Machine Learning Engineer Nanodegree¶
Unsupervised Learning¶
Project: Creating Customer Segments¶
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())
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.
# TODO: Select three indices of your choice you wish to sample from the dataset
indices = [95, 176, 200]
# 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)
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:
- I think the first customer is likely to be a small corner shop, given that they order very little fresh ingredients (3 vs a mean of 12000.3) while they do order a proportionately higher amount of Milk (2920 vs a mean of 5796.27) and Grocery type foods (6252 vs a mean of 7951.28) than other types of goods. Corner shops typically have a small frozen section (440 vs a mean of 3071.93) and household items area (223 vs a mean of 2881.49), but can sometimes have a large delicatessen area (709 vs a mean of 1524.87) depending on the demographic makeup of the area the shop is in. Looking at the heatmap of normalized expenditures below, this sample purchases much less goods overall than other customers, but seems to purchase proportionately more Milk, Grocery, and Delicatessen goods than other types of goods.
- The second customer is more likely to be a big market-like shop, with a huge fresh produce section (likely organic produce given the cost, with an expenditure of 45640 compared to a mean of 12000.3) and smaller and equal areas for milk (6958 vs a mean of 5796.27), normal groceries (6536 vs a mean of 7951.28), and frozen foods (7368 vs a mean of 3071.93). I would assume a place like this would also have a bigger delicatessen area, though it appears not to be the case (230 vs a mean of 1524.87). Looking at the heatmap of normalized expenditures below, this sample purchases significantly more fresh produce than other customers and substantially more frozen goods than other customers, but is closer to the mean for both Milk and Grocery products, and has below average consumption of Detergents_Paper and Delicatessen products.
- The final customer strikes me as a typical supermarket with a modest fresh produce area (3067 vs a mean of 12000.3), but a shop where you're more likely to go for typical grocery items like bread, cereals, tins of food, etc. (23127 vs a mean of 7951.28). These kind of stores typically have a substantial dairy selection (13240 vs a mean of 5796.27) and frozen area (3941 vs a mean of 3071.93), and also have aisles dedicated solely to household items like detergent and paper towels (9959 vs a mean of 2881.49). You're less likely to find a delicatessen area in a store like this (731 vs a mean of 1524.87), though there would appear to be a small part of the store that caters to customers interested in those types of goods. Looking at the heatmap of normalized expenditures below, this sample purchases significantly more Milk, Grocery, and Delicatessen_Paper products, slightly more frozen goods and slightly less delicatessen products, and a below average amount of fresh produce than other customers.
import seaborn as sns
sns.heatmap((samples-data.mean())/data.std(ddof=0), annot=True, cbar=False, square=True)
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.
print new_data
from sklearn.model_selection import train_test_split
from sklearn.tree import DecisionTreeRegressor
# TODO: Make a copy of the DataFrame, using the 'drop' function to drop the given feature
new_data = data.copy()
new_data.drop(['Grocery'], axis=1, inplace = True)
# TODO: 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['Grocery'], test_size = 0.25, random_state = 1)
# TODO: Create a decision tree regressor and fit it to the training set
regressor = DecisionTreeRegressor(random_state = 1)
regressor.fit(X_train, y_train)
# TODO: Report the score of the prediction using the testing set
score = regressor.score(X_test, y_test)
print score
Question 2¶
Which feature did you attempt to predict? What was the reported prediction score? Is this feature 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 attempted to predict the 'Grocery' feature. The reported prediction score was 0.7958, which means that the model was able to predict its value reasonably well and could mean that it's not a necessary feature for identifying customers' spending habits. Other features could be used to predict customers' purchasing behaviour of groceries with a reasonable degree of accuracy.
from sklearn.cross_validation import train_test_split
from sklearn.tree import DecisionTreeRegressor
def calculate_r_2_for_feature(data,feature):
new_data = data.drop(feature, axis=1)
X_train, X_test,y_train, y_test = train_test_split(new_data,data[feature],test_size=0.25)
regressor = DecisionTreeRegressor()
regressor.fit(X_train,y_train)
score = regressor.score(X_test,y_test)
return score
def r_2_mean(data,feature,runs=200):
return np.array([calculate_r_2_for_feature(data,feature)
for _ in range(200) ]).mean().round(4)
print "{0:17} {1}".format("Fresh: ", r_2_mean(data,'Fresh'))
print "{0:17} {1}".format("Milk: ", r_2_mean(data,'Milk'))
print "{0:17} {1}".format("Grocery: ", r_2_mean(data,'Grocery'))
print "{0:17} {1}".format("Frozen: ", r_2_mean(data,'Frozen'))
print "{0:17} {1}".format("Detergents_Paper: ", r_2_mean(data,'Detergents_Paper'))
print "{0:17} {1}".format("Delicatessen: ", r_2_mean(data,'Delicatessen'))
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
pd.scatter_matrix(data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');
corr = data.corr()
mask = np.zeros_like(corr)
mask[np.triu_indices_from(mask, 1)] = True
with sns.axes_style("white"):
ax = sns.heatmap(corr, mask=mask, square=True, annot=True,
cmap='RdBu', fmt='+.3f')
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:
It appears that Grocery and Detergents_Paper have the strongest correlation of the pairs. It also looks like there is some correlation between Detergents_Paper and Milk, and Grocery and Milk. This confirms my suspicion above that Grocery was correlated with some other features that would allow for its value to be predicted with some degree of accuracy. All of the distributions appear to be skewed to the right, with more points hovering closer to the origin and some larger points extending it to the right. The shape of the distributions of Detergents_Paper, Grocery, and Milk are all quite similar.
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.copy())
# 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');
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)
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.
from collections import Counter
# For each feature find the data points with extreme high or low values
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)
step = (Q3 - Q1) * 1.5
# 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 = []
# 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:
75 is considered an outlier for both the Grocery and Detergents_Paper features; 154 is considered an outlier for all of Milk, Grocery, and Delicatessen features; 65 is in Fresh and Frozen; 66 is in Delicatessen and Fresh; 128 is in Delicatessen and Fresh. I think these data points should be removed from the dataset because they were outliers for more than one feature, and therefore may reduce the predictive capability of our model if it is trained on these noisy datapoints. Interestingly, one of the datapoints I selected for the sample, 95, turned out to be an outlier due to the amount of Fresh produce the customer purchased.
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.
from sklearn.decomposition import PCA
# TODO: Apply PCA by fitting the good data with the same number of dimensions as features
pca = PCA(n_components=6)
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)
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 first and second principal components explain .719 of the variance of the data, while the first four principal components explain .9314 of the variance of the data.
Dimension 1 primarily paired Detergents_Paper, Milk, and Grocery together; this dimension represents purchases of everyday household goods, likely by retailers.
Dimension 2 primarily paired Fresh, Frozen, and Delicatessen together, though all products are weighted in the same direction; this dimension represents that purchases of fresh produce, frozen goods, and delicatessen products, which could be typical of a restaurant or cafe.
Dimension 3 weakly paired Delicatessen and Frozen together, and strongly negated Fresh; this dimension represents purchases of delicatessen products and frozen goods, which could be typical of US convenience store-like companies (though the companies are based in Portugal).
Dimension 4 negatively paired Frozen against Delicatessen and to a lesser extent Fresh, and positively paired Detergents_Paper; this dimension could represent purchases by a gas station shop.
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))
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)
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'])
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?
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:
The major advantages of using a K-Means clustering algorithm are that it scales well to a large number of samples and always converges, however this converegence can sometimes be to a local minima and when this occurs it needs to be re-run. The Gaussian Mixture Model clustering algorithm, specifically Expectation Maximisation, is a more general case of a K-Means clustering algorithm. Its advantages are that it's quick to run, and doesn't require a distribution to be normal for it to work. It does also suffer from the possibility of 'getting stuck' in a local minima, at which point it would need to be re-run, though it never fully converges (though the step changes in the probabilities become small enough that it effectively does converge). Given that we know that the first and second principal components explain 71.9% of the variance, meaning we have a rough idea of how many clusters to expect, I think we should use a K-means clustering algorithm where the number of clusters is 2, though we should be sure to check how it performs for different numbers of clusters.
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.
from sklearn.metrics import silhouette_score
from sklearn.cluster import KMeans
# TODO: Apply your clustering algorithm of choice to the reduced data
clusterer = KMeans(n_clusters=2, random_state=1)
clusterer.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
score = silhouette_score(reduced_data, preds, random_state=1)
print 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:
- Two clusters: 0.4192
- Three clusters: 0.3943
- Four clusters: 0.3302
- Five clusters: 0.3478
- Six clusters: 0.3602
- Seven clsuters: 0.3641
- Eight clusters: 0.3417
- Nine clusters: 0.3517
- Ten clusters: 0.3653
Of these, the best silhouette score was computed from two clusters, with a score of 0.4192.
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.
# 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)
#repeated for ease of comparison
display(data.describe())
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:
- Segment 0 would fall somewhere between the 25th and 50th percentile for Fresh, 75th and 99th percentile for Milk, 75th and 99th percentile for Grocery, 25th and 50th percentile for Frozen, 75th and 99th percentile for Detergents_Paper, and likely somewhere between 50th and 51st percentile for Delicatessen. This customer segment purchases specifically dairy products, grocery items, and household items like detergent or paper, which means it could represent stores like supermarkets, and increasingly more in the US like some drug stores or a big retailer.
- Segment 1 would fall somewhere between the 50th to 75th percentile for Fresh, 25th to 50th percentile for Milk, 25th and 50th percentile for Grocery, 50th and 75th percentile for Frozen, just above the 25th percentile for Detergents_Paper, and somewhere between the 25th and 50th percentile for Delicatessen. This customer segment purchases an above average amount of fresh produce and frozen goods and a below average amount of other types of goods, which means it could represent chain restaurants or cafes as they are less likely to be making big purchases of goods to sell on, but rather turn the goods into meals to serve on a smaller scale.
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.
# Redisplayed samples for ease of comparison
display(samples)
# Display the predictions
for i, pred in enumerate(sample_preds):
print "Sample point", i, "predicted to be in Cluster", pred
Answer:
Sample point 0 shows a higher proportion of Milk and Grocery than it does the other categories when compared to their relative percentiles, so it would make sense for it to be classified into Cluster 0.
Sample point 1 shows a much higher proportion of Fresh and still a high proportion of Frozen relative to the other categories, so it would make sense for it to be classified into Cluster 1.
Sample point 2 again shows a very high proportion of Milk and Grocery and additionally a high proportion of Detergents_Paper than it does the other categories, so it again would make sense for it to be classified into Cluster 0.
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:
An A/B test could be conducted by trialing the 3 day a week delivery service for 20% of its customers, and leaving the 5 day a week delivery service as is for 80% of its customers as a control. It would be important to ensure that there's a representative proportion of each of the two customer segments for Group A receiving 3 day a week delivery and Group B receiving 5 day a week delivery, so that the company is able to see how each group reacts to the changes. Success could be measured qualitatively by direct feedback from the customers themselves (as there would only be 88 individual customers to track feedback from, which is 20% of the total 440), and quantitatively by comparing how the average orders and subsequent revenue for the firm increases or decreases for each group dependent on the changed delivery service.
We would hypothesise that for the customer segment that predominately purchases Milk, Grocery, and Detergents_Paper, changing the delivery service to 3 days a week from 5 days a week will likely have less of a negative effect than it would on the customer segment that predominately purchases Fresh and Frozen goods. Both purchase goods that can perish quickly; the first segment purchasing milk and baked goods (like loaves of bread), and the second purchasing fresh ingredients like fruits and vegetables. The customers would be less able to just purchase more of these goods and store them in advance than they would with non-perishable goods that make up Detergents_Paper and Frozen e.g. paper towels, washing up liquid, and frozen pizzas. However, since fresh ingredients are more likely to go off, and the second segment could be a restaurant / cafe that needs fresh ingredients each day, I think that the delivery changes would affect the second segment the most.
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:
The wholesale distributer could label the new customers using their estimated product spending by looking at the relative proportions of each good they are likely to purchase. The target variable for this binary clasification problem would be the customer segment, and a supervised learner could be deployed to classify the ten new customers based on the training data of the original customers. If the customer is more likely to purchase a higher proportion of Milk, Grocery, and Detergents_Paper, then they should likely be assigned to the first segment and could be better served by the less frequent, 3-day delivery service. Additionally, if a customer is more likely to purchase a higher proportion of Fresh and Frozen goods, then they should likely be assigned to the second segment and could be better served by a more frequent, 5-day delivery service.
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)
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:
All things considered, the clustering algorithm which identified 2 clusters does a good job of classifying the points compared to the underlying distribution of Hotel/Restaurant/Cafe customers to Retailer customers. It is the case that there are a decent chunk of Hotel/Restaurant/Cafe customers that appear in what we identified as cluster 0 above when we classified them as cluster 1 (roughly 25-30), and vice versa, where there are some, although fewer (roughly 7), Retailer customers that appear in what we identifed as cluster 1 when we classified them as cluster 0. There are no segments that would be classified purely as 'Retailers' or 'Hotels/Restaurant/Cafes' by this distribution, as mentioned above there is some overlap. However, I believe we can still consider these classifications as consistent with our previous definition of customer segments; there does appear to be a general trend in purchasing behaviour by these two segments / clusters, it just seems like the Hotel/Restaurant/Cafe segment includes perhaps too many different kind of customers which leads to the characteristic purchasing behaviour of the group being slightly more diverse.
Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to
File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.