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ch02.py
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# coding: utf-8
import sys
from python_environment_check import check_packages
import numpy as np
import os
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
# # Machine Learning with PyTorch and Scikit-Learn
# # -- Code Examples
# ## Package version checks
# Add folder to path in order to load from the check_packages.py script:
sys.path.insert(0, '..')
# Check recommended package versions:
d = {
'numpy': '1.21.2',
'matplotlib': '3.4.3',
'pandas': '1.3.2'
}
check_packages(d)
# # Chapter 2 - Training Machine Learning Algorithms for Classification
# ### Overview
#
# - [Artificial neurons – a brief glimpse into the early history of machine learning](#Artificial-neurons-a-brief-glimpse-into-the-early-history-of-machine-learning)
# - [The formal definition of an artificial neuron](#The-formal-definition-of-an-artificial-neuron)
# - [The perceptron learning rule](#The-perceptron-learning-rule)
# - [Implementing a perceptron learning algorithm in Python](#Implementing-a-perceptron-learning-algorithm-in-Python)
# - [An object-oriented perceptron API](#An-object-oriented-perceptron-API)
# - [Training a perceptron model on the Iris dataset](#Training-a-perceptron-model-on-the-Iris-dataset)
# - [Adaptive linear neurons and the convergence of learning](#Adaptive-linear-neurons-and-the-convergence-of-learning)
# - [Minimizing cost functions with gradient descent](#Minimizing-cost-functions-with-gradient-descent)
# - [Implementing an Adaptive Linear Neuron in Python](#Implementing-an-Adaptive-Linear-Neuron-in-Python)
# - [Improving gradient descent through feature scaling](#Improving-gradient-descent-through-feature-scaling)
# - [Large scale machine learning and stochastic gradient descent](#Large-scale-machine-learning-and-stochastic-gradient-descent)
# - [Summary](#Summary)
# # Artificial neurons - a brief glimpse into the early history of machine learning
# ## The formal definition of an artificial neuron
# ## The perceptron learning rule
# # Implementing a perceptron learning algorithm in Python
# ## An object-oriented perceptron API
class Perceptron:
"""Perceptron classifier.
Parameters
------------
eta : float
Learning rate (between 0.0 and 1.0)
n_iter : int
Passes over the training dataset.
random_state : int
Random number generator seed for random weight
initialization.
Attributes
-----------
w_ : 1d-array
Weights after fitting.
b_ : Scalar
Bias unit after fitting.
errors_ : list
Number of misclassifications (updates) in each epoch.
"""
def __init__(self, eta=0.01, n_iter=50, random_state=1):
self.eta = eta
self.n_iter = n_iter
self.random_state = random_state
def fit(self, X, y):
"""Fit training data.
Parameters
----------
X : {array-like}, shape = [n_examples, n_features]
Training vectors, where n_examples is the number of examples and
n_features is the number of features.
y : array-like, shape = [n_examples]
Target values.
Returns
-------
self : object
"""
rgen = np.random.RandomState(self.random_state)
self.w_ = rgen.normal(loc=0.0, scale=0.01, size=X.shape[1])
self.b_ = np.float_(0.)
self.errors_ = []
for _ in range(self.n_iter):
errors = 0
for xi, target in zip(X, y):
update = self.eta * (target - self.predict(xi))
self.w_ += update * xi
self.b_ += update
errors += int(update != 0.0)
self.errors_.append(errors)
return self
def net_input(self, X):
"""Calculate net input"""
return np.dot(X, self.w_) + self.b_
def predict(self, X):
"""Return class label after unit step"""
return np.where(self.net_input(X) >= 0.0, 1, 0)
v1 = np.array([1, 2, 3])
v2 = 0.5 * v1
np.arccos(v1.dot(v2) / (np.linalg.norm(v1) * np.linalg.norm(v2)))
# ## Training a perceptron model on the Iris dataset
# ...
# ### Reading-in the Iris data
try:
s = 'https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data'
print('From URL:', s)
df = pd.read_csv(s,
header=None,
encoding='utf-8')
except HTTPError:
s = 'iris.data'
print('From local Iris path:', s)
df = pd.read_csv(s,
header=None,
encoding='utf-8')
df.tail()
# ### Plotting the Iris data
# select setosa and versicolor
y = df.iloc[0:100, 4].values
y = np.where(y == 'Iris-setosa', 0, 1)
# extract sepal length and petal length
X = df.iloc[0:100, [0, 2]].values
# plot data
plt.scatter(X[:50, 0], X[:50, 1],
color='red', marker='o', label='Setosa')
plt.scatter(X[50:100, 0], X[50:100, 1],
color='blue', marker='s', label='Versicolor')
plt.xlabel('Sepal length [cm]')
plt.ylabel('Petal length [cm]')
plt.legend(loc='upper left')
# plt.savefig('images/02_06.png', dpi=300)
plt.show()
# ### Training the perceptron model
ppn = Perceptron(eta=0.1, n_iter=10)
ppn.fit(X, y)
plt.plot(range(1, len(ppn.errors_) + 1), ppn.errors_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('Number of updates')
# plt.savefig('images/02_07.png', dpi=300)
plt.show()
# ### A function for plotting decision regions
def plot_decision_regions(X, y, classifier, resolution=0.02):
# setup marker generator and color map
markers = ('o', 's', '^', 'v', '<')
colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')
cmap = ListedColormap(colors[:len(np.unique(y))])
# plot the decision surface
x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1
x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),
np.arange(x2_min, x2_max, resolution))
lab = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
lab = lab.reshape(xx1.shape)
plt.contourf(xx1, xx2, lab, alpha=0.3, cmap=cmap)
plt.xlim(xx1.min(), xx1.max())
plt.ylim(xx2.min(), xx2.max())
# plot class examples
for idx, cl in enumerate(np.unique(y)):
plt.scatter(x=X[y == cl, 0],
y=X[y == cl, 1],
alpha=0.8,
c=colors[idx],
marker=markers[idx],
label=f'Class {cl}',
edgecolor='black')
plot_decision_regions(X, y, classifier=ppn)
plt.xlabel('Sepal length [cm]')
plt.ylabel('Petal length [cm]')
plt.legend(loc='upper left')
#plt.savefig('images/02_08.png', dpi=300)
plt.show()
# # Adaptive linear neurons and the convergence of learning
# ...
# ## Minimizing cost functions with gradient descent
# ## Implementing an adaptive linear neuron in Python
class AdalineGD:
"""ADAptive LInear NEuron classifier.
Parameters
------------
eta : float
Learning rate (between 0.0 and 1.0)
n_iter : int
Passes over the training dataset.
random_state : int
Random number generator seed for random weight
initialization.
Attributes
-----------
w_ : 1d-array
Weights after fitting.
b_ : Scalar
Bias unit after fitting.
losses_ : list
Mean squared eror loss function values in each epoch.
"""
def __init__(self, eta=0.01, n_iter=50, random_state=1):
self.eta = eta
self.n_iter = n_iter
self.random_state = random_state
def fit(self, X, y):
""" Fit training data.
Parameters
----------
X : {array-like}, shape = [n_examples, n_features]
Training vectors, where n_examples is the number of examples and
n_features is the number of features.
y : array-like, shape = [n_examples]
Target values.
Returns
-------
self : object
"""
rgen = np.random.RandomState(self.random_state)
self.w_ = rgen.normal(loc=0.0, scale=0.01, size=X.shape[1])
self.b_ = np.float_(0.)
self.losses_ = []
for i in range(self.n_iter):
net_input = self.net_input(X)
# Please note that the "activation" method has no effect
# in the code since it is simply an identity function. We
# could write `output = self.net_input(X)` directly instead.
# The purpose of the activation is more conceptual, i.e.,
# in the case of logistic regression (as we will see later),
# we could change it to
# a sigmoid function to implement a logistic regression classifier.
output = self.activation(net_input)
errors = (y - output)
#for w_j in range(self.w_.shape[0]):
# self.w_[w_j] += self.eta * (2.0 * (X[:, w_j]*errors)).mean()
self.w_ += self.eta * 2.0 * X.T.dot(errors) / X.shape[0]
self.b_ += self.eta * 2.0 * errors.mean()
loss = (errors**2).mean()
self.losses_.append(loss)
return self
def net_input(self, X):
"""Calculate net input"""
return np.dot(X, self.w_) + self.b_
def activation(self, X):
"""Compute linear activation"""
return X
def predict(self, X):
"""Return class label after unit step"""
return np.where(self.activation(self.net_input(X)) >= 0.5, 1, 0)
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))
ada1 = AdalineGD(n_iter=15, eta=0.1).fit(X, y)
ax[0].plot(range(1, len(ada1.losses_) + 1), np.log10(ada1.losses_), marker='o')
ax[0].set_xlabel('Epochs')
ax[0].set_ylabel('log(Mean squared error)')
ax[0].set_title('Adaline - Learning rate 0.1')
ada2 = AdalineGD(n_iter=15, eta=0.0001).fit(X, y)
ax[1].plot(range(1, len(ada2.losses_) + 1), ada2.losses_, marker='o')
ax[1].set_xlabel('Epochs')
ax[1].set_ylabel('Mean squared error')
ax[1].set_title('Adaline - Learning rate 0.0001')
# plt.savefig('images/02_11.png', dpi=300)
plt.show()
# ## Improving gradient descent through feature scaling
# standardize features
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()
ada_gd = AdalineGD(n_iter=20, eta=0.5)
ada_gd.fit(X_std, y)
plot_decision_regions(X_std, y, classifier=ada_gd)
plt.title('Adaline - Gradient descent')
plt.xlabel('Sepal length [standardized]')
plt.ylabel('Petal length [standardized]')
plt.legend(loc='upper left')
plt.tight_layout()
#plt.savefig('images/02_14_1.png', dpi=300)
plt.show()
plt.plot(range(1, len(ada_gd.losses_) + 1), ada_gd.losses_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('Mean squared error')
plt.tight_layout()
#plt.savefig('images/02_14_2.png', dpi=300)
plt.show()
# ## Large scale machine learning and stochastic gradient descent
class AdalineSGD:
"""ADAptive LInear NEuron classifier.
Parameters
------------
eta : float
Learning rate (between 0.0 and 1.0)
n_iter : int
Passes over the training dataset.
shuffle : bool (default: True)
Shuffles training data every epoch if True to prevent cycles.
random_state : int
Random number generator seed for random weight
initialization.
Attributes
-----------
w_ : 1d-array
Weights after fitting.
b_ : Scalar
Bias unit after fitting.
losses_ : list
Mean squared error loss function value averaged over all
training examples in each epoch.
"""
def __init__(self, eta=0.01, n_iter=10, shuffle=True, random_state=None):
self.eta = eta
self.n_iter = n_iter
self.w_initialized = False
self.shuffle = shuffle
self.random_state = random_state
def fit(self, X, y):
""" Fit training data.
Parameters
----------
X : {array-like}, shape = [n_examples, n_features]
Training vectors, where n_examples is the number of examples and
n_features is the number of features.
y : array-like, shape = [n_examples]
Target values.
Returns
-------
self : object
"""
self._initialize_weights(X.shape[1])
self.losses_ = []
for i in range(self.n_iter):
if self.shuffle:
X, y = self._shuffle(X, y)
losses = []
for xi, target in zip(X, y):
losses.append(self._update_weights(xi, target))
avg_loss = np.mean(losses)
self.losses_.append(avg_loss)
return self
def partial_fit(self, X, y):
"""Fit training data without reinitializing the weights"""
if not self.w_initialized:
self._initialize_weights(X.shape[1])
if y.ravel().shape[0] > 1:
for xi, target in zip(X, y):
self._update_weights(xi, target)
else:
self._update_weights(X, y)
return self
def _shuffle(self, X, y):
"""Shuffle training data"""
r = self.rgen.permutation(len(y))
return X[r], y[r]
def _initialize_weights(self, m):
"""Initialize weights to small random numbers"""
self.rgen = np.random.RandomState(self.random_state)
self.w_ = self.rgen.normal(loc=0.0, scale=0.01, size=m)
self.b_ = np.float_(0.)
self.w_initialized = True
def _update_weights(self, xi, target):
"""Apply Adaline learning rule to update the weights"""
output = self.activation(self.net_input(xi))
error = (target - output)
self.w_ += self.eta * 2.0 * xi * (error)
self.b_ += self.eta * 2.0 * error
loss = error**2
return loss
def net_input(self, X):
"""Calculate net input"""
return np.dot(X, self.w_) + self.b_
def activation(self, X):
"""Compute linear activation"""
return X
def predict(self, X):
"""Return class label after unit step"""
return np.where(self.activation(self.net_input(X)) >= 0.5, 1, 0)
ada_sgd = AdalineSGD(n_iter=15, eta=0.01, random_state=1)
ada_sgd.fit(X_std, y)
plot_decision_regions(X_std, y, classifier=ada_sgd)
plt.title('Adaline - Stochastic gradient descent')
plt.xlabel('Sepal length [standardized]')
plt.ylabel('Petal length [standardized]')
plt.legend(loc='upper left')
plt.tight_layout()
plt.savefig('figures/02_15_1.png', dpi=300)
plt.show()
plt.plot(range(1, len(ada_sgd.losses_) + 1), ada_sgd.losses_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('Average loss')
plt.savefig('figures/02_15_2.png', dpi=300)
plt.show()
ada_sgd.partial_fit(X_std[0, :], y[0])
# # Summary
# ...
# ---
#
# Readers may ignore the following cell