Welcome to the third project of the Machine Learning Engineer Nanodegree! In this notebook, some template code has already been provided for you, and it will be your job to implement the additional functionality necessary to successfully complete this project. Sections that begin with 'Implementation' in the header indicate that the following block of code will require additional functionality which you must provide. Instructions will be provided for each section and the specifics of the implementation are marked in the code block with a 'TODO' statement. Please be sure to read the instructions carefully!
In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a 'Question X' header. Carefully read each question and provide thorough answers in the following text boxes that begin with 'Answer:'. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.
Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.
Getting Started¶
In this project, you will analyze a dataset containing data on various customers' annual spending amounts (reported in monetary units) of diverse product categories for internal structure. One goal of this project is to best describe the variation in the different types of customers that a wholesale distributor interacts with. Doing so would equip the distributor with insight into how to best structure their delivery service to meet the needs of each customer.
The dataset for this project can be found on the UCI Machine Learning Repository. For the purposes of this project, the features 'Channel' and 'Region' will be excluded in the analysis — with focus instead on the six product categories recorded for customers.
Run the code block below to load the wholesale customers dataset, along with a few of the necessary Python libraries required for this project. You will know the dataset loaded successfully if the size of the dataset is reported.
# Import libraries necessary for this project
import numpy as np
import pandas as pd
from IPython.display import display # Allows the use of display() for DataFrames
# Import supplementary visualizations code visuals.py
import visuals as vs
# Pretty display for notebooks
%matplotlib inline
# Load the wholesale customers dataset
try:
data = pd.read_csv("customers.csv")
data.drop(['Region', 'Channel'], axis = 1, inplace = True)
print "Wholesale customers dataset has {} samples with {} features each.".format(*data.shape)
except:
print "Dataset could not be loaded. Is the dataset missing?"
Data Exploration¶
In this section, you will begin exploring the data through visualizations and code to understand how each feature is related to the others. You will observe a statistical description of the dataset, consider the relevance of each feature, and select a few sample data points from the dataset which you will track through the course of this project.
Run the code block below to observe a statistical description of the dataset. Note that the dataset is composed of six important product categories: 'Fresh', 'Milk', 'Grocery', 'Frozen', 'Detergents_Paper', and 'Delicatessen'. Consider what each category represents in terms of products you could purchase.
# Display a description of the dataset
display(data.describe())
# previewing the data
display(data.head())
# data ordered by the mean
display(data.mean().sort_values(ascending = False))
# checking if there is NaN
data.isnull().any().any()
# Mean and standard error sorted
import seaborn as sns
import matplotlib.pyplot as plt
ax = sns.barplot(data=data, order=['Fresh', 'Grocery', 'Milk', 'Frozen',
'Detergents_Paper', 'Delicatessen'])
plt.title('Mean and standard error')
# horizontal box plot
import seaborn as sns
import matplotlib.pyplot as plt
ax = sns.boxplot(data=data, order=['Fresh', 'Grocery', 'Milk', 'Frozen',
'Detergents_Paper', 'Delicatessen'], orient='h')
plt.title('horizontal box plot')
# points adjusted so that they don’t overlap
ax = sns.swarmplot(data=data, order=['Fresh', 'Grocery', 'Milk', 'Frozen',
'Detergents_Paper', 'Delicatessen'], orient='h')
plt.title('swarmplot')
# shows the distribution of quantitative data
ax = sns.violinplot(data=data, order=['Fresh', 'Grocery', 'Milk', 'Frozen',
'Detergents_Paper', 'Delicatessen'], orient='h')
ax = sns.stripplot(data=data, order=['Fresh', 'Grocery', 'Milk', 'Frozen',
'Detergents_Paper', 'Delicatessen'],
orient='h', color='white', edgecolor="gray")
plt.title('violinplot with stripplot', fontsize='small')
Implementation: Selecting Samples¶
To get a better understanding of the customers and how their data will transform through the analysis, it would be best to select a few sample data points and explore them in more detail. In the code block below, add three indices of your choice to the indices list which will represent the customers to track. It is suggested to try different sets of samples until you obtain customers that vary significantly from one another.
# selecting samples with pandas loc
data.loc[[1, 100, 200, 300, 439],:]
Interpreting box plots:¶
Fresh: Highest mean and highest dispersion.
Milk and Grocery: Similar mean and distribution, except grocery present more variance
Frozen and Detergents_Paper: Similar mean and distribution, positive skew
Delicatessen: Lowest mean, low variance.
All categories present outliers.
# High fresh and high grocery and very low frozen
q3_fresh = data.describe()['Fresh']['75%']
q3_grocery = data.describe()['Grocery']['75%']
q1_frozen = data.describe()['Frozen']['25%']
samples_1 = data[(data.Fresh > q3_fresh) & (data.Grocery > q3_grocery) &
(data.Frozen < q1_frozen)]
sample_1 = samples_1.sample(n=1, replace=True, random_state=2)
print sample_1
# High frozen and low fresh
q3_frozen = data.describe()['Frozen']['75%']
q1_fresh = data.describe()['Fresh']['25%']
samples_2 = data[(data.Frozen > q3_frozen) & (data.Fresh < q1_fresh )]
sample_2 = samples_2.sample(n=1, replace=True, random_state=2)
print sample_2
# high milk and delicatessen. low detergents_paper
q3_milk = data.describe()['Milk']['75%']
q3_delicatessen = data.describe()['Delicatessen']['75%']
q1_detergents_paper = data.describe()['Detergents_Paper']['25%']
samples_3 = data[(data.Grocery > q3_grocery) & (data.Delicatessen > q3_delicatessen)
& (data.Detergents_Paper < q1_detergents_paper)]
sample_3 = samples_3.sample(n=1, replace=True, random_state=2)
print sample_3
# TODO: Select three indices of your choice you wish to sample from the dataset
indices = [12, 339, 183]
# Create a DataFrame of the chosen samples
samples = pd.DataFrame(data.loc[indices], columns = data.keys()).reset_index(drop = True)
print "Chosen samples of wholesale customers dataset:"
display(samples)
# Comparing samples
ax = sns.heatmap(samples)
Question 1¶
Consider the total purchase cost of each product category and the statistical description of the dataset above for your sample customers.
What kind of establishment (customer) could each of the three samples you've chosen represent?
Hint: Examples of establishments include places like markets, cafes, and retailers, among many others. Avoid using names for establishments, such as saying "McDonalds" when describing a sample customer as a restaurant.
Answer:
- Sample 0 (index=12):
High spending in: Fresh
Low spending in: Frozen Detergents_Paper Delicatessen
Represented establishment: Maybe a fresh food market with perhaps milk or some grocery stores
- Sample 1 (index=339):
High spending in: Frozen
Low spending in: Most of the other categories
Represented establishment: An all frozen store, that sells from frozen vegetables to frozen meals
- Sample 2 (index=183):
High spending in: Delicatessen Milk
Low spending in: Detergents_Paper Grocery
Represented establishment: Definitely a bar that sells a selection of unusual foods, cakes, cofee, etc.
Implementation: Feature Relevance¶
One interesting thought to consider is if one (or more) of the six product categories is actually relevant for understanding customer purchasing. That is to say, is it possible to determine whether customers purchasing some amount of one category of products will necessarily purchase some proportional amount of another category of products? We can make this determination quite easily by training a supervised regression learner on a subset of the data with one feature removed, and then score how well that model can predict the removed feature.
In the code block below, you will need to implement the following:
- Assign
new_dataa copy of the data by removing a feature of your choice using theDataFrame.dropfunction. - Use
sklearn.cross_validation.train_test_splitto split the dataset into training and testing sets.- Use the removed feature as your target label. Set a
test_sizeof0.25and set arandom_state.
- Use the removed feature as your target label. Set a
- Import a decision tree regressor, set a
random_state, and fit the learner to the training data. - Report the prediction score of the testing set using the regressor's
scorefunction.
categories = data.keys()
for categorie in categories:
print categorie
# look trhough all categories
categories = data.keys()
for category in categories:
# TODO: Make a copy of the DataFrame, using the 'drop' function to drop the given feature
new_data = data.drop(category, axis = 1)
target = data[category]
# TODO: Split the data into training and testing sets using the given feature as the target
from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(
new_data, target, test_size=0.2, random_state=2
)
# TODO: Create a decision tree regressor and fit it to the training set
from sklearn.tree import DecisionTreeRegressor
regressor = DecisionTreeRegressor(random_state = 2)
regressor.fit(X_train, y_train)
# TODO: Report the score of the prediction using the testing set
from sklearn.metrics import r2_score
score = regressor.score(X_test, y_test)
print 'r2 score for {} is: {}'.format(category, score)
Question 2¶
Which feature did you attempt to predict? What was the reported prediction score? Is this feature is necessary for identifying customers' spending habits?
Hint: The coefficient of determination, R^2, is scored between 0 and 1, with 1 being a perfect fit. A negative R^2 implies the model fails to fit the data.
Answer:
I first attempted to predict Delicatessen and I got a negative r2 value of -2.676. Then I calculated r2 for every individual category. r2 score is higher in Grocery, Milk and Detergents_Paper so these categories are correlated with some or with all of the remaining five categories. And Fresh, Frozen and Delicatessen are not, meaning this predictor variables are necessary for identifying the costumers spending habits.
Visualize Feature Distributions¶
To get a better understanding of the dataset, we can construct a scatter matrix of each of the six product features present in the data. If you found that the feature you attempted to predict above is relevant for identifying a specific customer, then the scatter matrix below may not show any correlation between that feature and the others. Conversely, if you believe that feature is not relevant for identifying a specific customer, the scatter matrix might show a correlation between that feature and another feature in the data. Run the code block below to produce a scatter matrix.
# Produce a scatter matrix for each pair of features in the data
axes = pd.scatter_matrix(data, alpha = 0.3, figsize = (14,8), diagonal = 'kde')
# Reformat data.corr() for plotting
corr = data.corr().as_matrix()
# Plot scatter matrix with correlations
for i,j in zip(*np.triu_indices_from(axes, k=1)):
axes[i,j].annotate("%.2f"%corr[i,j], (0.8,0.8), xycoords='axes fraction')
# correlation between the categories
data.corr()
# seaborn heatmap showing the correlation between the categories
ax = sns.heatmap(data.corr())
# symmetric analysis, if value > 20 then skewed
categories = data.keys()
for category in categories:
data_analysis = data[category]
symmetric_value = int(abs((data_analysis.mean() - data_analysis.median())
/ data_analysis.std()) * 100)
print 'symmetric value for {} is: {}'.format(category, symmetric_value)
Question 3¶
Are there any pairs of features which exhibit some degree of correlation? Does this confirm or deny your suspicions about the relevance of the feature you attempted to predict? How is the data for those features distributed?
Hint: Is the data normally distributed? Where do most of the data points lie?
Answer:
There some pairs of data that show some correlation in the scatter matrix:
Milk - Detergents_Paper
Milk - Grocery
Grocery - Detergents_Paper
Those correlations can be confirmed observing the correlation table and the correlation heat map.
It confirms my suspicion since there is no category to which Delicatessen is correlated. The features show positive-skew distributions. This is also confirmed by the fact that the symmetric values for all the features are higher than 20, what means the distribution is skewed.
Data Preprocessing¶
In this section, you will preprocess the data to create a better representation of customers by performing a scaling on the data and detecting (and optionally removing) outliers. Preprocessing data is often times a critical step in assuring that results you obtain from your analysis are significant and meaningful.
Implementation: Feature Scaling¶
If data is not normally distributed, especially if the mean and median vary significantly (indicating a large skew), it is most often appropriate to apply a non-linear scaling — particularly for financial data. One way to achieve this scaling is by using a Box-Cox test, which calculates the best power transformation of the data that reduces skewness. A simpler approach which can work in most cases would be applying the natural logarithm.
In the code block below, you will need to implement the following:
- Assign a copy of the data to
log_dataafter applying logarithmic scaling. Use thenp.logfunction for this. - Assign a copy of the sample data to
log_samplesafter applying logarithmic scaling. Again, usenp.log.
# TODO: Scale the data using the natural logarithm
log_data = np.log(data)
# TODO: Scale the sample data using the natural logarithm
log_samples = np.log(samples)
# Produce a scatter matrix for each pair of newly-transformed features
pd.scatter_matrix(log_data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');
# correlation between transformed features
log_data.corr()
# seaborn heatmap showing the correlation between the categories
ax = sns.heatmap(log_data.corr())
# symmetric analysis transformed features, if value < 10 then symmetric
categories = log_data.keys()
for category in categories:
data_analysis = log_data[category]
symmetric_value = int(abs((data_analysis.mean() - data_analysis.median())
/ data_analysis.std()) * 100)
print 'symmetric value for {} is: {}'.format(category, symmetric_value)
Observation¶
After applying a natural logarithm scaling to the data, the distribution of each feature should appear much more normal. For any pairs of features you may have identified earlier as being correlated, observe here whether that correlation is still present (and whether it is now stronger or weaker than before).
Run the code below to see how the sample data has changed after having the natural logarithm applied to it.
# Display the log-transformed sample data
display(log_samples)
Correlation changes¶
Milk - Detergents_Pape and Milk - Grocery: stronger correlations
Grocery - Detergents_Paper: weaker correlation
Implementation: Outlier Detection¶
Detecting outliers in the data is extremely important in the data preprocessing step of any analysis. The presence of outliers can often skew results which take into consideration these data points. There are many "rules of thumb" for what constitutes an outlier in a dataset. Here, we will use Tukey's Method for identfying outliers: An outlier step is calculated as 1.5 times the interquartile range (IQR). A data point with a feature that is beyond an outlier step outside of the IQR for that feature is considered abnormal.
In the code block below, you will need to implement the following:
- Assign the value of the 25th percentile for the given feature to
Q1. Usenp.percentilefor this. - Assign the value of the 75th percentile for the given feature to
Q3. Again, usenp.percentile. - Assign the calculation of an outlier step for the given feature to
step. - Optionally remove data points from the dataset by adding indices to the
outlierslist.
NOTE: If you choose to remove any outliers, ensure that the sample data does not contain any of these points!
Once you have performed this implementation, the dataset will be stored in the variable good_data.
# pandas percentile
print log_data.describe()['Fresh']['25%']
# numpy percentile
print np.percentile(log_data['Fresh'], 25)
# For each feature find the data points with extreme high or low values
all_outliers = []
for feature in log_data.keys():
# TODO: Calculate Q1 (25th percentile of the data) for the given feature
Q1 = np.percentile(log_data[feature], 25)
# TODO: Calculate Q3 (75th percentile of the data) for the given feature
Q3 = np.percentile(log_data[feature], 75)
# TODO: Use the interquartile range to calculate an outlier step (1.5 times the interquartile range)
IQR = Q3 - Q1
step = 1.5 * IQR
# Display the outliers
print "Data points considered outliers for the feature '{}':".format(feature)
display(log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))])
all_outliers.append(log_data[~((log_data[feature] >= Q1 - step) &
(log_data[feature] <= Q3 + step))].index.values)
outliers = pd.Series(np.concatenate(all_outliers))
duplicated_outliers = np.array(outliers[outliers.duplicated()])
print "duplicated outliers: \n{}".format(duplicated_outliers)
# Remove the outliers, if any were specified
good_data = log_data.drop(log_data.index[outliers]).reset_index(drop = True)
Question 4¶
Are there any data points considered outliers for more than one feature based on the definition above? Should these data points be removed from the dataset? If any data points were added to the outliers list to be removed, explain why.
Answer:
Yes, the following datapoints are considered outliers in one or more categories: [154 65 75 66 128 154].
Yes, these datapoints are outliers and should be removed because k-means clustering is very sensitive to the presence of these values.
All the outliers detected were added to the outliers list because k-means can be quite sensitive to outliers because it tries to optimize the sum of squares.
Feature Transformation¶
In this section you will use principal component analysis (PCA) to draw conclusions about the underlying structure of the wholesale customer data. Since using PCA on a dataset calculates the dimensions which best maximize variance, we will find which compound combinations of features best describe customers.
Implementation: PCA¶
Now that the data has been scaled to a more normal distribution and has had any necessary outliers removed, we can now apply PCA to the good_data to discover which dimensions about the data best maximize the variance of features involved. In addition to finding these dimensions, PCA will also report the explained variance ratio of each dimension — how much variance within the data is explained by that dimension alone. Note that a component (dimension) from PCA can be considered a new "feature" of the space, however it is a composition of the original features present in the data.
In the code block below, you will need to implement the following:
- Import
sklearn.decomposition.PCAand assign the results of fitting PCA in six dimensions withgood_datatopca. - Apply a PCA transformation of
log_samplesusingpca.transform, and assign the results topca_samples.
# TODO: Apply PCA by fitting the good data with the same number of dimensions as features
from sklearn.decomposition import PCA
pca = PCA(n_components=6, random_state=2)
pca.fit(good_data)
# TODO: Transform log_samples using the PCA fit above
pca_samples = pca.transform(log_samples)
# Generate PCA results plot
pca_results = vs.pca_results(good_data, pca)
# calculate cummulative sum of explained variance
print pca_results['Explained Variance'].cumsum()
Question 5¶
How much variance in the data is explained in total by the first and second principal component? What about the first four principal components? Using the visualization provided above, discuss what the first four dimensions best represent in terms of customer spending.
Hint: A positive increase in a specific dimension corresponds with an increase of the positive-weighted features and a decrease of the negative-weighted features. The rate of increase or decrease is based on the indivdual feature weights.
Answer:
The total variance explained by the first and second principal component is 0.7252.
The total variance explained by the four principal component is 0.9279.
Representation of the first four principal components:
First PC: A positive increase in the first PC would represent an increase in: Grocery, Milk and Detergents_Paper. This finding corroborate our previous hypothesis that these three features were correlated.
Second PC: A positive increase in the second PC would represent an increase in: Frozen, Fresh and Delicatessen.
Third PC: A positive increase would represent an increase in: Delicatessen and a decrease in: Fresh.
Fourth PC: A positive increase would represent an increase in: Delicatessen and a decrease in: Frozen.
Observation¶
Run the code below to see how the log-transformed sample data has changed after having a PCA transformation applied to it in six dimensions. Observe the numerical value for the first four dimensions of the sample points. Consider if this is consistent with your initial interpretation of the sample points.
# Display sample log-data after having a PCA transformation applied
display(pd.DataFrame(np.round(pca_samples, 4), columns = pca_results.index.values))
# seaborn heatmap showing the correlation between samples and pca dimensions
ax = sns.heatmap(pd.DataFrame(np.round(pca_samples, 4), columns = pca_results.index.values))
Implementation: Dimensionality Reduction¶
When using principal component analysis, one of the main goals is to reduce the dimensionality of the data — in effect, reducing the complexity of the problem. Dimensionality reduction comes at a cost: Fewer dimensions used implies less of the total variance in the data is being explained. Because of this, the cumulative explained variance ratio is extremely important for knowing how many dimensions are necessary for the problem. Additionally, if a signifiant amount of variance is explained by only two or three dimensions, the reduced data can be visualized afterwards.
In the code block below, you will need to implement the following:
- Assign the results of fitting PCA in two dimensions with
good_datatopca. - Apply a PCA transformation of
good_datausingpca.transform, and assign the results toreduced_data. - Apply a PCA transformation of
log_samplesusingpca.transform, and assign the results topca_samples.
# TODO: Apply PCA by fitting the good data with only two dimensions
pca = PCA(n_components=2, random_state=2)
pca.fit(good_data)
# TODO: Transform the good data using the PCA fit above
reduced_data = pca.transform(good_data)
# TODO: Transform log_samples using the PCA fit above
pca_samples = pca.transform(log_samples)
# Create a DataFrame for the reduced data
reduced_data = pd.DataFrame(reduced_data, columns = ['Dimension 1', 'Dimension 2'])
# Produce a scatter matrix for pca reduced data
pd.scatter_matrix(reduced_data, alpha = 0.8, figsize = (8,4), diagonal = 'kde');
Observation¶
Run the code below to see how the log-transformed sample data has changed after having a PCA transformation applied to it using only two dimensions. Observe how the values for the first two dimensions remains unchanged when compared to a PCA transformation in six dimensions.
# Display sample log-data after applying PCA transformation in two dimensions
display(pd.DataFrame(np.round(pca_samples, 4), columns = ['Dimension 1', 'Dimension 2']))
Visualizing a Biplot¶
A biplot is a scatterplot where each data point is represented by its scores along the principal components. The axes are the principal components (in this case Dimension 1 and Dimension 2). In addition, the biplot shows the projection of the original features along the components. A biplot can help us interpret the reduced dimensions of the data, and discover relationships between the principal components and original features.
Run the code cell below to produce a biplot of the reduced-dimension data.
# Create a biplot
vs.biplot(good_data, reduced_data, pca)
Observation¶
Once we have the original feature projections (in red), it is easier to interpret the relative position of each data point in the scatterplot. For instance, a point the lower right corner of the figure will likely correspond to a customer that spends a lot on 'Milk', 'Grocery' and 'Detergents_Paper', but not so much on the other product categories.
From the biplot, which of the original features are most strongly correlated with the first component? What about those that are associated with the second component? Do these observations agree with the pca_results plot you obtained earlier?
Most correlated with the first PC: Milk, Grocery and Detergents_Paper
Most correlated with the second PC: Fresh, Frozen and Delicatessen
In concordance with previous observations
Clustering¶
In this section, you will choose to use either a K-Means clustering algorithm or a Gaussian Mixture Model clustering algorithm to identify the various customer segments hidden in the data. You will then recover specific data points from the clusters to understand their significance by transforming them back into their original dimension and scale.
Question 6¶
What are the advantages to using a K-Means clustering algorithm? What are the advantages to using a Gaussian Mixture Model clustering algorithm? Given your observations about the wholesale customer data so far, which of the two algorithms will you use and why?
Answer:
K-Means clustering: simple, generally faster and more efficient than other algorithms, especially over large datasets. The weaknesses of k-means are its sensitivity to outliers, and its sensitivity to the initial choice of centroids.
Gaussian Mixture Model clustering algorithm: flexibility due to clusters having unconstrained covariances and it allows mixed memberships, a point can belong to two clusters with different probability. Not scalable.
Optimizing the loss function for GMM is not trivial and GMM is more complicated to interpret. Furthermore, k-means is designed to operate on continuous data, and the two weakness of the model can be mitigated. All outliers have been removed and with parameters tunning n_init can be optimized.
Implementation: Creating Clusters¶
Depending on the problem, the number of clusters that you expect to be in the data may already be known. When the number of clusters is not known a priori, there is no guarantee that a given number of clusters best segments the data, since it is unclear what structure exists in the data — if any. However, we can quantify the "goodness" of a clustering by calculating each data point's silhouette coefficient. The silhouette coefficient for a data point measures how similar it is to its assigned cluster from -1 (dissimilar) to 1 (similar). Calculating the mean silhouette coefficient provides for a simple scoring method of a given clustering.
In the code block below, you will need to implement the following:
- Fit a clustering algorithm to the
reduced_dataand assign it toclusterer. - Predict the cluster for each data point in
reduced_datausingclusterer.predictand assign them topreds. - Find the cluster centers using the algorithm's respective attribute and assign them to
centers. - Predict the cluster for each sample data point in
pca_samplesand assign themsample_preds. - Import
sklearn.metrics.silhouette_scoreand calculate the silhouette score ofreduced_dataagainstpreds.- Assign the silhouette score to
scoreand print the result.
- Assign the silhouette score to
for n_clusters in range(2,20):
# TODO: Apply your clustering algorithm of choice to the reduced data
from sklearn.cluster import KMeans
clusterer = KMeans(n_clusters=n_clusters, random_state=2).fit(reduced_data)
# TODO: Predict the cluster for each data point
preds = clusterer.predict(reduced_data)
# TODO: Find the cluster centers
centers = clusterer.cluster_centers_
# TODO: Predict the cluster for each transformed sample data point
sample_preds = clusterer.predict(pca_samples)
# TODO: Calculate the mean silhouette coefficient for the number of clusters chosen
from sklearn import metrics
score = metrics.silhouette_score(reduced_data, preds, metric='euclidean')
print "mean silhouette coefficient for n_clusters = {} is: {:.3f}".format(n_clusters, score)
Question 7¶
Report the silhouette score for several cluster numbers you tried. Of these, which number of clusters has the best silhouette score?
Answer:
mean silhouette coefficient for n_clusters = 2 is: 0.447
mean silhouette coefficient for n_clusters = 3 is: 0.365
mean silhouette coefficient for n_clusters = 4 is: 0.331
mean silhouette coefficient for n_clusters = 5 is: 0.351
mean silhouette coefficient for n_clusters = 6 is: 0.364
mean silhouette coefficient for n_clusters = 7 is: 0.367
mean silhouette coefficient for n_clusters = 8 is: 0.374
mean silhouette coefficient for n_clusters = 9 is: 0.366
mean silhouette coefficient for n_clusters = 10 is: 0.348
mean silhouette coefficient for n_clusters = 11 is: 0.358
mean silhouette coefficient for n_clusters = 12 is: 0.359
mean silhouette coefficient for n_clusters = 13 is: 0.364
mean silhouette coefficient for n_clusters = 14 is: 0.354
mean silhouette coefficient for n_clusters = 15 is: 0.360
mean silhouette coefficient for n_clusters = 16 is: 0.342
mean silhouette coefficient for n_clusters = 17 is: 0.350
mean silhouette coefficient for n_clusters = 18 is: 0.352
mean silhouette coefficient for n_clusters = 19 is: 0.355
The number of clusters with the best silhouette score is 2.
Cluster Visualization¶
Once you've chosen the optimal number of clusters for your clustering algorithm using the scoring metric above, you can now visualize the results by executing the code block below. Note that, for experimentation purposes, you are welcome to adjust the number of clusters for your clustering algorithm to see various visualizations. The final visualization provided should, however, correspond with the optimal number of clusters.
# TODO: Apply your clustering algorithm of choice to the reduced data
from sklearn.cluster import KMeans
clusterer = KMeans(n_clusters=2, random_state=2).fit(reduced_data)
# TODO: Predict the cluster for each data point
preds = clusterer.predict(reduced_data)
# TODO: Find the cluster centers
centers = clusterer.cluster_centers_
# TODO: Predict the cluster for each transformed sample data point
sample_preds = clusterer.predict(pca_samples)
# Display the results of the clustering from implementation
vs.cluster_results(reduced_data, preds, centers, pca_samples)
Implementation: Data Recovery¶
Each cluster present in the visualization above has a central point. These centers (or means) are not specifically data points from the data, but rather the averages of all the data points predicted in the respective clusters. For the problem of creating customer segments, a cluster's center point corresponds to the average customer of that segment. Since the data is currently reduced in dimension and scaled by a logarithm, we can recover the representative customer spending from these data points by applying the inverse transformations.
In the code block below, you will need to implement the following:
- Apply the inverse transform to
centersusingpca.inverse_transformand assign the new centers tolog_centers. - Apply the inverse function of
np.logtolog_centersusingnp.expand assign the true centers totrue_centers.
# TODO: Inverse transform the centers
log_centers = pca.inverse_transform(centers)
# TODO: Exponentiate the centers
true_centers = np.exp(log_centers)
# Display the true centers
segments = ['Segment {}'.format(i) for i in range(0,len(centers))]
true_centers = pd.DataFrame(np.round(true_centers), columns = data.keys())
true_centers.index = segments
display(true_centers)
# deviation from the mean true centers - data
display(true_centers - data.mean().round())
# deviation from the median true centers - data
display(true_centers - data.median().round())
Question 8¶
Consider the total purchase cost of each product category for the representative data points above, and reference the statistical description of the dataset at the beginning of this project. What set of establishments could each of the customer segments represent?
Hint: A customer who is assigned to 'Cluster X' should best identify with the establishments represented by the feature set of 'Segment X'.
Answer:
Since the distribution before transformation is skewed Right / Positive, the median is more representative of the sample than the mean. Therefore, all references to the overall category spending will be done using the deviations from the median calculated above.
Segment 0 (left cluster):
Left side cluster center is higher than median in Frozen and Fresh. This customer segment could represent food markets with frozen and fresh food.
Segment 1 (right cluster):
Right side cluster center is higher than median spending in Milk, Grocery, & Detergents_Paper. This customer segment could represent Grocery stores.
Question 9¶
For each sample point, which customer segment from Question 8 best represents it? Are the predictions for each sample point consistent with this?
Run the code block below to find which cluster each sample point is predicted to be.
# Display the predictions
for i, pred in enumerate(sample_preds):
print "Sample point", i, "predicted to be in Cluster", pred
# heatmap for true centers
ax = sns.heatmap(true_centers)
plt.title('true centers heatmap', fontsize='small')
# heatmap for samples
ax = sns.heatmap(samples)
plt.title('samples heatmap', fontsize='small')
# deviation from the median samples - data
display(samples - data.median().round())
Answer:
Sample 0 (index=12): For Sample point 0, the values for Fresh are above average.
This mirrors the category spending for the Segment 0 center, so the predicted cluster seems not to be consistent with the sample.
Sample 1 (index=339):
For Sample point 1, the values for Frozen are above average.
This mirrors the category spending for the Segment 0 center, so the predicted cluster seems to be consistent with the sample.
Sample 2 (index=183):
For Sample point 2, the values for Delicatessen, Milk, Frozen and Fresh are above average.
This perhaps mirrors the category spending for the Segment 0 center, but it doesn't seem too clear to which segment belongs. This is corroborated by observing the Sample mark (higher mark) on the vs.cluster_results graph. The predicted cluster seems to be consistent with the sample.
Conclusion¶
In this final section, you will investigate ways that you can make use of the clustered data. First, you will consider how the different groups of customers, the customer segments, may be affected differently by a specific delivery scheme. Next, you will consider how giving a label to each customer (which segment that customer belongs to) can provide for additional features about the customer data. Finally, you will compare the customer segments to a hidden variable present in the data, to see whether the clustering identified certain relationships.
Question 10¶
Companies will often run A/B tests when making small changes to their products or services to determine whether making that change will affect its customers positively or negatively. The wholesale distributor is considering changing its delivery service from currently 5 days a week to 3 days a week. However, the distributor will only make this change in delivery service for customers that react positively. How can the wholesale distributor use the customer segments to determine which customers, if any, would react positively to the change in delivery service?
Hint: Can we assume the change affects all customers equally? How can we determine which group of customers it affects the most?
Answer:
Segment 0 is related to high spending in Milk, Grocery and Frozen. The costumers who bought mostly items from the first two categories may be impacted by changes in the delivery system.
Segment 1 is related to high spending in Grocery, Milk, Fresh. This group of costumers is more likely to be directly affected by changes in the delivery system.
To some random representative samples from the two segments, delivery changes may be made and surveys to this costumers will show further insight.
Question 11¶
Additional structure is derived from originally unlabeled data when using clustering techniques. Since each customer has a customer segment it best identifies with (depending on the clustering algorithm applied), we can consider 'customer segment' as an engineered feature for the data. Assume the wholesale distributor recently acquired ten new customers and each provided estimates for anticipated annual spending of each product category. Knowing these estimates, the wholesale distributor wants to classify each new customer to a customer segment to determine the most appropriate delivery service.
How can the wholesale distributor label the new customers using only their estimated product spending and the customer segment data?
Hint: A supervised learner could be used to train on the original customers. What would be the target variable?
Answer:
Indeed, a supervised learner like logistic regression, naive bayes, KNN, etc. could be used to predict which segment will represent more reliably the new costumers. The target variable will be the segment cluster.
Visualizing Underlying Distributions¶
At the beginning of this project, it was discussed that the 'Channel' and 'Region' features would be excluded from the dataset so that the customer product categories were emphasized in the analysis. By reintroducing the 'Channel' feature to the dataset, an interesting structure emerges when considering the same PCA dimensionality reduction applied earlier to the original dataset.
Run the code block below to see how each data point is labeled either 'HoReCa' (Hotel/Restaurant/Cafe) or 'Retail' the reduced space. In addition, you will find the sample points are circled in the plot, which will identify their labeling.
# Display the clustering results based on 'Channel' data
vs.channel_results(reduced_data, outliers, pca_samples)
# Display the clustering results based on 'Channel' data
vs.channel_results(reduced_data, outliers, centers)
Question 12¶
How well does the clustering algorithm and number of clusters you've chosen compare to this underlying distribution of Hotel/Restaurant/Cafe customers to Retailer customers? Are there customer segments that would be classified as purely 'Retailers' or 'Hotels/Restaurants/Cafes' by this distribution? Would you consider these classifications as consistent with your previous definition of the customer segments?
Answer:
The algorithm chosen has the same numbers of clusters and a somewhat similar distribution, therefore the clustering algorithm did well. The overall alignment is actually pretty good
Yes, as shown in the second graph in which the previous centroids were plotted, costumers corresponding to segment 0 are extremely likely to be classified as pure Hotels/Restaurants/Cafes.
These classifications are consistent with previous assumptions segment 0 fresh market can be indeed a restaurant instead and the segment 1 are classic retailer/grocery stores.