10_kmeans_class_exercise.py

'''
CLUSTER ANALYSIS
How do we implement a k-means clustering algorithm?

scikit-learn KMeans documentation for reference:
http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html
'''

from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
from sklearn import datasets
import pandas as pd
import numpy as np

# ------------------------------------------
# EXERCISE: Compute the centoid of the following data
#           [2, 5], [4, 4], [3, 3]
# ------------------------------------------

d = np.array([[2, 5], [4, 4], [3, 3]])
# ANSWER HERE







x, y = d.mean(axis=0)

x, y # (3, 4)

# Import iris data
iris = datasets.load_iris()
d = iris.data

np.random.seed(0)

# Run KMeans using 3 clusters
est = KMeans(n_clusters=3, init='random')
est.fit(d)
y_kmeans = est.predict(d)

colors = np.array(['#FF0054','#FBD039','#23C2BC'])
plt.figure()
plt.scatter(d[:, 2], d[:, 0], c=colors[y_kmeans], s=50)
plt.xlabel(iris.feature_names[2])
plt.ylabel(iris.feature_names[0])

# ------------------------------------------
# Find the centers and plot them 
#     on the same graph.
# ------------------------------------------

centers = est.cluster_centers_
plt.scatter(centers[:, 2], centers[:, 0], c='k', linewidths=3,
            marker='+', s=300)

'''
VISUALIZING THE CLUSTERS
What are some different options to visualize 
multi-dimensional data? Let's look at three ways you can do this.
- Scatter Plot Grid
- 3D Plot
- Parallel Coordinates
'''

#================================
# Option #1: Scatter Plot Grid
plt.figure(figsize=(8, 8))
plt.suptitle('Scatter Plot Grid',  fontsize=14)
# Upper Left
plt.subplot(221)
plt.scatter(d[:,2], d[:,0], c = colors[y_kmeans])
plt.ylabel(iris.feature_names[0])

# Upper Right
plt.subplot(222)
plt.scatter(d[:,3], d[:,0], c = colors[y_kmeans])

# Lower Left
plt.subplot(223)
plt.scatter(d[:,2], d[:,1], c = colors[y_kmeans])
plt.ylabel(iris.feature_names[1])
plt.xlabel(iris.feature_names[2])

# Lower Right
plt.subplot(224)
plt.scatter(d[:,3], d[:,1], c = colors[y_kmeans])
plt.xlabel(iris.feature_names[3])

#================================
# Option #2: 3d plot
from mpl_toolkits.mplot3d import Axes3D
plt.suptitle('3d plot', fontsize=15)
ax = Axes3D(plt.figure(figsize=(10, 9)), rect=[.01, 0, 0.95, 1], elev=30, azim=134)
ax.scatter(d[:,0], d[:,1], d[:,2], c = colors[y_kmeans], s=120)
ax.set_xlabel('Sepal Width')
ax.set_ylabel('Sepal Width')
ax.set_zlabel('Petal Length')
# Modified from the example here: 
# http://scikit-learn.org/stable/auto_examples/cluster/plot_cluster_iris.html

# ---------------------------------------
# EXERCISE: Create a Parallel Coordinates 
#           visualization with the classes
# ---------------------------------------


#================================
# Option 3: Parallel Coordinates

from pandas.tools.plotting import parallel_coordinates
# I'm going to convert to a pandas dataframe
# Using a snippet of code we learned from one of Kevin's lectures!
features = [name[:-5].title().replace(' ', '') for name in iris.feature_names]
iris_df = pd.DataFrame(iris.data, columns = features)
iris_df['Name'] = iris.target_names[iris.target]
parallel_coordinates(data=iris_df, class_column='Name', 
                     colors=('#FF0054', '#FBD039', '#23C2BC'))
                     
'''
DETERMINING THE NUMBER OF CLUSTERS
How do you choose k? There isn't a bright line, but we can evaluate 
performance metrics such as the silhouette coefficient and within sum of 
squared errors across values of k.

scikit-learn Clustering metrics documentation:
http://scikit-learn.org/stable/modules/classes.html#clustering-metrics
'''

# Create a bunch of different models
k_rng = range(1,15)
est = [KMeans(n_clusters = k).fit(d) for k in k_rng]

#================================
# Option 1: Silhouette Coefficient
# Generally want SC to be closer to 1, while also minimizing k

from sklearn import metrics
silhouette_scores = [metrics.silhouette_score(d, e.labels_, metric='euclidean') for e in est[1:]]

silhouette_scores

# Plot the results
plt.figure(figsize=(7, 8))
plt.subplot(211)
plt.title('Using the elbow method to inform k choice')
plt.plot(k_rng[1:], silhouette_scores, 'b*-')
plt.xlim([1,15])
plt.grid(True)
plt.ylabel('Silhouette Coefficient')
plt.plot(3,silhouette_scores[1], 'o', markersize=12, markeredgewidth=1.5,
         markerfacecolor='None', markeredgecolor='r')

# -----------------------------------------------------
# EXERCISE: Calculate the within sum of squared errors 
#           and plot over a range of k
# -----------------------------------------------------


#================================
# Option 2: Within Sum of Squares (a.k.a., inertia)
# Generally want to minimize WSS, while also minimizing k

within_sum_squares = [e.inertia_ for e in est]

within_sum_squares


# Plot the results
plt.plot(k_rng, within_sum_squares, 'b*-')
plt.xlim([1,15])
plt.grid(True)
plt.xlabel('k')
plt.ylabel('Within Sum of Squares')
plt.plot(3,within_sum_squares[2], 'ro', markersize=12, markeredgewidth=1.5,
         markerfacecolor='None', markeredgecolor='r')
         
         
# Without using the "species column" the data are
# telling us that three is the optimal number of clusters!