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.

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?"

Wholesale customers dataset has 440 samples with 6 features each.

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())

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.

# Select three indices of your choice you wish to sample from the dataset
indices = [39,56,71]

# 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)

Chosen samples of wholesale customers dataset:

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.

print 'Total purchase costs for each category:'
print data.sum()
print 'Average purchase costs for each category:'
print data.sum() / 440

# Visualize samples
import seaborn as sns
samples_bar = samples.append(data.describe().loc['mean'])
samples_bar.index = indices + ['mean']
_ = samples_bar.plot(kind='bar', figsize=(14,6))

Total purchase costs for each category:
Fresh               5280131
Milk                2550357
Grocery             3498562
Frozen              1351650
Detergents_Paper    1267857
Delicatessen         670943
dtype: int64
Average purchase costs for each category:
Fresh               12000.297727
Milk                 5796.265909
Grocery              7951.277273
Frozen               3071.931818
Detergents_Paper     2881.493182
Delicatessen         1524.870455
dtype: float64

Answer:

Establishment 1 is your typical fresh produce market, with a small selection of frozen foods. Compared to the mean, it needs significantly more Fresh foods (56159 vs 12000) and Frozen foods (10002 vs 3072).

Establishment 2 is your typical cafe or restaurant with a need for a variety of food staples, basic ingredients, and supplies for supporting customers that dine in or take out. A cafe might particularly use a lot more milk since they'll serve coffee. Compared to the mean, it needs significantly more Milk (29892 vs 5796), Grocery foods (26866 vs 7951), and Detergents_Paper (17740 vs 2881).

Establishment 3 is your typical deli, with a great diversty of food offerings, perhaps even a selection ethnic or unusual foods. Compared to the mean, it needs significantly more Delicatessen (14472 vs 1525) and Grocery foods (21042 vs 7951), and somewhat more Fresh foods (18291 vs 12000) than other establishments.

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_data a copy of the data by removing a feature of your choice using the DataFrame.drop function.
• Use sklearn.cross_validation.train_test_split to split the dataset into training and testing sets.
  • Use the removed feature as your target label. Set a test_size of 0.25 and set a random_state.
• 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 score function.

from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.tree import DecisionTreeRegressor

# Make a copy of the DataFrame, using the 'drop' function to drop the given feature
new_data = data.copy().drop('Detergents_Paper', 1)

# Split the data into training and testing sets using the given feature as the target
X_train, X_test, y_train, y_test = train_test_split(new_data, data['Detergents_Paper'], test_size=0.25, random_state=0)

# Create a decision tree regressor and fit it to the training set
regressor = DecisionTreeRegressor(random_state=0)
regressor.fit(X_train, y_train)

# Report the score of the prediction using the testing set
score = regressor.score(X_test, y_test)
print "Model has a coefficient of determination, R^2, of {:.3f}.".format(score)

Model has a coefficient of determination, R^2, of 0.729.

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 tried to predict annual spending on detergents and paper products and got a R^2 score of 0.729. This model performs predictions on this feature quite well, so it's not absolutely necessary that we need this feature to identify customers' spending habits.

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
pd.scatter_matrix(data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');

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:

Detergents_Paper appears to be somewhat correlated with Milk and rather highly correlated with Grocery. This confirms my suspicions that it's not too relevant for identifying a specific customer with our model. All features appear to have a heavily positively skewed distribution.

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.

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_data after applying logarithmic scaling. Use the np.log function for this.
• Assign a copy of the sample data to log_samples after applying logarithmic scaling. Again, use np.log.

# Scale the data using the natural logarithm
log_data = np.log(data.copy())

# 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');

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)

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. Use np.percentile for this.
• Assign the value of the 75th percentile for the given feature to Q3. Again, use np.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 outliers list.

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.

# For each feature find the data points with extreme high or low values
for feature in log_data.keys():

    # Calculate Q1 (25th percentile of the data) for the given feature
    Q1 = np.percentile(log_data[feature], 25)

    # Calculate Q3 (75th percentile of the data) for the given feature
    Q3 = np.percentile(log_data[feature], 75)

    # Use the interquartile range to calculate an outlier step (1.5 times the interquartile range)
    step = 1.5 * (Q3 - Q1)

    # 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))])

# OPTIONAL: Select the indices for data points you wish to remove
outliers  = [65, 66, 75, 128, 154]

# Remove the outliers, if any were specified
good_data = log_data.drop(log_data.index[outliers]).reset_index(drop = True)

Data points considered outliers for the feature 'Fresh':

Data points considered outliers for the feature 'Milk':

Data points considered outliers for the feature 'Grocery':

Data points considered outliers for the feature 'Frozen':

Data points considered outliers for the feature 'Detergents_Paper':

Data points considered outliers for the feature 'Delicatessen':

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:

Data points considered outliers in multiple features:

• 65 in Milk and Frozen
• 75 in Grocery and Detergents_Paper
• 154 in Milk, Grocery, and Delicatessen
• both 66 and 128 were outliers in Fresh and Delicatessen

I opted to remove these multi-outlier data points from the dataset, since being an extreme spender or saver in a multiple product categories is poorly representative of typical customer's spending habits. I could've opted to remove every data point with an outliers in any single product category, but there were 42 of those, which represents 9.54% of the data. Since we're unsure about the model's ability to accurately determine what is or is not "good data", we can't be very confident about removing so many outliers.

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.

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.PCA and assign the results of fitting PCA in six dimensions with good_data to pca.
• Apply a PCA transformation of log_samples using pca.transform, and assign the results to pca_samples.

from sklearn.decomposition import PCA

# Apply PCA by fitting the good data with the same number of dimensions as features
pca = PCA(n_components=6)
pca.fit(good_data)

# 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)

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.

# Display cumulative sums of the explained variance ratios
pca_results.cumsum()

Answer:

Total variance explained by first two PCs: 0.7068

Total variance explained by first four PCs: 0.9311

In Dimension 1 a significant positive weight is placed on Detergents_Paper with meaningful positive weight on Milk and Grocery. This dimension is best categorized by customer spending on retail goods.

In Dimension 2 a significant positive weight is placed on Fresh with meaningful positive weight on Frozen and Delicatessen. This dimension is best categorized by general customer spending on foods.

In Dimension 3 a significant positive weight is placed on Fresh and a significant negative weight is placed on Delicatessen, with meaningful negative weight on Frozen. This dimension is best categorized by customer spending on produce and health foods.

In Dimension 4 a significant positive weight is placed on Delicatessen, and a significant negative weight is placed on Frozen. This dimension is best categorized by customer spending on unique and ethnic foods.

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))

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_data to pca.
• Apply a PCA transformation of good_data using pca.transform, and assign the results to reduced_data.
• Apply a PCA transformation of log_samples using pca.transform, and assign the results to pca_samples.

# Apply PCA by fitting the good data with only two dimensions
pca = PCA(n_components=2)
pca.fit(good_data)

# Transform the good data using the PCA fit above
reduced_data = pca.transform(good_data)

# Transform the 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'])

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']))

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)

<matplotlib.axes._subplots.AxesSubplot at 0x11d8271d0>

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?

Answer:

Fresh, Frozen, and Delicatessen are the features most strongly correlated with the Dimension 1.

Detergents_Paper, Grocery, and Milk are the features most strongly correlated with the Dimension 2.

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.

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:

• Hard assign a data point to one particular cluster on convergence.
• It makes use of the euclidean norm when optimizing its centroid coordinates.
• Speed and simplicity

Gaussian Mixture Model:

• Soft assigns a point to clusters (so its give a probability of any point belonging to any centroid).
• It doesn't depend on the euclidean norm, but is based on the expectation, i.e. the probability of the point belonging to a particular cluster. This makes K-means biased towards spherical clusters.

K-means is more useful when we want certainty in which data points belong in which clusters and we want to produce more spherical clusters. GMM gives you probabilities instead to express the uncertainty, providing more information and flexibility than K-means. In fact K-means is a special case of GMM, where probabilities of being in a certain cluster is mapped to 1, with the rest of mapped to 0.

I think our model might have some hidden non-observable parameters within the wholesale customer data, so I'll be using a gaussian mixture model. Plus I like the flexibility and added information from gaussian mixture models 😁

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_data and assign it to clusterer.
• Predict the cluster for each data point in reduced_data using clusterer.predict and assign them to preds.
• 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_samples and assign them sample_preds.
• Import sklearn.metrics.silhouette_score and calculate the silhouette score of reduced_data against preds.
  • Assign the silhouette score to score and print the result.

from sklearn.mixture import GaussianMixture
from sklearn.metrics import silhouette_score

best_num_clusters = 0
best_score = 0

# Apply your clustering algorithm of choice to the reduced data
clusterer = GaussianMixture(n_components=2, covariance_type='full')
clusterer.fit(reduced_data)

# Predict the cluster for each data point
preds = clusterer.predict(reduced_data)

# Find the cluster centers
centers = clusterer.means_

# Predict the cluster for each transformed sample data point
sample_preds = clusterer.predict(pca_samples)

# Calculate the mean silhouette coefficient for the number of clusters chosen
score = silhouette_score(reduced_data, preds)
print "Silhouette coefficient for {} clusters: {:.3f}".format(2, score)

Silhouette coefficient for 2 clusters: 0.422

Report the silhouette score for several cluster numbers you tried. Of these, which number of clusters has the best silhouette score?

Answer:

Silhouette coefficient for 2 clusters: 0.422

Silhouette coefficient for 3 clusters: 0.318

Silhouette coefficient for 4 clusters: 0.276

Silhouette coefficient for 5 clusters: 0.284

Silhouette coefficient for 6 clusters: 0.328

Silhouette coefficient for 7 clusters: 0.296

Silhouette coefficient for 8 clusters: 0.226

Silhouette coefficient for 9 clusters: 0.323

The best number of clusters of the ones I've tried is 2 with a silhousette coefficient of 0.422

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.

# Display the results of the clustering from implementation
vs.cluster_results(reduced_data, preds, centers, pca_samples)

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 centers using pca.inverse_transform and assign the new centers to log_centers.
• Apply the inverse function of np.log to log_centers using np.exp and assign the true centers to true_centers.

# Inverse transform the centers
log_centers = pca.inverse_transform(centers)

# 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)

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'.

print 'Average purchase costs for each category:'
print data.sum() / 440

# Visualize samples
import seaborn as sns
true_centers_bar = true_centers.append(data.describe().loc['mean'])
_ = true_centers_bar.plot(kind='bar', figsize=(14,6))

Average purchase costs for each category:
Fresh               12000.297727
Milk                 5796.265909
Grocery              7951.277273
Frozen               3071.931818
Detergents_Paper     2881.493182
Delicatessen         1524.870455
dtype: float64

Answer:

A customer assigned to Cluster 0 should best itentify with cafes and restaurants. They have nearly identical needs as my Establishment 2 example, with a need for Milk and Grocery foods to prepare their foods, and a supply of Detergents_Paper to clean dishes, supply napkins, and generally support their dining experience. Compared to the mean, they'll typically need more Milk (7837 vs 5796), Grocery foods (12219 vs 7951), and Detergents_Paper (4696 vs 2881).

A customer assigned to Cluster 1 should best identify with the small fresh produce markets. They have nearly identical needs as my Establishment 1 example, with Fresh foods as their primary product, and a small selection of Frozen foods, but with reduced volume. Compared to the mean, they'll typically need less of everything across the board, but will have more similar needs of Fresh foods compared to the mean (8953 vs 12000) than the rest of the product categories.

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

Sample point 0 predicted to be in Cluster 0
Sample point 1 predicted to be in Cluster 1
Sample point 2 predicted to be in Cluster 1

Answer:

My initial prediction for Sample point 0 is completely consistent with it's predicted classification of Cluster 1. It has a very similar distribution of needs as Cluster 1, where your typical fresh produce market has Fresh foods as their primary product, and a small selection of Frozen foods.

My initial prediction for Sample point 1 is completely consistent with it's predicted classification of Cluster 0. It has a very similar distribution of needs as Cluster 0, where your typical cafe or restaurant needs a good supply Milk and Grocery ingredients, and a good supply of Detergents_Paper to clean & sanitize the place and provide paper napkins for their customers.

It's hard to say whether my initial prediction for Sample point 2 is consistent with it's predicted classification of Cluster 0. Your typical deli inherently needs a lot of Delicatessen foods and some need for Grocery and Fresh foods. Neither clusters put too much importance on Delicatessen foods, and while it's Grocery needs matches Cluster 0, it's Fresh foods needs better matches Cluster 1. We can see it's on the border between the two clusters in the cluster visualization (after Question 7), so we can't have much confidence in which cluster it belongs to either way.

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.

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:

We can run an A/B test by changing the delivery schedule on a sample of each segment individually. Once you get some responses from each sample, you can then identify how much this schedule change affects customers from this customer segment.

If you find that a cluster's customers respond positively, you can roll out this schedule change to the remaining customers in the cluster. Conversely if you find that a cluster's customers respond negatively, you can rule option that out for that cluster cluster of customers.

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:

You could use a supervised learner to train on the existing customer base, using annual spending of each product category as it's features and labelling each customer with their respective the customer segment. With this model, you can try to predict which customer segment each of those ten new customers belong to using their estimated product spending and suggest the most appropriate delivery service for them.

We can actually still use the supervised learner from this exercise to classify these ten new customers to their respective customer segments. In addition, we can always use the predicted labels as an engineered input feature for another supervised learning model to predict something else.

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)

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:

My Gaussian mixture model with two clusters has quite a similar distribution to the Hotel/Restaurant/Cafe & Retailer distribution. Along the Detergents_Paper, Grocery, Milk dimension, the more extreme parts of my customer segments would confidently classify as purely Retailer or Hotel/Restaurant/Cafe by this distribution.

I'd say these classifications are somewhat consistent with my previous definitions of customer segments. Hotel/Restaurant/Cafe's have similar food needs as my Cafe/Restaurant definition for Cluster 1. And although Retailer's don't might not intuitively fit how I defined Cluster 0 as a typical "small fresh produce market", they Retailers are still kind of a blanket statement to classify things as Other and my small fresh produce market definition had low enough volume to not pull in any direction either way.