我正在尝试使用平均感知器模型拟合二进制分类。
我按照多美的书的指示逐行
（http://ciml.info/dl/v0_99/ciml-v0_99-ch04.pdf）（平均感知器的第53页）。
这是我的实现：
def aperceptron_sgd(X, Y,epochs):
# initialize weights
w = u = np.zeros(X.shape[1] )
b = beta = 0
# counters
final_iter = epochs
c = 1
converged = False
# main average perceptron algorithm
for epoch in range(epochs):
# initialize misclassified
misclassified = 0
# go through all training examples
for x,y in zip(X,Y):
h = np.dot(x, w)*y
if h <= 0:
w = w + y*x
b = b + y
u = u+ y*c*x
beta = beta + y*c
misclassified += 1
# update counter regardless of good or bad classification
c = c + 1
# break loop if w converges
if misclassified == 0:
final_iter = epoch
converged = True
print("Averaged Perceptron converged after: {} iterations".format(final_iter))
break
if converged == False:
print("Averaged Perceptron DID NOT converged.")
# prints
# print("final_iter = {}".format(final_iter))
# print("b, beta, c , (b-beta/c)= {} {} {} {}".format(b, beta, c, (b-beta/c)))
# print("w, u, (w-u/c) {} {} {}".format(w, u, (w-u/c)) )
# return w and final_iter
w = w - u/c
b = np.array([b- beta/c])
w = np.append(b, w)
return w, final_iter
但是，当我用数据测试时，它给出的预测不准确。
数据在这里给出：
1.36 3.57 1
1.78 -0.79 -1
-0.88 0.96 1
1.64 -0.63 -1
-0.98 1.34 1
1.50 0.33 -1
0.15 1.48 1
1.39 -1.71 -1
0.08 2.24 1
1.87 -0.35 -1
0.25 2.52 1
1.68 -0.56 -1
0.23 2.75 1
2.05 -0.85 -1
-0.53 1.40 1
1.92 -0.60 -1
0.12 2.77 1
1.70 -0.40 -1
0.72 2.01 1
0.44 -0.51 -1
-1.84 1.13 1
1.46 1.65 -1
0.48 1.94 1
1.57 -0.22 -1
-0.45 2.14 1
2.71 -0.19 -1
-1.04 1.82 1
2.56 0.49 -1
0.26 2.29 1
1.51 -1.11 -1
0.27 1.36 1
2.99 0.84 -1
0.37 2.89 1
2.81 0.19 -1
-0.48 1.23 1
2.12 -0.26 -1
-0.46 0.47 1
0.77 -0.65 -1
1.52 2.75 1
4.01 1.79 -1
0.67 2.24 1
1.75 0.52 -1
0.19 1.80 1
2.61 0.44 -1
-0.54 0.36 1
0.67 -0.59 -1
0.71 2.94 1
1.82 -0.99 -1
0.88 3.82 1
0.78 -1.33 -1
1.17 2.82 1
2.17 0.46 -1
1.05 2.52 1
0.71 -1.14 -1
-0.25 2.07 1
1.77 0.29 -1
0.33 3.12 1
0.37 -2.22 -1
0.35 1.79 1
1.10 0.71 -1
0.73 2.74 1
2.26 -0.93 -1
-0.20 1.81 1
1.07 -1.21 -1
1.70 3.04 1
2.86 1.26 -1
-0.75 1.72 1
2.38 0.12 -1
-0.41 0.69 1
2.19 0.71 -1
1.42 3.66 1
1.50 0.46 -1
0.50 2.06 1
1.84 -0.46 -1
-1.53 0.12 1
0.78 -0.52 -1
-0.21 0.96 1
3.54 2.02 -1
-0.14 1.16 1
2.09 0.39 -1
-0.79 1.64 1
0.75 0.47 -1
1.02 3.60 1
0.07 -1.45 -1
-0.79 1.48 1
2.75 0.24 -1
-0.10 1.92 1
1.99 0.31 -1
0.86 2.10 1
2.49 -0.05 -1
1.31 3.54 1
1.04 -1.65 -1
-1.45 0.31 1
1.75 -1.01 -1
-1.53 0.47 1
2.13 -0.42 -1
0.06 2.06 1
2.20 -0.40 -1
0.94 1.37 1
3.52 1.63 -1
1.79 3.07 1
2.48 0.44 -1
2.48 4.50 1
-1.71 -1.60 -1
0.35 2.07 1
0.34 -1.02 -1
-0.12 1.90 1
0.56 -1.65 -1
-0.03 1.50 1
1.92 -0.76 -1
1.05 3.11 1
1.49 -0.46 -1
0.73 1.98 1
1.26 0.10 -1
0.71 1.90 1
0.70 -1.50 -1
-1.55 0.89 1
1.41 0.39 -1
1.68 3.60 1
1.77 0.41 -1
0.64 3.94 1
1.23 -0.71 -1
1.52 2.82 1
3.03 1.18 -1
0.65 1.75 1
1.15 -1.15 -1
-0.79 1.20 1
2.87 1.03 -1
-0.99 1.49 1
1.75 -0.34 -1
1.63 2.88 1
2.62 0.25 -1
-1.39 1.22 1
2.65 0.90 -1
1.07 2.97 1
3.68 0.59 -1
1.23 3.30 1
1.19 0.54 -1
-0.76 1.51 1
0.35 -2.90 -1
1.39 2.98 1
1.38 -0.28 -1
-0.51 1.21 1
0.80 -0.41 -1
-1.63 0.16 1
2.26 0.10 -1
0.27 2.76 1
1.84 0.14 -1
-0.05 1.73 1
3.82 1.46 -1
-1.87 0.02 1
2.98 0.97 -1
-0.48 1.70 1
1.84 -0.39 -1
0.63 1.90 1
1.36 -0.80 -1
-1.20 0.35 1
0.88 -1.37 -1
-0.84 1.01 1
1.93 -0.48 -1
0.18 1.84 1
1.70 0.33 -1
-0.12 0.86 1
2.16 0.05 -1
-1.17 -0.08 1
0.99 -0.32 -1
-0.41 2.19 1
2.17 0.51 -1
1.71 3.66 1
3.70 1.87 -1
0.28 1.22 1
2.77 1.36 -1
0.03 1.60 1
3.61 1.62 -1
-0.52 2.73 1
2.96 1.07 -1
-0.43 1.56 1
1.61 1.35 -1
0.78 1.92 1
2.23 -0.44 -1
0.50 2.36 1
1.83 -0.84 -1
-0.01 1.30 1
3.16 1.37 -1
-0.96 0.89 1
3.61 1.71 -1
0.78 2.40 1
1.78 0.52 -1
-0.75 1.52 1
2.14 0.60 -1
-1.65 0.68 1
2.16 0.10 -1
-1.64 1.68 1
2.32 0.24 -1
0.18 2.59 1
1.86 -0.02 -1
-0.18 2.47 1
3.47 1.96 -1
0.00 3.00 1
2.57 -0.18 -1
这是产生数据的代码：
def gen_lin_separable_data(data, data_tr, data_ts,data_size):
mean1 = np.array([0, 2])
mean2 = np.array([2, 0])
cov = np.array([[0.8, 0.6], [0.6, 0.8]])
X1 = np.random.multivariate_normal(mean1, cov, size=int(data_size/2))
y1 = np.ones(len(X1))
X2 = np.random.multivariate_normal(mean2, cov, size=int(data_size/2))
y2 = np.ones(len(X2)) * -1
with open(data,'w') as fo, \
open(data_tr,'w') as fo1, \
open(data_ts,'w') as fo2:
for i in range( len(X1)):
line = '{:5.2f} {:5.2f} {:5.0f} \n'.format(X1[i][0], X1[i][1], y1[i])
line2 = '{:5.2f} {:5.2f} {:5.0f} \n'.format(X2[i][0], X2[i][1], y2[i])
fo.write(line)
fo.write(line2)
for i in range( len(X1) - 20):
line = '{:5.2f} {:5.2f} {:5.0f} \n'.format(X1[i][0], X1[i][1], y1[i])
line2 = '{:5.2f} {:5.2f} {:5.0f} \n'.format(X2[i][0], X2[i][1], y2[i])
fo1.write(line)
fo1.write(line2)
for i in range((len(X1) - 20), len(X1) ):
line = '{:5.2f} {:5.2f} {:5.0f} \n'.format(X1[i][0], X1[i][1], y1[i])
line2 = '{:5.2f} {:5.2f} {:5.0f} \n'.format(X2[i][0], X2[i][1], y2[i])
fo2.write(line)
fo2.write(line2)
读取数据的代码：
def read_data(infile):
data = np.loadtxt(infile)
X = data[:,:-1]
Y = data[:,-1]
# add bias to X's first column
ones = np.ones(X.shape[0]).reshape(X.shape[0],1)
X1 = np.append(ones, X, axis=1)
# X is needed for plot
return X, X1, Y
预测标签的代码是这样的：
def predict(X,w):
return np.sign(np.dot(X, w))
测试方法：
data = 'data.txt'
data_tr = 'data_train.txt'
data_ts = 'data_test.txt'
data_size = 200
gen_lin_separable_data(data, data_tr, data_ts,data_size)
epochs = 200
X_train, X1_train, Y_train = read_data(data_tr)
X_test, X1_test, Y_test = read_data(data_ts)
w, final_iter = aperceptrons(X_train, Y_train, epochs)
score = perceptron_test(w, X1_test)
correct = np.sum(score == Y_test)
print("Total: {} Correct: {} Accuracy = {} %".format(
len(score), correct, correct/ len(score) * 100))
题
我尽力解决了该错误，但找不到解决方法
蟒蛇。我说的是用numpy而不是scikit或任何其他高级软件包的实现。
因此问题仍然存在：
我们如何用numpy实现平均感知？
最佳答案
在这本书的第6步中，我在思考w = [w0，w1，...，wk]。
但是，我必须单独包括偏差项。
因此，代码中存在一个错误，我已将其修复。
我修复了代码，现在可以正常运行了。
#!python
# -*- coding: utf-8 -*-#
"""
Perceptron Algorithm.
@author: Bhishan Poudel
@date: Oct 31, 2017
"""
# Imports
import numpy as np
import matplotlib.pyplot as plt
from numpy.linalg import norm
import os, shutil
np.random.seed(100)
def read_data(infile):
data = np.loadtxt(infile)
X = data[:,:-1]
Y = data[:,-1]
return X, Y
def plot_boundary(X,Y,w,epoch):
try:
plt.style.use('seaborn-darkgrid')
# plt.style.use('ggplot')
#plt.style.available
except:
pass
# Get data for two classes
idxN = np.where(np.array(Y)==-1)
idxP = np.where(np.array(Y)==1)
XN = X[idxN]
XP = X[idxP]
# plot two classes
plt.scatter(XN[:,0],XN[:,1],c='b', marker='_', label="Negative class")
plt.scatter(XP[:,0],XP[:,1],c='r', marker='+', label="Positive class")
# plt.plot(XN[:,0],XN[:,1],'b_', markersize=8, label="Negative class")
# plt.plot(XP[:,0],XP[:,1],'r+', markersize=8, label="Positive class")
plt.title("Perceptron Algorithm iteration: {}".format(epoch))
# plot decision boundary orthogonal to w
# w is w2,w1, w0 last term is bias.
if len(w) == 3:
a = -w[0] / w[1]
b = -w[0] / w[2]
xx = [ 0, a]
yy = [b, 0]
plt.plot(xx,yy,'--g',label='Decision Boundary')
if len(w) == 2:
x2=[ w[0], w[1], -w[1], w[0]]
x3=[ w[0], w[1], w[1], -w[0]]
x2x3 =np.array([x2,x3])
XX,YY,U,V = list(zip(*x2x3))
ax = plt.gca()
ax.quiver(XX,YY,U,V,scale=1, color='g')
# Add labels
plt.xlabel('X')
plt.ylabel('Y')
# limits
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
plt.xlim(x_min,x_max)
plt.ylim(y_min,y_max)
# lines from origin
plt.axhline(y=0, color='k', linestyle='--',alpha=0.2)
plt.axvline(x=0, color='k', linestyle='--',alpha=0.2)
plt.grid(True)
plt.legend(loc=1)
plt.show()
plt.savefig('img/iter_{:03d}'.format(int(epoch)))
# Always clost the plot
plt.close()
def predict(X,w):
return np.sign(np.dot(X, w))
def plot_contour(X,Y,w,mesh_stepsize):
try:
plt.style.use('seaborn-darkgrid')
# plt.style.use('ggplot')
#plt.style.available
except:
pass
# Get data for two classes
idxN = np.where(np.array(Y)==-1)
idxP = np.where(np.array(Y)==1)
XN = X[idxN]
XP = X[idxP]
# plot two classes with + and - sign
fig, ax = plt.subplots()
ax.set_title('Perceptron Algorithm')
plt.xlabel("X")
plt.ylabel("Y")
plt.plot(XN[:,0],XN[:,1],'b_', markersize=8, label="Negative class")
plt.plot(XP[:,0],XP[:,1],'y+', markersize=8, label="Positive class")
plt.legend()
# create a mesh for contour plot
# We first make a meshgrid (rectangle full of pts) from xmin to xmax and ymin to ymax.
# We then predict the label for each grid point and color it.
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
# Get 2D array for grid axes xx and yy (shape = 700, 1000)
# xx has 700 rows.
# xx[0] has 1000 values.
xx, yy = np.meshgrid(np.arange(x_min, x_max, mesh_stepsize),
np.arange(y_min, y_max, mesh_stepsize))
# Get 1d array for x and y axes
xxr = xx.ravel() # shape (700000,)
yyr = yy.ravel() # shape (700000,)
# ones vector
# ones = np.ones(xxr.shape[0]) # shape (700000,)
ones = np.ones(len(xxr)) # shape (700000,)
# Predict the score
Xvals = np.c_[ones, xxr, yyr]
scores = predict(Xvals, w)
# Plot contour plot
scores = scores.reshape(xx.shape)
ax.contourf(xx, yy, scores, cmap=plt.cm.Paired)
# print("xx.shape = {}".format(xx.shape)) # (700, 1000)
# print("scores.shape = {}".format(scores.shape)) # (700, 1000)
# print("scores[0].shape = {}".format(scores[0].shape)) # (1000,)
# show the plot
plt.savefig("Perceptron.png")
plt.show()
plt.close()
def perceptron_sgd(X, Y,epochs):
"""
X: data matrix without bias.
Y: target
"""
# add bias to X's first column
ones = np.ones(X.shape[0]).reshape(X.shape[0],1)
X1 = np.append(ones, X, axis=1)
w = np.zeros(X1.shape[1])
final_iter = epochs
for epoch in range(epochs):
print("\n")
print("epoch: {} {}".format(epoch, '-'*30))
misclassified = 0
for i, x in enumerate(X1):
y = Y[i]
h = np.dot(x, w)*y
if h <= 0:
w = w + x*y
misclassified += 1
print('misclassified? yes w: {} '.format(w,i))
else:
print('misclassified? no w: {}'.format(w))
pass
if misclassified == 0:
final_iter = epoch
break
return w, final_iter
def aperceptron_sgd(X, Y,epochs):
# initialize weights
w = np.zeros(X.shape[1] )
u = np.zeros(X.shape[1] )
b = 0
beta = 0
# counters
final_iter = epochs
c = 1
converged = False
# main average perceptron algorithm
for epoch in range(epochs):
# initialize misclassified
misclassified = 0
# go through all training examples
for x,y in zip(X,Y):
h = y * (np.dot(x, w) + b)
if h <= 0:
w = w + y*x
b = b + y
u = u+ y*c*x
beta = beta + y*c
misclassified += 1
# update counter regardless of good or bad classification
c = c + 1
# break loop if w converges
if misclassified == 0:
final_iter = epoch
converged = True
print("Averaged Perceptron converged after: {} iterations".format(final_iter))
break
if converged == False:
print("Averaged Perceptron DID NOT converged.")
# prints
# print("final_iter = {}".format(final_iter))
# print("b, beta, c , (b-beta/c)= {} {} {} {}".format(b, beta, c, (b-beta/c)))
# print("w, u, (w-u/c) {} {} {}".format(w, u, (w-u/c)) )
# return w and final_iter
w = w - u/c
b = np.array([b- beta/c])
w = np.append(b, w)
return w, final_iter
def main():
"""Run main function."""
X, Y = read_data('data.txt') # X is without bias
max_iter = 20
w, final_iter = aperceptron_sgd(X,Y,max_iter)
print('w = ', w)
plot_boundary(X,Y,w,final_iter)
# contour plot
mesh_stepsize = 0.01
plot_contour(X,Y,w,mesh_stepsize)
if __name__ == "__main__":
main()