Perceptron Classifier



In [1]:

    
%load_ext watermark
%watermark -a 'Sebastian Raschka' -d -v -p matplotlib









    



Sebastian Raschka 02/04/2015 

CPython 3.4.3
IPython 3.0.0

matplotlib 1.4.3



In [2]:

    
import sys
sys.path = ['/Users/sebastian/github/mlxtend'] + sys.path

import mlxtend
from mlxtend.data import iris_data
from mlxtend.evaluate import plot_decision_regions
from mlxtend.classifier import Perceptron
mlxtend.__version__









    Out[2]:





'0.2.3'

Loading Iris Data



In [3]:

    
import numpy as np

X, y = iris_data()
X = X[:, [0, 3]] # sepal length and petal width
X = X[0:100] # class 0 and class 1

y = np.where(y[0:100] == 0, -1, 1) # class -1 and class 1

# standardize
X_std = np.copy(X)
X_std[:,0] = (X[:,0] - X[:,0].mean()) / X[:,0].std()
X_std[:,1] = (X[:,1] - X[:,1].mean()) / X[:,1].std()

Rosenblatt Perceptron Rule

2D



In [4]:

    
%matplotlib inline
import matplotlib.pyplot as plt

ppn = Perceptron(epochs=15, eta=0.01, random_seed=1)

## Standardized

ppn.fit(X_std, y)
print(ppn.w_)
plot_decision_regions(X_std, y, clf=ppn)
plt.title('Perceptron - Standardized, y {-1, 1}')
plt.show()

plt.plot(range(len(ppn.cost_)), ppn.cost_, marker='o')
plt.xlabel('Iterations')
plt.ylabel('Missclassifications')
plt.show()

## Non Standardized

ppn = Perceptron(epochs=40, eta=0.01, random_seed=1)

ppn.fit(X, y)
print(ppn.w_)
plot_decision_regions(X, y, clf=ppn)
plt.title('Perceptron - Non-Standardized, y {-1, 1}')
plt.show()

plt.plot(range(len(ppn.cost_)), ppn.cost_, marker='o')
plt.xlabel('Iterations')
plt.ylabel('Missclassifications')
plt.show()









    



[ 0.177022    0.40557785  0.4977635 ]






    












    












    



[ 0.077022   -0.07367551  0.46211437]

1D



In [5]:

    
ppn = Perceptron(epochs=15, eta=0.01, random_seed=1)

## Standardized

ppn.fit(X_std[:,1, None], y)
print(ppn.w_)
plot_decision_regions(X_std[:,1, None], y, clf=ppn)
plt.title('Perceptron - Standardized, y {-1, 1}')
plt.show()

plt.plot(range(len(ppn.cost_)), ppn.cost_, marker='o')
plt.xlabel('Iterations')
plt.ylabel('Missclassifications')
plt.show()

## Non Standardized

ppn = Perceptron(epochs=15, eta=0.01, random_seed=1)

ppn.fit(X[:,1, None], y)
print(ppn.w_)
plot_decision_regions(X[:,1, None], y, clf=ppn)
plt.title('Perceptron - Non-Standardized, y {-1, 1}')
plt.show()

plt.plot(range(len(ppn.cost_)), ppn.cost_, marker='o')
plt.xlabel('Iterations')
plt.ylabel('Missclassifications')
plt.show()









    



[ 0.237022   0.7865239]






    












    












    



[-0.302978    0.49832449]



In [6]:

    
X, y = iris_data()
X = X[:, [0, 1]] # sepal length and sepal width
X = X[50:150] # class 0 and class 1

y = np.where(y[50:150] == 2, -1, 1) # class -1 and class 1

# standardize
X_std = np.copy(X)
X_std[:,0] = (X[:,0] - X[:,0].mean()) / X[:,0].std()
X_std[:,1] = (X[:,1] - X[:,1].mean()) / X[:,1].std()

Convergence



In [8]:

    
ppn = Perceptron(epochs=80, eta=0.001, random_seed=1)

ppn.fit(X_std, y)
print(ppn.w_)
plot_decision_regions(X_std, y, clf=ppn)
plt.title('Perceptron - Standardized, y {-1, 1}')
plt.show()

plt.plot(range(len(ppn.cost_)), ppn.cost_, marker='o')
plt.xlabel('Iterations')
plt.ylabel('Missclassifications')
plt.show()









    



[-0.004978   -0.00086942 -0.00114211]



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