Perceptrons¶
Implementation of the classic Perceptron by Frank Rosenblatt for binary classification (here: 0/1 class labels) in PyTorch
Imports¶
In [1]:
import numpy as np
import matplotlib.pyplot as plt
import torch
%matplotlib inline
Preparing a toy dataset¶
In [2]:
##########################
### DATASET
##########################
data = np.genfromtxt(‘perceptron_toydata.txt’, delimiter=’\t’)
X, y = data[:, :2], data[:, 2]
y = y.astype(np.int)
print(‘Class label counts:’, np.bincount(y))
print(‘X.shape:’, X.shape)
print(‘y.shape:’, y.shape)
# Shuffling & train/test split
shuffle_idx = np.arange(y.shape[0])
shuffle_rng = np.random.RandomState(123)
shuffle_rng.shuffle(shuffle_idx)
X, y = X[shuffle_idx], y[shuffle_idx]
X_train, X_test = X[shuffle_idx[:70]], X[shuffle_idx[70:]]
y_train, y_test = y[shuffle_idx[:70]], y[shuffle_idx[70:]]
# Normalize (mean zero, unit variance)
mu, sigma = X_train.mean(axis=0), X_train.std(axis=0)
X_train = (X_train – mu) / sigma
X_test = (X_test – mu) / sigma
Class label counts: [50 50]
X.shape: (100, 2)
y.shape: (100,)
In [3]:
plt.scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], label=’class 0′, marker=’o’)
plt.scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], label=’class 1′, marker=’s’)
plt.title(‘Training set’)
plt.xlabel(‘feature 1’)
plt.ylabel(‘feature 2′)
plt.xlim([-3, 3])
plt.ylim([-3, 3])
plt.legend()
plt.show()

In [4]:
plt.scatter(X_test[y_test==0, 0], X_test[y_test==0, 1], label=’class 0′, marker=’o’)
plt.scatter(X_test[y_test==1, 0], X_test[y_test==1, 1], label=’class 1′, marker=’s’)
plt.title(‘Test set’)
plt.xlabel(‘feature 1’)
plt.ylabel(‘feature 2’)
plt.xlim([-3, 3])
plt.ylim([-3, 3])
plt.legend()
plt.show()

Defining the Perceptron model¶
In [5]:
device = torch.device(“cuda:0” if torch.cuda.is_available() else “cpu”)
class Perceptron():
def __init__(self, num_features):
self.num_features = num_features
self.weights = torch.zeros(num_features, 1,
dtype=torch.float32, device=device)
self.bias = torch.zeros(1, dtype=torch.float32, device=device)
# placeholder vectors so they don’t
# need to be recreated each time
self.ones = torch.ones(1)
self.zeros = torch.zeros(1)
def forward(self, x):
linear = torch.add(torch.mm(x, self.weights), self.bias)
predictions = torch.where(linear > 0., self.ones, self.zeros)
return predictions
def backward(self, x, y):
predictions = self.forward(x)
errors = y – predictions
return errors
def train(self, x, y, epochs):
for e in range(epochs):
for i in range(y.shape[0]):
# use view because backward expects a matrix (i.e., 2D tensor)
errors = self.backward(x[i].reshape(1, self.num_features), y[i]).reshape(-1)
self.weights += (errors * x[i]).reshape(self.num_features, 1)
self.bias += errors
def evaluate(self, x, y):
predictions = self.forward(x).reshape(-1)
accuracy = torch.sum(predictions == y).float() / y.shape[0]
return accuracy
Training the Perceptron¶
In [6]:
ppn = Perceptron(num_features=2)
X_train_tensor = torch.tensor(X_train, dtype=torch.float32, device=device)
y_train_tensor = torch.tensor(y_train, dtype=torch.float32, device=device)
ppn.train(X_train_tensor, y_train_tensor, epochs=5)
print(‘Model parameters:’)
print(‘ Weights: %s’ % ppn.weights)
print(‘ Bias: %s’ % ppn.bias)
Model parameters:
Weights: tensor([[1.2734],
[1.3464]])
Bias: tensor([-1.])
Evaluating the model¶
In [7]:
X_test_tensor = torch.tensor(X_test, dtype=torch.float32, device=device)
y_test_tensor = torch.tensor(y_test, dtype=torch.float32, device=device)
test_acc = ppn.evaluate(X_test_tensor, y_test_tensor)
print(‘Test set accuracy: %.2f%%’ % (test_acc*100))
Test set accuracy: 93.33%
In [8]:
##########################
### 2D Decision Boundary
##########################
w, b = ppn.weights, ppn.bias
x_min = -2
y_min = ( (-(w[0] * x_min) – b[0])
/ w[1] )
x_max = 2
y_max = ( (-(w[0] * x_max) – b[0])
/ w[1] )
fig, ax = plt.subplots(1, 2, sharex=True, figsize=(7, 3))
ax[0].plot([x_min, x_max], [y_min, y_max])
ax[1].plot([x_min, x_max], [y_min, y_max])
ax[0].scatter(X_train[y_train==0, 0], X_train[y_train==0, 1], label=’class 0′, marker=’o’)
ax[0].scatter(X_train[y_train==1, 0], X_train[y_train==1, 1], label=’class 1′, marker=’s’)
ax[1].scatter(X_test[y_test==0, 0], X_test[y_test==0, 1], label=’class 0′, marker=’o’)
ax[1].scatter(X_test[y_test==1, 0], X_test[y_test==1, 1], label=’class 1′, marker=’s’)
ax[1].legend(loc=’upper left’)
plt.show()