',marker='o', s=12)
ax.set_xlabel('Observed Area(km $^{2}$)',fontsize=14)
ax.set_ylabel('Simulated Area(km $^{2}$)',fontsize=14)
# find support vectors
positive_instances=[]
negative_instances=[]
for i in range(X.shape[0]):
y_pre=(np.dot(wt_b,X[i]))+b
if y[i]-y_pre<=epsilon:
positive_instances.append([y[i]-y_pre,[X[i],y[i]]])
elif y[i]-y_pre>=-epsilon:
negative_instances.append([y[i]-y_pre,[X[i],y[i]]])
len(positive_instances)+len(negative_instances)
sort_positive=sorted([n for n in positive_instances])
sort_negative=sorted([n for n in negative_instances])
positive_support_vector=sort_positive[0][1]
negative_support_vector=sort_negative[-1][1]
model_support_vectors=np.stack((positive_support_vector,negative_support_vector),axis=-1)
# visualize the data-set
colors = {1:'r',-1:'b'}
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
plt.scatter(X,y,marker='o',c=y)
# plot support vectors
ax.scatter(model_support_vectors[0, :],model_support_vectors[1, :],s=200, linewidth=1,facecolors='none', edgecolors='b')
# hyperplane = x.w+b
# 0 = x.w+b
# psv = epsilon
# nsv = -epsilon
# dec = 0
def hyperplane_value(x,w,b,e):
return (np.dot(w,x)+b+e)
datarange = (min_feature_value*1.,max_feature_value*1.)
hyp_x_min = datarange[0]
hyp_x_max = datarange[1]
# (w.x+b) = epsilon
# positive support vector hyperplane
psv1 = hyperplane_value(hyp_x_min, wt_b, b, epsilon)
psv2 = hyperplane_value(hyp_x_max, wt_b, b, epsilon)
ax.plot([hyp_x_min,hyp_x_max],[psv1,psv2], 'k')
# (w.x+b) = -epsilon
# negative support vector hyperplane
nsv1 = hyperplane_value(hyp_x_min, wt_b, b, -epsilon)
nsv2 = hyperplane_value(hyp_x_max, wt_b, b, -epsilon)
ax.plot([hyp_x_min,hyp_x_max],[nsv1,nsv2], 'k')
# (w.x+b) = 0
# positive support vector hyperplane
db1 = hyperplane_value(hyp_x_min, wt_b, b, 0)
db2 = hyperplane_value(hyp_x_max, wt_b, b, 0)
ax.plot([hyp_x_min,hyp_x_max],[db1,db2], 'y--')
#plt.axis([-5,10,-12,-1])
plt.show()
我改进了程序，问题解决了。如您所见，决策边界和支持向量绘制在正确的位置。
完整代码如下：
import pandas as pd
import numpy as np
from pandas import DataFrame
from sklearn import metrics
Data = pd.read_csv("Data.txt",delimiter="\t")
X=Data['waterlevel(x)'].values
y=Data['Area(y)'].values
# Plot Data
import matplotlib.pyplot as plt
fig,ax = plt.subplots(1, 1,constrained_layout=True,figsize=(8, 4))
ax.plot(X, y,'k.')
ax.set_title('Urmia lake Area versus Level')
ax.set_xlabel('Water level (M)',fontsize=15)
ax.set_ylabel('Area (km^2)',fontsize=15)
#plt.axis([0, 25, 0, 25])
plt.grid(True)
plt.show()
# find max and min values of predictor variables (here X) to use it to specify initial values of w and b
max_feature_value=np.amax(X)
min_feature_value=np.amin(X)
w_optimum = max_feature_value*0.5
w = [w_optimum for i in range(1)] # w shoulb be a vector with dimension of the independent features (here:1)
wt_b=w
b_sum=0
for i in range(X.shape[0]):
b_sum+=y[i]-np.dot(wt_b,X[i])
b_ini=b_sum/len(X)
b_step_size_lower = 0.9
b_step_size_upper = 0.1
b_multiple = 500 # step size for b
b_range = np.arange((b_ini*b_step_size_lower), -b_ini*b_step_size_upper, b_multiple)
print(len(b_range))
# Estimate w and b using stochastic gradient descent and trial and error
l_rate=0.1
n_epoch = 250
epsilon=500 # acceptable error
length_Wvector_list=[]
for i in range (len(b_range)):
print(i)
optimized = False
while not optimized:
correctly_regressed = True
for j in range(X.shape[0]):
# every data point should be satisfies the constraint yi-(np.dot(w_t,xi)+b) <=epsilon or yi-(np.dot(w_t,xi)+b)>=-epsilon
if (y[j]-(np.dot(wt_b,X[j])+b_range[i]) > epsilon) or (y[j]-(np.dot(wt_b,X[j])+b_range[i]) < -epsilon)==True:
correctly_regressed = False
wt_b = np.asarray(wt_b) - l_rate
if correctly_regressed==True:
length_Wvector_list.append([wt_b[0],wt_b,b_range[i]]) #store w, b for minimum magnitude , magnitude or length of a vector w_t is called the norm
optimized = True
if wt_b[0] < 0:
optimized = True
wt_b_temp=wt_b
wt_b=w
norms = sorted([n for n in length_Wvector_list])
wt_b=norms[0][1]
b=norms[0][2]
# Predict using the optimized values of w and b
y_predict=[]
for i in range (X.shape[0]):
y_hat=np.dot(wt_b,X[i])+b
y_predict.append(y_hat)
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y, y_predict)))
print('Coefficient of determination (R2):', metrics.r2_score(y, y_predict))
# plot
fig,ax = plt.subplots(1, 1,figsize=(8, 5.2))
ax.scatter(y, y_predict, cmap='K', edgecolor='b',linewidth='0.5',alpha=1, label='testing points',marker='o', s=12)
ax.set_xlabel('Observed Area(km $^{2}$)',fontsize=14)
ax.set_ylabel('Simulated Area(km $^{2}$)',fontsize=14)
ax.set_xlim([min(y)-100, max(y)+100])
ax.set_ylim([min(y)-100, max(y)+100])
# find support vectors
positive_instances=[]
negative_instances=[]
for i in range(X.shape[0]):
y_pre=(np.dot(wt_b,X[i]))+b
if ((y[i]-y_pre>0) and (y[i]-y_pre<=epsilon))==True:
positive_instances.append([y[i]-y_pre,[X[i],y[i]]])
elif ((y[i]-y_pre<0) and (y[i]-y_pre>=-epsilon))==True:
negative_instances.append([y[i]-y_pre,[X[i],y[i]]])
len(positive_instances)+len(negative_instances)
sort_positive=sorted([n for n in positive_instances])
sort_negative=sorted([n for n in negative_instances])
positive_support_vector=sort_positive[-1][1]
negative_support_vector=sort_negative[0][1]
model_support_vectors=np.stack((positive_support_vector,negative_support_vector),axis=-1)
# visualize the data-set
colors = {1:'r',-1:'b'}
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
plt.scatter(X,y,marker='o',c=y)
# plot support vectors
ax.scatter(model_support_vectors[0, :],model_support_vectors[1, :],s=200, linewidth=1,facecolors='none', edgecolors='b')
# hyperplane = x.w+b
# 0 = x.w+b
# psv = epsilon
# nsv = -epsilon
# dec = 0
def hyperplane_value(x,w,b,e):
return (np.dot(w,x)+b+e)
datarange = (min_feature_value*1.,max_feature_value*1.)
hyp_x_min = datarange[0]
hyp_x_max = datarange[1]
# (w.x+b) = epsilon
# positive support vector hyperplane
psv1 = hyperplane_value(hyp_x_min, wt_b, b, epsilon)
psv2 = hyperplane_value(hyp_x_max, wt_b, b, epsilon)
ax.plot([hyp_x_min,hyp_x_max],[psv1,psv2], 'k')
# (w.x+b) = -epsilon
# negative support vector hyperplane
nsv1 = hyperplane_value(hyp_x_min, wt_b, b, -epsilon)
nsv2 = hyperplane_value(hyp_x_max, wt_b, b, -epsilon)
ax.plot([hyp_x_min,hyp_x_max],[nsv1,nsv2], 'k')
# (w.x+b) = 0
# positive support vector hyperplane
db1 = hyperplane_value(hyp_x_min, wt_b, b, 0)
db2 = hyperplane_value(hyp_x_max, wt_b, b, 0)
ax.plot([hyp_x_min,hyp_x_max],[db1,db2], 'y--')
#plt.axis([-5,10,-12,-1])
plt.show()