以下述两类模式为样本，用感知器算法求判别函数：ω1:{(0 0 0)t,(1 0 0)t,(1 0 1)t,(1 1 0)t}; ω2:{(0 0 1)t,(0 1 1)t,(0 1 0)t,(1 1 1)t}.且令W(1)=(-1 –2 –2 0)t， C=1.
画出上题所给的二类样本，及所求的判决界面。
用LMSE算法对题1所给的两样本求判别函数 (可取C=1或C=2) 。
用势函数算法对题1所给的两样本求判别函数。
代码1
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189import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
np1 = np.array([[0, 0, 0], [1, 0, 0], [1, 0, 1], [1, 1, 0]])
np2 = np.array([[0, 0, 1], [0, 1, 1], [0, 1, 0], [1, 1, 1]])
new_np1 = np.c_[np1, np.array([1, 1, 1, 1])]
new_np2 = np.c_[np2, np.array([1, 1, 1, 1])]
# print(new_np1)
# print(new_np2)
C = 1
args = [[0, 0, 0, 1]]
def question1():
w = dict()
w[1] = np.array([-1, -2, -2, 0])
change_w = list()
i = 1
error = 1
while error != 0:
error = 0
for row in new_np1:
# 在new_np1中的计算结果必须>0，惩罚为+C*row
# if (w[i] * row).sum() > 0:
if w[i].dot(row) > 0:
w[i + 1] = w[i]
else:
w[i + 1] = w[i] + C * row
error += 1
print("the new w[%s] is :%s" % (i + 1, str(w[i + 1])))
change_w.append(w[i + 1])
i += 1
for row in new_np2:
# 在new_np1中的计算结果必须<0，惩罚为-C*row
# if (w[i] * row).sum() < 0:
if w[i].dot(row) < 0:
w[i + 1] = w[i]
else:
w[i + 1] = w[i] - C * row
error += 1
print("the new w[%s] is :%s" % (i + 1, str(w[i + 1])))
change_w.append(w[i + 1])
i += 1
print(w)
return change_w
def question2(w):
for np_w in w[-1:]:
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(np.array([0, 1, 1, 1]), np.array([0, 0, 0, 1]), np.array([0, 0, 1, 0]), c='red', marker='o')
ax.scatter(np.array([0, 0, 0, 1]), np.array([0, 1, 1, 1]), np.array([1, 1, 0, 1]), c='blue', marker='^')
print(np_w)
# 生成[0，2] 间隔0.5的数列，间隔越小，曲面越平滑
X = np.arange(0, 2, 0.5)
Y = np.arange(0, 2, 0.5)
# 原为F(x)= ax1+bx2+cx3+d,x3作为z放到左边,右边全为负且需要除以参数c
X_arg = np_w[0] / np_w[2]
Y_arg = np_w[1] / np_w[2]
H = np_w[3] / np_w[2]
# 格点矩阵
X, Y = np.meshgrid(X, Y)
Z = - X * X_arg - Y * Y_arg - H
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='rainbow')
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
plt.show()
def question3():
C = 2
lmse_np = np.concatenate((new_np1, -new_np2), axis=0)
lmse_pinv_np = np.linalg.pinv(lmse_np)
b = dict()
print(lmse_pinv_np)
b[1] = np.array([1, 1, 1, 1, 1, 1, 1, 1])
w = dict()
w[1] = lmse_pinv_np @ b[1]
e = dict()
e[1] = lmse_np @ w[1] - b[1]
print(e[1])
error = 1
i = 1
# 向量的模 np.sum(vector**2)**0.5
while error != 0:
if all(e[i] <= 0.01):
error = 0
else:
b[i + 1] = b[i] + C * (e[i] + abs(e[i]))
w[i + 1] = lmse_pinv_np @ b[i + 1]
e[i + 1] = lmse_np @ w[i + 1] - b[i + 1]
# print(e[i])
print("b[%s]:%s" % (i, b[i]))
print("w[%s]:%s" % (i, w[i]))
print("e[%s]:%s" % (i, e[i]))
i += 1
# np.around()四舍五入取近似值
print("判别函数为：" + str(np.around(w[i])))
def f(x, y, z, args=args):
sum = 0
for l in args:
sum += l[3] * np.exp(-((x - l[0]) ** 2 + (y - l[1]) ** 2 + (z - l[2]) ** 2))
return sum
def plot_implicit(fn, bbox=(-1, 1)):
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
''' create a plot of an implicit function
fn ...implicit function (plot where fn==0)
bbox ..the x,y,and z limits of plotted interval'''
xmin, xmax, ymin, ymax, zmin, zmax = bbox * 3
A = np.linspace(xmin, xmax, 100) # resolution of the contour
B = np.linspace(xmin, xmax, 15) # number of slices
A1, A2 = np.meshgrid(A, A) # grid on which the contour is plotted
ax.scatter(np.array([0, 1, 1, 1]), np.array([0, 0, 0, 1]), np.array([0, 0, 1, 0]), c='red', marker='o')
ax.scatter(np.array([0, 0, 0, 1]), np.array([0, 1, 1, 1]), np.array([1, 1, 0, 1]), c='blue', marker='^')
for z in B: # plot contours in the XY plane
X, Y = A1, A2
Z = fn(X, Y, z)
cset = ax.contour(X, Y, Z + z, [z], zdir='z')
# [z] defines the only level to plot for this contour for this value of z
for y in B: # plot contours in the XZ plane
X, Z = A1, A2
Y = fn(X, y, Z)
cset = ax.contour(X, Y + y, Z, [y], zdir='y')
for x in B: # plot contours in the YZ plane
Y, Z = A1, A2
X = fn(x, Y, Z)
cset = ax.contour(X + x, Y, Z, [x], zdir='x')
# must set plot limits because the contour will likely extend
# way beyond the displayed level. Otherwise matplotlib extends the plot limits
# to encompass all values in the contour.
ax.set_zlim3d(zmin, zmax)
ax.set_xlim3d(xmin, xmax)
ax.set_ylim3d(ymin, ymax)
plt.show()
def question4():
error = 1
while error != 0:
error = 0
for f_arg in np1:
if f(f_arg[0], f_arg[1], f_arg[2]) > 0:
continue
else:
args.append([f_arg[0], f_arg[1], f_arg[2], 1])
print("修正：" + str(args))
error = 1
for f_arg in np2:
if f(f_arg[0], f_arg[1], f_arg[2]) < 0:
continue
else:
args.append([f_arg[0], f_arg[1], f_arg[2], -1])
print("修正：" + str(args))
error = 1
plot_implicit(f, bbox=(-1, 1))
if __name__ == '__main__':
list_for_q2 = question1()
question2(list_for_q2)
question3()
question4()