"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "ada = AdalineSGD(n_iter=15, eta=0.01, random_state=1)\n",
+ "ada.fit(X_std, y)\n",
+ "\n",
+ "plot_decision_regions(X_std, y, classifier=ada)\n",
+ "plt.title('Adaline - Stochastic Gradient Descent')\n",
+ "plt.xlabel('sepal length [standardized]')\n",
+ "plt.ylabel('petal length [standardized]')\n",
+ "plt.legend(loc='upper left')\n",
+ "\n",
+ "plt.tight_layout()\n",
+ "# plt.savefig('images/02_15_1.png', dpi=300)\n",
+ "plt.show()\n",
+ "\n",
+ "plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker='o')\n",
+ "plt.xlabel('Epochs')\n",
+ "plt.ylabel('Average Cost')\n",
+ "\n",
+ "plt.tight_layout()\n",
+ "# plt.savefig('images/02_15_2.png', dpi=300)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<__main__.AdalineSGD at 0x7f95f8f79588>"
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "ada.partial_fit(X_std[0, :], y[0])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Summary"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "--- \n",
+ "\n",
+ "Readers may ignore the following cell"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[NbConvertApp] Converting notebook ch02.ipynb to script\n",
+ "[NbConvertApp] Writing 16482 bytes to ch02.py\n"
+ ]
+ }
+ ],
+ "source": [
+ "! python ../.convert_notebook_to_script.py --input ch02.ipynb --output ch02.py"
+ ]
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/ch02/ch02.py b/ch02/ch02.py
new file mode 100644
index 00000000..535e2cb3
--- /dev/null
+++ b/ch02/ch02.py
@@ -0,0 +1,591 @@
+# coding: utf-8
+
+
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from matplotlib.colors import ListedColormap
+
+# Copyright (c) 2019 [Sebastian Raschka](sebastianraschka.com)
+#
+# https://github.com/rasbt/python-machine-learning-book-3rd-edition
+#
+# [MIT License](https://github.com/rasbt/python-machine-learning-book-3rd-edition/blob/master/LICENSE.txt)
+
+# # Python Machine Learning - Code Examples
+
+# # Chapter 2 - Training Machine Learning Algorithms for Classification
+
+# Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s).
+
+
+
+
+
+# *The use of `watermark` is optional. You can install this IPython extension via "`pip install watermark`". For more information, please see: https://github.com/rasbt/watermark.*
+
+# ### 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(object):
+ """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.
+ 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_samples, n_features]
+ Training vectors, where n_samples is the number of samples and
+ n_features is the number of features.
+ y : array-like, shape = [n_samples]
+ Target values.
+
+ Returns
+ -------
+ self : object
+
+ """
+ rgen = np.random.RandomState(self.random_state)
+ self.w_ = rgen.normal(loc=0.0, scale=0.01, size=1 + X.shape[1])
+ 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_[1:] += update * xi
+ self.w_[0] += 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_[1:]) + self.w_[0]
+
+ def predict(self, X):
+ """Return class label after unit step"""
+ return np.where(self.net_input(X) >= 0.0, 1, -1)
+
+
+
+
+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
+
+
+
+
+df = pd.read_csv('https://archive.ics.uci.edu/ml/'
+ 'machine-learning-databases/iris/iris.data',
+ header=None,
+ encoding='utf-8')
+df.tail()
+
+
+#
+# ### Note:
+#
+#
+# You can find a copy of the Iris dataset (and all other datasets used in this book) in the code bundle of this book, which you can use if you are working offline or the UCI server at https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data is temporarily unavailable. For instance, to load the Iris dataset from a local directory, you can replace the line
+#
+# df = pd.read_csv('https://archive.ics.uci.edu/ml/'
+# 'machine-learning-databases/iris/iris.data', header=None)
+#
+# by
+#
+# df = pd.read_csv('your/local/path/to/iris.data', header=None)
+#
+
+
+
+df = pd.read_csv('iris.data', 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', -1, 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='x', 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 = ('s', 'x', 'o', '^', '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))
+ Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
+ Z = Z.reshape(xx1.shape)
+ plt.contourf(xx1, xx2, Z, alpha=0.3, cmap=cmap)
+ plt.xlim(xx1.min(), xx1.max())
+ plt.ylim(xx2.min(), xx2.max())
+
+ # plot class samples
+ 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=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(object):
+ """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.
+ cost_ : list
+ Sum-of-squares cost function value 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_samples, n_features]
+ Training vectors, where n_samples is the number of samples and
+ n_features is the number of features.
+ y : array-like, shape = [n_samples]
+ Target values.
+
+ Returns
+ -------
+ self : object
+
+ """
+ rgen = np.random.RandomState(self.random_state)
+ self.w_ = rgen.normal(loc=0.0, scale=0.01, size=1 + X.shape[1])
+ self.cost_ = []
+
+ 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)
+ self.w_[1:] += self.eta * X.T.dot(errors)
+ self.w_[0] += self.eta * errors.sum()
+ cost = (errors**2).sum() / 2.0
+ self.cost_.append(cost)
+ return self
+
+ def net_input(self, X):
+ """Calculate net input"""
+ return np.dot(X, self.w_[1:]) + self.w_[0]
+
+ 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)) >= 0.0, 1, -1)
+
+
+
+
+fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))
+
+ada1 = AdalineGD(n_iter=10, eta=0.01).fit(X, y)
+ax[0].plot(range(1, len(ada1.cost_) + 1), np.log10(ada1.cost_), marker='o')
+ax[0].set_xlabel('Epochs')
+ax[0].set_ylabel('log(Sum-squared-error)')
+ax[0].set_title('Adaline - Learning rate 0.01')
+
+ada2 = AdalineGD(n_iter=10, eta=0.0001).fit(X, y)
+ax[1].plot(range(1, len(ada2.cost_) + 1), ada2.cost_, marker='o')
+ax[1].set_xlabel('Epochs')
+ax[1].set_ylabel('Sum-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 = AdalineGD(n_iter=15, eta=0.01)
+ada.fit(X_std, y)
+
+plot_decision_regions(X_std, y, classifier=ada)
+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.cost_) + 1), ada.cost_, marker='o')
+plt.xlabel('Epochs')
+plt.ylabel('Sum-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(object):
+ """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.
+ cost_ : list
+ Sum-of-squares cost function value averaged over all
+ training samples 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_samples, n_features]
+ Training vectors, where n_samples is the number of samples and
+ n_features is the number of features.
+ y : array-like, shape = [n_samples]
+ Target values.
+
+ Returns
+ -------
+ self : object
+
+ """
+ self._initialize_weights(X.shape[1])
+ self.cost_ = []
+ for i in range(self.n_iter):
+ if self.shuffle:
+ X, y = self._shuffle(X, y)
+ cost = []
+ for xi, target in zip(X, y):
+ cost.append(self._update_weights(xi, target))
+ avg_cost = sum(cost) / len(y)
+ self.cost_.append(avg_cost)
+ 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=1 + m)
+ 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_[1:] += self.eta * xi.dot(error)
+ self.w_[0] += self.eta * error
+ cost = 0.5 * error**2
+ return cost
+
+ def net_input(self, X):
+ """Calculate net input"""
+ return np.dot(X, self.w_[1:]) + self.w_[0]
+
+ 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)) >= 0.0, 1, -1)
+
+
+
+
+ada = AdalineSGD(n_iter=15, eta=0.01, random_state=1)
+ada.fit(X_std, y)
+
+plot_decision_regions(X_std, y, classifier=ada)
+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('images/02_15_1.png', dpi=300)
+plt.show()
+
+plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker='o')
+plt.xlabel('Epochs')
+plt.ylabel('Average Cost')
+
+plt.tight_layout()
+# plt.savefig('images/02_15_2.png', dpi=300)
+plt.show()
+
+
+
+
+ada.partial_fit(X_std[0, :], y[0])
+
+
+
+# # Summary
+
+# ...
+
+# ---
+#
+# Readers may ignore the following cell
+
+
+
+
diff --git a/ch02/images/02-to-address.txt b/ch02/images/02-to-address.txt
new file mode 100644
index 00000000..5912f0f9
--- /dev/null
+++ b/ch02/images/02-to-address.txt
@@ -0,0 +1,25 @@
+<--------------------------------------------------------------------------------------------
+Alfredo Canziani
+
+Ch2: you never explained ravel and zip
+
+----------------------
+
+activation function should be used in adaline
+
+=================
+
+mention logistic regression implementation
+
+
+=========
+
+vector scaling, see mail by makarov@cl.uzh.ch
+
+=========
+
+make datasets locally available
+
+========
+
+badly vs well-conditioned problem
\ No newline at end of file
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diff --git a/ch02/iris.data b/ch02/iris.data
new file mode 100644
index 00000000..5c4316cd
--- /dev/null
+++ b/ch02/iris.data
@@ -0,0 +1,151 @@
+5.1,3.5,1.4,0.2,Iris-setosa
+4.9,3.0,1.4,0.2,Iris-setosa
+4.7,3.2,1.3,0.2,Iris-setosa
+4.6,3.1,1.5,0.2,Iris-setosa
+5.0,3.6,1.4,0.2,Iris-setosa
+5.4,3.9,1.7,0.4,Iris-setosa
+4.6,3.4,1.4,0.3,Iris-setosa
+5.0,3.4,1.5,0.2,Iris-setosa
+4.4,2.9,1.4,0.2,Iris-setosa
+4.9,3.1,1.5,0.1,Iris-setosa
+5.4,3.7,1.5,0.2,Iris-setosa
+4.8,3.4,1.6,0.2,Iris-setosa
+4.8,3.0,1.4,0.1,Iris-setosa
+4.3,3.0,1.1,0.1,Iris-setosa
+5.8,4.0,1.2,0.2,Iris-setosa
+5.7,4.4,1.5,0.4,Iris-setosa
+5.4,3.9,1.3,0.4,Iris-setosa
+5.1,3.5,1.4,0.3,Iris-setosa
+5.7,3.8,1.7,0.3,Iris-setosa
+5.1,3.8,1.5,0.3,Iris-setosa
+5.4,3.4,1.7,0.2,Iris-setosa
+5.1,3.7,1.5,0.4,Iris-setosa
+4.6,3.6,1.0,0.2,Iris-setosa
+5.1,3.3,1.7,0.5,Iris-setosa
+4.8,3.4,1.9,0.2,Iris-setosa
+5.0,3.0,1.6,0.2,Iris-setosa
+5.0,3.4,1.6,0.4,Iris-setosa
+5.2,3.5,1.5,0.2,Iris-setosa
+5.2,3.4,1.4,0.2,Iris-setosa
+4.7,3.2,1.6,0.2,Iris-setosa
+4.8,3.1,1.6,0.2,Iris-setosa
+5.4,3.4,1.5,0.4,Iris-setosa
+5.2,4.1,1.5,0.1,Iris-setosa
+5.5,4.2,1.4,0.2,Iris-setosa
+4.9,3.1,1.5,0.1,Iris-setosa
+5.0,3.2,1.2,0.2,Iris-setosa
+5.5,3.5,1.3,0.2,Iris-setosa
+4.9,3.1,1.5,0.1,Iris-setosa
+4.4,3.0,1.3,0.2,Iris-setosa
+5.1,3.4,1.5,0.2,Iris-setosa
+5.0,3.5,1.3,0.3,Iris-setosa
+4.5,2.3,1.3,0.3,Iris-setosa
+4.4,3.2,1.3,0.2,Iris-setosa
+5.0,3.5,1.6,0.6,Iris-setosa
+5.1,3.8,1.9,0.4,Iris-setosa
+4.8,3.0,1.4,0.3,Iris-setosa
+5.1,3.8,1.6,0.2,Iris-setosa
+4.6,3.2,1.4,0.2,Iris-setosa
+5.3,3.7,1.5,0.2,Iris-setosa
+5.0,3.3,1.4,0.2,Iris-setosa
+7.0,3.2,4.7,1.4,Iris-versicolor
+6.4,3.2,4.5,1.5,Iris-versicolor
+6.9,3.1,4.9,1.5,Iris-versicolor
+5.5,2.3,4.0,1.3,Iris-versicolor
+6.5,2.8,4.6,1.5,Iris-versicolor
+5.7,2.8,4.5,1.3,Iris-versicolor
+6.3,3.3,4.7,1.6,Iris-versicolor
+4.9,2.4,3.3,1.0,Iris-versicolor
+6.6,2.9,4.6,1.3,Iris-versicolor
+5.2,2.7,3.9,1.4,Iris-versicolor
+5.0,2.0,3.5,1.0,Iris-versicolor
+5.9,3.0,4.2,1.5,Iris-versicolor
+6.0,2.2,4.0,1.0,Iris-versicolor
+6.1,2.9,4.7,1.4,Iris-versicolor
+5.6,2.9,3.6,1.3,Iris-versicolor
+6.7,3.1,4.4,1.4,Iris-versicolor
+5.6,3.0,4.5,1.5,Iris-versicolor
+5.8,2.7,4.1,1.0,Iris-versicolor
+6.2,2.2,4.5,1.5,Iris-versicolor
+5.6,2.5,3.9,1.1,Iris-versicolor
+5.9,3.2,4.8,1.8,Iris-versicolor
+6.1,2.8,4.0,1.3,Iris-versicolor
+6.3,2.5,4.9,1.5,Iris-versicolor
+6.1,2.8,4.7,1.2,Iris-versicolor
+6.4,2.9,4.3,1.3,Iris-versicolor
+6.6,3.0,4.4,1.4,Iris-versicolor
+6.8,2.8,4.8,1.4,Iris-versicolor
+6.7,3.0,5.0,1.7,Iris-versicolor
+6.0,2.9,4.5,1.5,Iris-versicolor
+5.7,2.6,3.5,1.0,Iris-versicolor
+5.5,2.4,3.8,1.1,Iris-versicolor
+5.5,2.4,3.7,1.0,Iris-versicolor
+5.8,2.7,3.9,1.2,Iris-versicolor
+6.0,2.7,5.1,1.6,Iris-versicolor
+5.4,3.0,4.5,1.5,Iris-versicolor
+6.0,3.4,4.5,1.6,Iris-versicolor
+6.7,3.1,4.7,1.5,Iris-versicolor
+6.3,2.3,4.4,1.3,Iris-versicolor
+5.6,3.0,4.1,1.3,Iris-versicolor
+5.5,2.5,4.0,1.3,Iris-versicolor
+5.5,2.6,4.4,1.2,Iris-versicolor
+6.1,3.0,4.6,1.4,Iris-versicolor
+5.8,2.6,4.0,1.2,Iris-versicolor
+5.0,2.3,3.3,1.0,Iris-versicolor
+5.6,2.7,4.2,1.3,Iris-versicolor
+5.7,3.0,4.2,1.2,Iris-versicolor
+5.7,2.9,4.2,1.3,Iris-versicolor
+6.2,2.9,4.3,1.3,Iris-versicolor
+5.1,2.5,3.0,1.1,Iris-versicolor
+5.7,2.8,4.1,1.3,Iris-versicolor
+6.3,3.3,6.0,2.5,Iris-virginica
+5.8,2.7,5.1,1.9,Iris-virginica
+7.1,3.0,5.9,2.1,Iris-virginica
+6.3,2.9,5.6,1.8,Iris-virginica
+6.5,3.0,5.8,2.2,Iris-virginica
+7.6,3.0,6.6,2.1,Iris-virginica
+4.9,2.5,4.5,1.7,Iris-virginica
+7.3,2.9,6.3,1.8,Iris-virginica
+6.7,2.5,5.8,1.8,Iris-virginica
+7.2,3.6,6.1,2.5,Iris-virginica
+6.5,3.2,5.1,2.0,Iris-virginica
+6.4,2.7,5.3,1.9,Iris-virginica
+6.8,3.0,5.5,2.1,Iris-virginica
+5.7,2.5,5.0,2.0,Iris-virginica
+5.8,2.8,5.1,2.4,Iris-virginica
+6.4,3.2,5.3,2.3,Iris-virginica
+6.5,3.0,5.5,1.8,Iris-virginica
+7.7,3.8,6.7,2.2,Iris-virginica
+7.7,2.6,6.9,2.3,Iris-virginica
+6.0,2.2,5.0,1.5,Iris-virginica
+6.9,3.2,5.7,2.3,Iris-virginica
+5.6,2.8,4.9,2.0,Iris-virginica
+7.7,2.8,6.7,2.0,Iris-virginica
+6.3,2.7,4.9,1.8,Iris-virginica
+6.7,3.3,5.7,2.1,Iris-virginica
+7.2,3.2,6.0,1.8,Iris-virginica
+6.2,2.8,4.8,1.8,Iris-virginica
+6.1,3.0,4.9,1.8,Iris-virginica
+6.4,2.8,5.6,2.1,Iris-virginica
+7.2,3.0,5.8,1.6,Iris-virginica
+7.4,2.8,6.1,1.9,Iris-virginica
+7.9,3.8,6.4,2.0,Iris-virginica
+6.4,2.8,5.6,2.2,Iris-virginica
+6.3,2.8,5.1,1.5,Iris-virginica
+6.1,2.6,5.6,1.4,Iris-virginica
+7.7,3.0,6.1,2.3,Iris-virginica
+6.3,3.4,5.6,2.4,Iris-virginica
+6.4,3.1,5.5,1.8,Iris-virginica
+6.0,3.0,4.8,1.8,Iris-virginica
+6.9,3.1,5.4,2.1,Iris-virginica
+6.7,3.1,5.6,2.4,Iris-virginica
+6.9,3.1,5.1,2.3,Iris-virginica
+5.8,2.7,5.1,1.9,Iris-virginica
+6.8,3.2,5.9,2.3,Iris-virginica
+6.7,3.3,5.7,2.5,Iris-virginica
+6.7,3.0,5.2,2.3,Iris-virginica
+6.3,2.5,5.0,1.9,Iris-virginica
+6.5,3.0,5.2,2.0,Iris-virginica
+6.2,3.4,5.4,2.3,Iris-virginica
+5.9,3.0,5.1,1.8,Iris-virginica
+
diff --git a/ch02/iris.names.txt b/ch02/iris.names.txt
new file mode 100644
index 00000000..062b486d
--- /dev/null
+++ b/ch02/iris.names.txt
@@ -0,0 +1,69 @@
+1. Title: Iris Plants Database
+ Updated Sept 21 by C.Blake - Added discrepency information
+
+2. Sources:
+ (a) Creator: R.A. Fisher
+ (b) Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)
+ (c) Date: July, 1988
+
+3. Past Usage:
+ - Publications: too many to mention!!! Here are a few.
+ 1. Fisher,R.A. "The use of multiple measurements in taxonomic problems"
+ Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions
+ to Mathematical Statistics" (John Wiley, NY, 1950).
+ 2. Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.
+ (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.
+ 3. Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System
+ Structure and Classification Rule for Recognition in Partially Exposed
+ Environments". IEEE Transactions on Pattern Analysis and Machine
+ Intelligence, Vol. PAMI-2, No. 1, 67-71.
+ -- Results:
+ -- very low misclassification rates (0% for the setosa class)
+ 4. Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule". IEEE
+ Transactions on Information Theory, May 1972, 431-433.
+ -- Results:
+ -- very low misclassification rates again
+ 5. See also: 1988 MLC Proceedings, 54-64. Cheeseman et al's AUTOCLASS II
+ conceptual clustering system finds 3 classes in the data.
+
+4. Relevant Information:
+ --- This is perhaps the best known database to be found in the pattern
+ recognition literature. Fisher's paper is a classic in the field
+ and is referenced frequently to this day. (See Duda & Hart, for
+ example.) The data set contains 3 classes of 50 instances each,
+ where each class refers to a type of iris plant. One class is
+ linearly separable from the other 2; the latter are NOT linearly
+ separable from each other.
+ --- Predicted attribute: class of iris plant.
+ --- This is an exceedingly simple domain.
+ --- This data differs from the data presented in Fishers article
+ (identified by Steve Chadwick, spchadwick@espeedaz.net )
+ The 35th sample should be: 4.9,3.1,1.5,0.2,"Iris-setosa"
+ where the error is in the fourth feature.
+ The 38th sample: 4.9,3.6,1.4,0.1,"Iris-setosa"
+ where the errors are in the second and third features.
+
+5. Number of Instances: 150 (50 in each of three classes)
+
+6. Number of Attributes: 4 numeric, predictive attributes and the class
+
+7. Attribute Information:
+ 1. sepal length in cm
+ 2. sepal width in cm
+ 3. petal length in cm
+ 4. petal width in cm
+ 5. class:
+ -- Iris Setosa
+ -- Iris Versicolour
+ -- Iris Virginica
+
+8. Missing Attribute Values: None
+
+Summary Statistics:
+ Min Max Mean SD Class Correlation
+ sepal length: 4.3 7.9 5.84 0.83 0.7826
+ sepal width: 2.0 4.4 3.05 0.43 -0.4194
+ petal length: 1.0 6.9 3.76 1.76 0.9490 (high!)
+ petal width: 0.1 2.5 1.20 0.76 0.9565 (high!)
+
+9. Class Distribution: 33.3% for each of 3 classes.
diff --git a/ch05/README.md b/ch05/README.md
new file mode 100644
index 00000000..fad4312e
--- /dev/null
+++ b/ch05/README.md
@@ -0,0 +1,57 @@
+Python Machine Learning - Code Examples
+
+
+## Chapter 5: Compressing Data via Dimensionality Reduction
+
+### Chapter Outline
+
+- Unsupervised dimensionality reduction via principal component analysis
+ - The main steps behind principal component analysis
+ - Extracting the principal components step by step
+ - Total and explained variance
+ - Feature transformation
+ - Principal component analysis in scikit-learn
+- Supervised data compression via linear discriminant analysis
+ - Principal component analysis versus linear discriminant analysis
+ - The inner workings of linear discriminant analysis
+ - Computing the scatter matrices
+ - Selecting linear discriminants for the new feature subspace
+ - Projecting samples onto the new feature space
+ - LDA via scikit-learn
+- Using kernel principal component analysis for nonlinear mappings
+ - Kernel functions and the kernel trick
+ - Implementing a kernel principal component analysis in Python
+ - Example 1 – separating half-moon shapes
+ - Example 2 – separating concentric circles
+ - Projecting new data points
+ - Kernel principal component analysis in scikit-learn
+- Summary
+
+### A note on using the code examples
+
+The recommended way to interact with the code examples in this book is via Jupyter Notebook (the `.ipynb` files). Using Jupyter Notebook, you will be able to execute the code step by step and have all the resulting outputs (including plots and images) all in one convenient document.
+
+
+
+
+
+Setting up Jupyter Notebook is really easy: if you are using the Anaconda Python distribution, all you need to install jupyter notebook is to execute the following command in your terminal:
+
+ conda install jupyter notebook
+
+Then you can launch jupyter notebook by executing
+
+ jupyter notebook
+
+A window will open up in your browser, which you can then use to navigate to the target directory that contains the `.ipynb` file you wish to open.
+
+**More installation and setup instructions can be found in the [README.md file of Chapter 1](../ch01/README.md)**.
+
+**(Even if you decide not to install Jupyter Notebook, note that you can also view the notebook files on GitHub by simply clicking on them: [`ch05.ipynb`](ch05.ipynb))**
+
+In addition to the code examples, I added a table of contents to each Jupyter notebook as well as section headers that are consistent with the content of the book. Also, I included the original images and figures in hope that these make it easier to navigate and work with the code interactively as you are reading the book.
+
+
+
+
+When I was creating these notebooks, I was hoping to make your reading (and coding) experience as convenient as possible! However, if you don't wish to use Jupyter Notebooks, I also converted these notebooks to regular Python script files (`.py` files) that can be viewed and edited in any plaintext editor.
\ No newline at end of file
diff --git a/ch05/ch05.ipynb b/ch05/ch05.ipynb
new file mode 100644
index 00000000..b4d5d814
--- /dev/null
+++ b/ch05/ch05.ipynb
@@ -0,0 +1,2137 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "*Python Machine Learning 2nd Edition* by [Sebastian Raschka](https://sebastianraschka.com), Packt Publishing Ltd. 2017\n",
+ "\n",
+ "Code Repository: https://github.com/rasbt/python-machine-learning-book-2nd-edition\n",
+ "\n",
+ "Code License: [MIT License](https://github.com/rasbt/python-machine-learning-book-2nd-edition/blob/master/LICENSE.txt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Python Machine Learning - Code Examples"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 5 - Compressing Data via Dimensionality Reduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Sebastian Raschka \n",
+ "last updated: 2018-07-02 \n",
+ "\n",
+ "numpy 1.14.5\n",
+ "scipy 1.1.0\n",
+ "matplotlib 2.2.2\n",
+ "sklearn 0.19.1\n"
+ ]
+ }
+ ],
+ "source": [
+ "%load_ext watermark\n",
+ "%watermark -a \"Sebastian Raschka\" -u -d -p numpy,scipy,matplotlib,sklearn"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "*The use of `watermark` is optional. You can install this IPython extension via \"`pip install watermark`\". For more information, please see: https://github.com/rasbt/watermark.*"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Overview"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "- [Unsupervised dimensionality reduction via principal component analysis 128](#Unsupervised-dimensionality-reduction-via-principal-component-analysis-128)\n",
+ " - [The main steps behind principal component analysis](#The-main-steps-behind-principal-component-analysis)\n",
+ " - [Extracting the principal components step-by-step](#Extracting-the-principal-components-step-by-step)\n",
+ " - [Total and explained variance](#Total-and-explained-variance)\n",
+ " - [Feature transformation](#Feature-transformation)\n",
+ " - [Principal component analysis in scikit-learn](#Principal-component-analysis-in-scikit-learn)\n",
+ "- [Supervised data compression via linear discriminant analysis](#Supervised-data-compression-via-linear-discriminant-analysis)\n",
+ " - [Principal component analysis versus linear discriminant analysis](#Principal-component-analysis-versus-linear-discriminant-analysis)\n",
+ " - [The inner workings of linear discriminant analysis](#The-inner-workings-of-linear-discriminant-analysis)\n",
+ " - [Computing the scatter matrices](#Computing-the-scatter-matrices)\n",
+ " - [Selecting linear discriminants for the new feature subspace](#Selecting-linear-discriminants-for-the-new-feature-subspace)\n",
+ " - [Projecting samples onto the new feature space](#Projecting-samples-onto-the-new-feature-space)\n",
+ " - [LDA via scikit-learn](#LDA-via-scikit-learn)\n",
+ "- [Using kernel principal component analysis for nonlinear mappings](#Using-kernel-principal-component-analysis-for-nonlinear-mappings)\n",
+ " - [Kernel functions and the kernel trick](#Kernel-functions-and-the-kernel-trick)\n",
+ " - [Implementing a kernel principal component analysis in Python](#Implementing-a-kernel-principal-component-analysis-in-Python)\n",
+ " - [Example 1 – separating half-moon shapes](#Example-1:-Separating-half-moon-shapes)\n",
+ " - [Example 2 – separating concentric circles](#Example-2:-Separating-concentric-circles)\n",
+ " - [Projecting new data points](#Projecting-new-data-points)\n",
+ " - [Kernel principal component analysis in scikit-learn](#Kernel-principal-component-analysis-in-scikit-learn)\n",
+ "- [Summary](#Summary)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from IPython.display import Image\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Unsupervised dimensionality reduction via principal component analysis"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## The main steps behind principal component analysis"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {
+ "image/png": {
+ "width": 400
+ }
+ },
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Image(filename='images/05_01.png', width=400) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Extracting the principal components step-by-step"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "
Class label
\n",
+ "
Alcohol
\n",
+ "
Malic acid
\n",
+ "
Ash
\n",
+ "
Alcalinity of ash
\n",
+ "
Magnesium
\n",
+ "
Total phenols
\n",
+ "
Flavanoids
\n",
+ "
Nonflavanoid phenols
\n",
+ "
Proanthocyanins
\n",
+ "
Color intensity
\n",
+ "
Hue
\n",
+ "
OD280/OD315 of diluted wines
\n",
+ "
Proline
\n",
+ "
\n",
+ " \n",
+ " \n",
+ "
\n",
+ "
0
\n",
+ "
1
\n",
+ "
14.23
\n",
+ "
1.71
\n",
+ "
2.43
\n",
+ "
15.6
\n",
+ "
127
\n",
+ "
2.80
\n",
+ "
3.06
\n",
+ "
0.28
\n",
+ "
2.29
\n",
+ "
5.64
\n",
+ "
1.04
\n",
+ "
3.92
\n",
+ "
1065
\n",
+ "
\n",
+ "
\n",
+ "
1
\n",
+ "
1
\n",
+ "
13.20
\n",
+ "
1.78
\n",
+ "
2.14
\n",
+ "
11.2
\n",
+ "
100
\n",
+ "
2.65
\n",
+ "
2.76
\n",
+ "
0.26
\n",
+ "
1.28
\n",
+ "
4.38
\n",
+ "
1.05
\n",
+ "
3.40
\n",
+ "
1050
\n",
+ "
\n",
+ "
\n",
+ "
2
\n",
+ "
1
\n",
+ "
13.16
\n",
+ "
2.36
\n",
+ "
2.67
\n",
+ "
18.6
\n",
+ "
101
\n",
+ "
2.80
\n",
+ "
3.24
\n",
+ "
0.30
\n",
+ "
2.81
\n",
+ "
5.68
\n",
+ "
1.03
\n",
+ "
3.17
\n",
+ "
1185
\n",
+ "
\n",
+ "
\n",
+ "
3
\n",
+ "
1
\n",
+ "
14.37
\n",
+ "
1.95
\n",
+ "
2.50
\n",
+ "
16.8
\n",
+ "
113
\n",
+ "
3.85
\n",
+ "
3.49
\n",
+ "
0.24
\n",
+ "
2.18
\n",
+ "
7.80
\n",
+ "
0.86
\n",
+ "
3.45
\n",
+ "
1480
\n",
+ "
\n",
+ "
\n",
+ "
4
\n",
+ "
1
\n",
+ "
13.24
\n",
+ "
2.59
\n",
+ "
2.87
\n",
+ "
21.0
\n",
+ "
118
\n",
+ "
2.80
\n",
+ "
2.69
\n",
+ "
0.39
\n",
+ "
1.82
\n",
+ "
4.32
\n",
+ "
1.04
\n",
+ "
2.93
\n",
+ "
735
\n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " Class label Alcohol Malic acid Ash Alcalinity of ash Magnesium \\\n",
+ "0 1 14.23 1.71 2.43 15.6 127 \n",
+ "1 1 13.20 1.78 2.14 11.2 100 \n",
+ "2 1 13.16 2.36 2.67 18.6 101 \n",
+ "3 1 14.37 1.95 2.50 16.8 113 \n",
+ "4 1 13.24 2.59 2.87 21.0 118 \n",
+ "\n",
+ " Total phenols Flavanoids Nonflavanoid phenols Proanthocyanins \\\n",
+ "0 2.80 3.06 0.28 2.29 \n",
+ "1 2.65 2.76 0.26 1.28 \n",
+ "2 2.80 3.24 0.30 2.81 \n",
+ "3 3.85 3.49 0.24 2.18 \n",
+ "4 2.80 2.69 0.39 1.82 \n",
+ "\n",
+ " Color intensity Hue OD280/OD315 of diluted wines Proline \n",
+ "0 5.64 1.04 3.92 1065 \n",
+ "1 4.38 1.05 3.40 1050 \n",
+ "2 5.68 1.03 3.17 1185 \n",
+ "3 7.80 0.86 3.45 1480 \n",
+ "4 4.32 1.04 2.93 735 "
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "import pandas as pd\n",
+ "\n",
+ "df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/'\n",
+ " 'machine-learning-databases/wine/wine.data',\n",
+ " header=None)\n",
+ "\n",
+ "# if the Wine dataset is temporarily unavailable from the\n",
+ "# UCI machine learning repository, un-comment the following line\n",
+ "# of code to load the dataset from a local path:\n",
+ "\n",
+ "# df_wine = pd.read_csv('wine.data', header=None)\n",
+ "\n",
+ "df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash',\n",
+ " 'Alcalinity of ash', 'Magnesium', 'Total phenols',\n",
+ " 'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins',\n",
+ " 'Color intensity', 'Hue',\n",
+ " 'OD280/OD315 of diluted wines', 'Proline']\n",
+ "\n",
+ "df_wine.head()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Splitting the data into 70% training and 30% test subsets."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from sklearn.model_selection import train_test_split\n",
+ "\n",
+ "X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values\n",
+ "\n",
+ "X_train, X_test, y_train, y_test = \\\n",
+ " train_test_split(X, y, test_size=0.3, \n",
+ " stratify=y,\n",
+ " random_state=0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Standardizing the data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from sklearn.preprocessing import StandardScaler\n",
+ "\n",
+ "sc = StandardScaler()\n",
+ "X_train_std = sc.fit_transform(X_train)\n",
+ "X_test_std = sc.transform(X_test)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "**Note**\n",
+ "\n",
+ "Accidentally, I wrote `X_test_std = sc.fit_transform(X_test)` instead of `X_test_std = sc.transform(X_test)`. In this case, it wouldn't make a big difference since the mean and standard deviation of the test set should be (quite) similar to the training set. However, as remember from Chapter 3, the correct way is to re-use parameters from the training set if we are doing any kind of transformation -- the test set should basically stand for \"new, unseen\" data.\n",
+ "\n",
+ "My initial typo reflects a common mistake is that some people are *not* re-using these parameters from the model training/building and standardize the new data \"from scratch.\" Here's simple example to explain why this is a problem.\n",
+ "\n",
+ "Let's assume we have a simple training set consisting of 3 samples with 1 feature (let's call this feature \"length\"):\n",
+ "\n",
+ "- train_1: 10 cm -> class_2\n",
+ "- train_2: 20 cm -> class_2\n",
+ "- train_3: 30 cm -> class_1\n",
+ "\n",
+ "mean: 20, std.: 8.2\n",
+ "\n",
+ "After standardization, the transformed feature values are\n",
+ "\n",
+ "- train_std_1: -1.21 -> class_2\n",
+ "- train_std_2: 0 -> class_2\n",
+ "- train_std_3: 1.21 -> class_1\n",
+ "\n",
+ "Next, let's assume our model has learned to classify samples with a standardized length value < 0.6 as class_2 (class_1 otherwise). So far so good. Now, let's say we have 3 unlabeled data points that we want to classify:\n",
+ "\n",
+ "- new_4: 5 cm -> class ?\n",
+ "- new_5: 6 cm -> class ?\n",
+ "- new_6: 7 cm -> class ?\n",
+ "\n",
+ "If we look at the \"unstandardized \"length\" values in our training datast, it is intuitive to say that all of these samples are likely belonging to class_2. However, if we standardize these by re-computing standard deviation and and mean you would get similar values as before in the training set and your classifier would (probably incorrectly) classify samples 4 and 5 as class 2.\n",
+ "\n",
+ "- new_std_4: -1.21 -> class 2\n",
+ "- new_std_5: 0 -> class 2\n",
+ "- new_std_6: 1.21 -> class 1\n",
+ "\n",
+ "However, if we use the parameters from your \"training set standardization,\" we'd get the values:\n",
+ "\n",
+ "- sample5: -18.37 -> class 2\n",
+ "- sample6: -17.15 -> class 2\n",
+ "- sample7: -15.92 -> class 2\n",
+ "\n",
+ "The values 5 cm, 6 cm, and 7 cm are much lower than anything we have seen in the training set previously. Thus, it only makes sense that the standardized features of the \"new samples\" are much lower than every standardized feature in the training set.\n",
+ "\n",
+ "---"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Eigendecomposition of the covariance matrix."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Eigenvalues \n",
+ "[4.84274532 2.41602459 1.54845825 0.96120438 0.84166161 0.6620634\n",
+ " 0.51828472 0.34650377 0.3131368 0.10754642 0.21357215 0.15362835\n",
+ " 0.1808613 ]\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "cov_mat = np.cov(X_train_std.T)\n",
+ "eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)\n",
+ "\n",
+ "print('\\nEigenvalues \\n%s' % eigen_vals)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Note**: \n",
+ "\n",
+ "Above, I used the [`numpy.linalg.eig`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html) function to decompose the symmetric covariance matrix into its eigenvalues and eigenvectors.\n",
+ "