feat: Add supporting code for visualizing graphs

File contains additional code provided by Udacity necessary to visualize the graphs in the project

visuals.py

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+###########################################
+# Suppress matplotlib user warnings
+# Necessary for newer version of matplotlib
+import warnings
+warnings.filterwarnings("ignore", category = UserWarning, module = "matplotlib")
+#
+# Display inline matplotlib plots with IPython
+from IPython import get_ipython
+get_ipython().run_line_magic('matplotlib', 'inline')
+###########################################
+
+import matplotlib.pyplot as plt
+import matplotlib.cm as cm
+import pandas as pd
+import numpy as np
+
+def pca_results(good_data, pca):
+	'''
+	Create a DataFrame of the PCA results
+	Includes dimension feature weights and explained variance
+	Visualizes the PCA results
+	'''
+
+	# Dimension indexing
+	dimensions = dimensions = ['Dimension {}'.format(i) for i in range(1,len(pca.components_)+1)]
+
+	# PCA components
+	components = pd.DataFrame(np.round(pca.components_, 4), columns = good_data.keys())
+	components.index = dimensions
+
+	# PCA explained variance
+	ratios = pca.explained_variance_ratio_.reshape(len(pca.components_), 1)
+	variance_ratios = pd.DataFrame(np.round(ratios, 4), columns = ['Explained Variance'])
+	variance_ratios.index = dimensions
+
+	# Create a bar plot visualization
+	fig, ax = plt.subplots(figsize = (14,8))
+
+	# Plot the feature weights as a function of the components
+	components.plot(ax = ax, kind = 'bar');
+	ax.set_ylabel("Feature Weights")
+	ax.set_xticklabels(dimensions, rotation=0)
+
+
+	# Display the explained variance ratios
+	for i, ev in enumerate(pca.explained_variance_ratio_):
+		ax.text(i-0.40, ax.get_ylim()[1] + 0.05, "Explained Variance\n          %.4f"%(ev))
+
+	# Return a concatenated DataFrame
+	return pd.concat([variance_ratios, components], axis = 1)
+
+def cluster_results(reduced_data, preds, centers, pca_samples):
+	'''
+	Visualizes the PCA-reduced cluster data in two dimensions
+	Adds cues for cluster centers and student-selected sample data
+	'''
+
+	predictions = pd.DataFrame(preds, columns = ['Cluster'])
+	plot_data = pd.concat([predictions, reduced_data], axis = 1)
+
+	# Generate the cluster plot
+	fig, ax = plt.subplots(figsize = (14,8))
+
+	# Color map
+	cmap = cm.get_cmap('gist_rainbow')
+
+	# Color the points based on assigned cluster
+	for i, cluster in plot_data.groupby('Cluster'):   
+	    cluster.plot(ax = ax, kind = 'scatter', x = 'Dimension 1', y = 'Dimension 2', \
+	                 color = cmap((i)*1.0/(len(centers)-1)), label = 'Cluster %i'%(i), s=30);
+
+	# Plot centers with indicators
+	for i, c in enumerate(centers):
+	    ax.scatter(x = c[0], y = c[1], color = 'white', edgecolors = 'black', \
+	               alpha = 1, linewidth = 2, marker = 'o', s=200);
+	    ax.scatter(x = c[0], y = c[1], marker='$%d$'%(i), alpha = 1, s=100);
+
+	# Plot transformed sample points 
+	ax.scatter(x = pca_samples[:,0], y = pca_samples[:,1], \
+	           s = 150, linewidth = 4, color = 'black', marker = 'x');
+
+	# Set plot title
+	ax.set_title("Cluster Learning on PCA-Reduced Data - Centroids Marked by Number\nTransformed Sample Data Marked by Black Cross");
+
+
+def biplot(good_data, reduced_data, pca):
+    '''
+    Produce a biplot that shows a scatterplot of the reduced
+    data and the projections of the original features.
+    
+    good_data: original data, before transformation.
+               Needs to be a pandas dataframe with valid column names
+    reduced_data: the reduced data (the first two dimensions are plotted)
+    pca: pca object that contains the components_ attribute
+
+    return: a matplotlib AxesSubplot object (for any additional customization)
+    
+    This procedure is inspired by the script:
+    https://github.com/teddyroland/python-biplot
+    '''
+
+    fig, ax = plt.subplots(figsize = (14,8))
+    # scatterplot of the reduced data    
+    ax.scatter(x=reduced_data.loc[:, 'Dimension 1'], y=reduced_data.loc[:, 'Dimension 2'], 
+        facecolors='b', edgecolors='b', s=70, alpha=0.5)
+
+    feature_vectors = pca.components_.T
+
+    # we use scaling factors to make the arrows easier to see
+    arrow_size, text_pos = 7.0, 8.0,
+
+    # projections of the original features
+    for i, v in enumerate(feature_vectors):
+        ax.arrow(0, 0, arrow_size*v[0], arrow_size*v[1], 
+                  head_width=0.2, head_length=0.2, linewidth=2, color='red')
+        ax.text(v[0]*text_pos, v[1]*text_pos, good_data.columns[i], color='black', 
+                 ha='center', va='center', fontsize=18)
+
+    ax.set_xlabel("Dimension 1", fontsize=14)
+    ax.set_ylabel("Dimension 2", fontsize=14)
+    ax.set_title("PC plane with original feature projections.", fontsize=16);
+    return ax
+
+
+def channel_results(reduced_data, outliers, pca_samples):
+	'''
+	Visualizes the PCA-reduced cluster data in two dimensions using the full dataset
+	Data is labeled by "Channel" and cues added for student-selected sample data
+	'''
+
+	# Check that the dataset is loadable
+	try:
+	    full_data = pd.read_csv("customers.csv")
+	except:
+	    print "Dataset could not be loaded. Is the file missing?"
+	    return False
+
+	# Create the Channel DataFrame
+	channel = pd.DataFrame(full_data['Channel'], columns = ['Channel'])
+	channel = channel.drop(channel.index[outliers]).reset_index(drop = True)
+	labeled = pd.concat([reduced_data, channel], axis = 1)
+
+	# Generate the cluster plot
+	fig, ax = plt.subplots(figsize = (14,8))
+
+	# Color map
+	cmap = cm.get_cmap('gist_rainbow')
+
+	# Color the points based on assigned Channel
+	labels = ['Hotel/Restaurant/Cafe', 'Retailer']
+	grouped = labeled.groupby('Channel')
+	for i, channel in grouped:   
+	    channel.plot(ax = ax, kind = 'scatter', x = 'Dimension 1', y = 'Dimension 2', \
+	                 color = cmap((i-1)*1.0/2), label = labels[i-1], s=30);
+
+	# Plot transformed sample points   
+	for i, sample in enumerate(pca_samples):
+		ax.scatter(x = sample[0], y = sample[1], \
+	           s = 200, linewidth = 3, color = 'black', marker = 'o', facecolors = 'none');
+		ax.scatter(x = sample[0]+0.25, y = sample[1]+0.3, marker='$%d$'%(i), alpha = 1, s=125);
+
+	# Set plot title
+	ax.set_title("PCA-Reduced Data Labeled by 'Channel'\nTransformed Sample Data Circled");