Tutorial - Machine Learning Algorithms

import numpy as np

class Perceptron(object):
    """ Perceptron classifier. 
    
    Parameters
    ----------
    eta : float
        Learning rate (between 0.0 and 1.0)
    n_iter : int
        Passes over the training dataset. 
        
    Attributes
    ----------
    w_ : 1d-array
        Weights after fitting.
    errors_ : list
        Number of misclassifications in every epoch. 
    """
    def __init__(self, eta=0.01, n_iter=10):
        self.eta = eta
        self.n_iter = n_iter
        
    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
        
        """
        # Initialize weight vector to zeros.
        # X.shape[1] returns the numer of features. 
        self.w_ = np.zeros(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 the net input. (i.e. do dot prod)"""
        return np.dot(X, self.w_[1:]) + self.w_[0]
    
    def predict(self, X):
        """ Return class label after unit step. """
        # Evaluates if (the single number) self.net_input(X) is >= 0.0, and
        # if it is, returns 1, otherwise returns -1. 
        return np.where(self.net_input(X) >= 0.0, 1, -1)

# Step 1 : Load datset into a pandas DataFrame. 
import pandas as pd
df = pd.read_csv('https://archive.ics.uci.edu/ml/'
                'machine-learning-databases/iris/iris.data', header=None)
# Print the last five lines. 
# First feat column = sepal length
# Third feat column = petal length
df.tail() 

%matplotlib inline
# Steps 2 and 3 : Extract our (simpler) desired subset and plot. 
import matplotlib.pyplot as plt
import numpy as np

# Extract the first 50 Iris-Setosa and 50 Iris-Versicolor flowers, respectively.
# Syntax: df.iloc returns (index, value(s)) list, where
# (1) the 0:100 means "Get the first 100 data frame entries, and 
# (2) the 4 means "only the (zero-indexed) 4th column of those entries, specifically. 
# (3) .values means we only return the values, not their original indices. 
y = df.iloc[0:100, 4].values
# Convert the class labels to integer labels: Setosa(-1), Versicolor(1). 
y = np.where(y == 'Iris-setosa', -1, 1)

# Similarly, store the two features in X, obtained by
# getting the 0th and 2nd columns from the df object. 
X = df.iloc[0:100, [0, 2]].values

# _______ Plotting _______
# Plot setosas in 2D feature space and mark with circles.
plt.scatter(X[:50, 0], X[:50, 1], color='red', marker='o', label='setosa') # X[row_indexer, col_indexer]
# Plot setosas in 2D feature space and mark with circles.
plt.scatter(X[50:100, 0], X[50:100, 1], color='blue', marker='x', label='versicolor')
plt.xlabel('sepal length')
plt.ylabel('petal length')
plt.legend(loc='upper left')
plt.show()

# Step 4 : Train the perceptron and make plots. 
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 misclassifications')
plt.show()

# Figure above shows that convergence occurred after 6th epoch. 
# Implement awesome visualization function for decision boundaries of 2D datasets.
from matplotlib.colors import ListedColormap

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))])
    
    # Get the min/max (of each) feature values in the dataset. 
    x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1 
    x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1
   
    # Syntax overview:
    # (1) np.arange(start, stop, step) // Note: step will be nx or ny in meshgrid comment below.
    # (2) np.meshgrid(x, y):
    # ----> Input: x, y are arrays of length (nx, ny) respectively. 
    # ----> Returns: Two arrays, each with shape (ny, nx):
    # --------> xx1 = NY number of copies of the input array X. 
    # --------> xx2 = NY number of arrays where the ith array is the ith y-value from input Y, NX times.
    xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution), 
                          np.arange(x2_min, x2_max, resolution)) 
    
    # Assign class prediction on matrix grid of POSSIBLE (x1, x2) values (no real corresp with data yet). 
    # np.ravel() is basically np.flatten() except doesn't make a copy, but rather keeps original in some sense.
    Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
    Z = Z.reshape(xx1.shape)
    
    plt.contourf(xx1, xx2, Z, alpha=0.4, 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=cmap(idx), 
                    marker=markers[idx], label=cl)

# Draw a contour plot that maps different decision regions to different colors for each predicted class
# in the grid array. 
plot_decision_regions(X, y, classifier=ppn)
plt.xlabel('sepal length [cm]')
plt.ylabel('petal length [cm]')
plt.legend(loc='upper left')
plt.show()

# Implementation of ADALINE. (see perceptron class for more descriptive comments)
class AdalineGD(object):
    """ ADAptive LInear NEuron classifier. """
    def __init__(self, eta=0.01, n_iter=50):
        self.eta = eta
        self.n_iter = n_iter
        
    def fit(self, X, y):
        """ Learn the weights. """
        self.w_ = np.zeros(1 + X.shape[1])
        self.cost_ = []
        for _ in range(self.n_iter):
            # Output == np.array(all dot prods corresp. to all samples)
            output = self.net_input(X)
            # Obtain array of all differences y(i) - phi(z(i)) at once. J
            errors = (y - output) 
            # Weight update. Note:
            # X.T.dot(errors) is sum of input x^i vecs multiplied by scalar difference y^i - phi(z^i). 
            # So the weight vector is updated by summing over (samp_i predict err) * (sample i), 
            # and thus each _individual_ weight is updated by (samp_i predict err) * (jth feat of samp i)
            self.w_[1:] += self.eta * X.T.dot(errors)
            self.w_[0] += self.eta * errors.sum() # sum bc. sum(x) == x^T * (vec of ones)
            cost = (errors**2).sum() / 2.0
            self.cost_.append(cost)
        return self
    
    def net_input(self, X):
        """ Returns vector of dot products between samples and current weights. """
        return np.dot(X, self.w_[1:]) + self.w_[0]
    
    def activation(self, X):
        """ Adaline activation is the identity function. """
        return self.net_input(X)
    
    def predict(self, X):
        return np.where(self.activation(X) >= 0.0, 1, -1)

# Plot the cost against the number of epochs for two different learning rates.
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(12, 6))

# High learning rate will overshoot the global minimum by so much each update, that it will end up
# on the other side of the parabola at a higher value, thus doing the opposite of minimizing basically.
ada1 = AdalineGD(eta=0.01, n_iter=100).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(eta=0.0001, n_iter=100).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.show()

# Implement standardization with numpy methods 'mean' and 'std'. 
X_std = np.copy(X) # read "X standardized"
X_std[:, 0] = (X[:,0] - X[:,0].mean()) / X[:,0].std()
X_std[:, 1] = (X[:,1] - X[:,1].mean()) / X[:,1].std()

# Train the adaline again and see that is now converges with a learning rate of 0.01.
ada = AdalineGD(n_iter=15, eta=0.01).fit(X_std, y) # arg order doesn't matter??
plot_decision_regions(X_std, y, classifier=ada)
plt.title('Adaline - Gradient descent')
plt.xlabel('sepal length [standardized]')
plt.ylabel('petal legth [standardized]')
plt.legend(loc='upper left')
plt.show()

plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('Sum-squared-error')
plt.show()