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
import renders as rs
from IPython.display import display # Allows the use of display() for DataFrames
# Show matplotlib plots inline (nicely formatted in the notebook)
%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 = [0, 1, 2]
# 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 would say in item 0 all the purchases are in the mean values except for the Frozen products. This could mean an average convenience store or small supermarket where only fresh products and home supplies (detergents_papers are bought). It could also mean item 0 to be a cafeteria or restaurant where lot of Fresh, Milk is bought and an average quantity of Groceries. Frozend could hint ice-creams being sold
Item 1 has all the values in the mean except for the Fresh products. This could hint medium- large sice convenience store.
The third case, item 2, could correspond to a gourmet establishment, because all kinds of products are bought but highest value is for the Delicatessen products.
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.
# TODO: Make a copy of the DataFrame, using the 'drop' function to drop the given feature
new_data = data.copy(deep = True)
new_target = data['Delicatessen']
new_data = new_data.drop(['Delicatessen'], axis = 1)
# 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,new_target,
test_size=0.25,
random_state=1)
# TODO: Create a decision tree regressor and fit it to the training set
from sklearn.tree import DecisionTreeRegressor
regressor = DecisionTreeRegressor(random_state = 1).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 %.2f" %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: The feature I tried to predict is "Delicatessen". The score is -0.43, what indicates the model fails at predicting the target.
If it is not easily predictable it means it is uncorrelated with the other features and thus, it gives us new information to predict the spending habit, making it a necessary feature.
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 = (15,10), diagonal = 'kde');
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 is a clear correlation between these pairs of variables: Grocery-Milk, Grocery-Detergent_paper, Milk- Detergent_paper. These variables seem to have high covariance.
Delicatessen seems to be uncorrelated with other featues, what seems to confirm the necessity of this variable to give new information to describe the users in the problem.
The data seem to have positively or rightly skewed distributions, with a median above the mean. Most of the data lie in the right side, what creates the skew of the median.
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 a logarithm scaling. Use thenp.logfunction for this. - Assign a copy of the sample data to
log_samplesafter applying a logrithm 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 = (15,10), 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.
indexes = []
# 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], q = 25)
# TODO: Calculate Q3 (75th percentile of the data) for the given feature
Q3 = np.percentile(log_data[feature], q = 75)
# TODO: 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))])
# We create a list of list cointaining the outliers for each feature
indexes+=[log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))].index.values.tolist()]
# OPTIONAL: Select the indices for data points you wish to remove
# First I create a panda Series
sf = pd.Series(0,index = log_data.index)
for i in log_data.index.values: #iterate over the indexes and check how many times each index has been considered
# an outlier for any feature
sf[i] = sum([x.count(i) for x in indexes])
outliers = sf[sf>=2].index.values.tolist() # the outlier is removed if it has only appeared twice or more.
print "Data points considered outliers to be deleted \n'{}'".format(log_data.loc[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? 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, i.e., item 16 is an outlier for Fresh and Frozen. However, data should be removed carefully.
Outliers that should be removed are those that are either bad transcribed, or do not affect results and assumptions made or the outliers that create important associations.
Most of the times, outliers affect both results and assumptions and, thus, should not be dropped.
In this cases, there only a few outliers outliers appearing more than once and may not change significantly the result of the prediction, and for the sake of this last, can be dropped.
http://www.theanalysisfactor.com/outliers-to-drop-or-not-to-drop/
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 the sample log-data
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 = good_data.shape[1]).fit(good_data) # good_data.shape[1] = 6 : number of features
# TODO: Transform the sample log-data using the PCA fit above
pca_samples = pca.transform(log_samples)
# Generate PCA results plot
pca_results = rs.pca_results(good_data, pca)
# Plot explained variance
print pca.explained_variance_ratio_
#http://sebastianraschka.com/Articles/2015_pca_in_3_steps.html
total_var_exp = sum(pca.explained_variance_ratio_)
var_exp = [(i / total_var_exp)*100 for i in sorted(pca.explained_variance_ratio_, reverse=True)]
cum_var_exp = np.cumsum(var_exp)
import matplotlib.pyplot as plt
plt.figure(figsize=(10, 8))
plt.bar(range(1, 7), var_exp, alpha=0.5, align='center',label='individual explained variance')
plt.step(range(1,7), cum_var_exp, where='mid',label='cumulative explained variance')
plt.ylabel('Explained variance ratio')
plt.xlabel('Principal components')
plt.legend(loc='best')
plt.tight_layout()
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:
- First and second components explain, repectively, 44.3% and 26.38% of the variance, that adds up to a 70.68% total of the variance.
- The first four PCs explain 93.1% of the variance.
The frist four PCs seem to represent 4 main types of establishments. I will try to make a deduction for each PC, reviewing the absolute weight (+ or -) for each feature in the PC, ordered by importance of the weight:
D1: It seems to discriminate between establishments that have food (frozen and fresh) that can be cooked and those that serve other a broader spectrum of products, inlcuding non-food (detergent) and other types of food. It seems to me that it separates restaurants and food supermarkets.
+: Frozen, Fresh -: Detergents_paper, Grocery, Milk, DelicatessenD2: It adds a new dimension to discriminate. Positive is that the establishment is selling packaged products and negative other type of foods.
+: Detergents_paper, Grocery -: Fresh, Frozen, Delicatessen, MilkD3: Secondary products are now positively weighted. This could allow to discriminate the variety of products sold by the establishment.
+: Delicatessen, Frozen, Milk -: Fresh, Detergents_paper, GroceryD4: Non-fresh products are prositively weigthetd. This could hint convenience stores.
+: Frozen, Detergents_paper, Grocery -: Delicatessen, Fresh, Milk
https://algobeans.com/2016/06/15/principal-component-analysis-tutorial/
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 reuslts toreduced_data. - Apply a PCA transformation of the sample log-data
log_samplesusingpca.transform, and assign the results topca_samples.
# TODO: Apply PCA by fitting the good data with only two dimensions
from sklearn.decomposition import PCA
pca = PCA(n_components = 2).fit(good_data)
# TODO: Transform the good data using the PCA fit above
reduced_data = pca.transform(good_data)
# TODO: Transform the sample log-data 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']))
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 and Gaussian Mixture Model (GMM) are clustering algorithms.
GMMs are useful when hiddel relations between variables are to be discovered. Clusters may differ in size.
K-means is much faster and very easy to apply on large datasets. Clusters have similiar size. It is a special case of GMM. It can be applied when separations between clusters is clear or when we cant fast performance.
I choose K-means in order to speed up the process.
https://en.wikipedia.org/wiki/K-means_clustering https://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm#Gaussian_mixture
https://shapeofdata.wordpress.com/2013/07/30/k-means/
https://learning.cs.purdue.edu/_media/courses/fall2012/598g/kmeans.pdf
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_score and calculate the silhouette score of
reduced_dataagainstpreds.- Assign the silhouette score to
scoreand print the result.
- Assign the silhouette score to
# TODO: Apply your clustering algorithm of choice to the reduced data
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
# 1: ITERATION to find optimum number of clusters
score = []
number_of_clusters = range(2,10)
for i in number_of_clusters:
kmeans = KMeans(n_clusters=i, init='k-means++' , n_init= 10, random_state=1)
clusterer = kmeans.fit(reduced_data)
# TODO: Predict the cluster for each data point
preds = clusterer.predict(reduced_data)
# TODO: Calculate the mean silhouette coefficient for the number of clusters chosen
score.append( silhouette_score(reduced_data, preds))
print "The scores for clusters are...\n"
print "no of clusters, score \n"
for i, j in zip(number_of_clusters,score):
print " %d , %.5f \n" %(i,j)
#Pick the clusters thag gives the highest score
print "The optimum number of clusters is %d" %(number_of_clusters[np.argmax(score)])
#2: Create and fit kmeans for the optimum number of clusters
kmeans = KMeans(n_clusters=number_of_clusters[np.argmax(score)],
init='k-means++' , n_init= 10, random_state=1)
clusterer = kmeans.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)
Question 7¶
Report the silhouette score for several cluster numbers you tried. Of these, which number of clusters has the best silhouette score?
Answer:
The scores for clusters are...
no of clusters, score
2 , 0.42628 3 , 0.39742 4 , 0.33126 5 , 0.34075 6 , 0.36459 7 , 0.36488 8 , 0.34919 9 , 0.35988The optimum number of clusters 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.
# Display the results of the clustering from implementation
rs.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)
Answer:
Segment 0: has the values of Milk, Grocery and Detergents_paper in the Q4 (above 75%). Fresh is in the Q1 (0-25%) and Frozen Delicatessen are in the Q2 (25-50%). This could Segment 0 represents supermarkets where high variety of products are sold and not that much variety of Fresh and Frozen food.
Segment 1: has the value of Fresh in the median Q2 (50%). Frozen is in the Q3(50-75%). Milk, Grocery and Delicatessen are in the Q2 (25-50%). Detergent_papers is in the Q1 (0-25%). Segment 1 could be then Restaurant, where lots of Frozen and some less Fresh products are required, with a medium demand of Milk, Grocery and Delicatessen and very few purchase of Detergents_paper.
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'.
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
Answer: All the samples keep belonging to Cluster 1 after the inverse transformation of the space, as it was seen previously.
Conclusion¶
Question 10¶
Companies often run A/B tests when making small changes to their products or services. If the wholesale distributor wanted to change its delivery service from 5 days a week to 3 days a week, how would you use the structure of the data to help them decide on a group of customers to test?
Hint: Would such a change in the delivery service affect all customers equally? How could the distributor identify who it affects the most?
Answer
In an A/B test two verstions (A an B), which are identical except for one variation that might affect a user's behavior. Version A might be the currently used version (control), while version B is modified in some respect (treatment).
In this scenario I would run 2 A/B test (one per cluster), splitting randomly the clusters in two groups (A and B).
Then I would keep delivering 5 days a week for A and start delivering 3 days a week for B, and then I would check the repercusion in the features.
I think the changes would not affect equally to all the users, it will mostly depend on the cluster they belong to and the particular characteristics of the establishment within the cluster.
To check how the changes affect the users, I would track the features variation in the A/B groups made for each cluster.
If the changes affected positively to the group B (i.e. the total purchasing rate of each product would increase), I would consider making the changes.
If poor or negative changes are derived, I would switch to the new model.
Another thing to consider, is whether to average the changes from the 2 clusters or consider each cluster individually and apply the change depending on the nature of the resulting outcome (positive or negative) after the changes.
The first approach would consider to change the delivery rate to 3 times a week if the overall result is positive for the whole set of customers (the 3 clusters).
For the second approach, we could have segments where supplies would be delivered withing 5 days and other whithin 3 days, and the total change could be positive.
Question 11¶
Assume the wholesale distributor wanted to predict a new feature for each customer based on the purchasing information available. How could the wholesale distributor use the structure of the clustering data you've found to assist a supervised learning analysis?
Hint: What other input feature could the supervised learner use besides the six product features to help make a prediction?
Answer: Having a new feature to describe the customers would help to make better predictions, if the feature is representative enough.
New features could include, i.e., medecines, or other features that could help us to add more information about non-food products.
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 on 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
rs.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:
I chose 2 clusters and the underlying distributions states that there are 2 groups.
It is suprising that Cluster/ Segment 0 and Segment 1 correspond almost exactly to Retalers and Hotel/Restaurant/Cafe respectively. This makes the classification consistent with our previously defined customer segments.
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