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.
In [167]:
# 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?"
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.
In [168]:
# 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.
In [169]:
# TODO: Select three indices of your choice you wish to sample from the dataset
indices = [401, 98, 61]
# 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)
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:
0: This sample has a purchases of Fresh produce, Frozen and Delicatessen in the top quartile. However, puchase of Milk is below average, and purchase of grocery and detergents are in the first quartile. This could indicate that this is a Restaurant.
1: Sample 1 has purchase quantities for all product types well below the first quartile cut-off. This is therefore a small establishment. The ratios of frozen, grocery and fresh food are relatively high, which could indicate that it is a small cafe for instance
2: The quantities purchased by Sample 2 are in the top quartile for the all categories apart from Frozen food. It has a relatively diversified basket and could be a retailer / supermarket.
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:
new_data a copy of the data by removing a feature of your choice using the DataFrame.drop function.sklearn.cross_validation.train_test_split to split the dataset into training and testing sets.test_size of 0.25 and set a random_state.random_state, and fit the learner to the training data.score function.
In [170]:
# TODO: Make a copy of the DataFrame, using the 'drop' function to drop the given feature
new_data = data.drop('Milk', axis=1)
print new_data.head()
In [171]:
from sklearn.cross_validation import train_test_split
from sklearn.tree import DecisionTreeRegressor
# 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['Milk'], test_size=0.25, random_state=0)
# TODO: Create a decision tree regressor and fit it to the training set
regressor = DecisionTreeRegressor(random_state=0)
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
In [172]:
var_list=list(data)
for var in var_list:
new_data = data.drop(var, axis=1)
X_train, X_test, y_train, y_test = train_test_split(new_data, data[var], test_size=0.25, random_state=0)
regressor = DecisionTreeRegressor(random_state=0)
regressor.fit(X_train, y_train)
score = regressor.score(X_test, y_test)
#print 'R^2 for '+'%s'+score %var
print "R^2 for {}: ".format(var)+"{}".format(score)
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 initially attempted to predict milk purchase based on purchase of other products. The resulting R^2 was relatively small. I then looked at all other products. The best R^2 is obtained for Detergents_Paper. Thus means this feature may not be necessary 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.
In [173]:
# 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 seems to have a strong correlation with Grocery, which is likely driving the large R^2 obtained for both of these product categories. For some other products we also see some correlation, for instance between Milk and Grocety. However the distribution of purchase quantities is narrower. The scatter matrix also confirms that there is no clear correlation between purchase volumes of Delicatessen and other products. The distribution of purchase quantities are heavily skewed towards the right (positively skewed) and are not normal.
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:
log_data after applying logarithmic scaling. Use the np.log function for this.log_samples after applying logarithmic scaling. Again, use np.log.
In [174]:
# TODO: Scale the data using the natural logarithm
log_data = np.log(data)
# TODO: Scale the sample data using the natural logarithm
log_samples = np.log(samples)
# Produce a scatter matrix for each pair of newly-transformed features
pd.scatter_matrix(log_data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');
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.
In [175]:
# 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:
Q1. Use np.percentile for this.Q3. Again, use np.percentile.step.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.
In [176]:
# For each feature find the data points with extreme high or low values
potential_outliers=[]
for feature in log_data.keys():
# TODO: Calculate Q1 (25th percentile of the data) for the given feature
Q1 = np.percentile(log_data[feature], 25)
# TODO: Calculate Q3 (75th percentile of the data) for the given feature
Q3 = np.percentile(log_data[feature], 75)
# TODO: Use the interquartile range to calculate an outlier step (1.5 times the interquartile range)
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))])
potential_outliers += (log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))]).index.tolist()
print "Potential outliers: {}: ".format(potential_outliers)
# OPTIONAL: Select the indices for data points you wish to remove
outliers=[65, 66, 75, 128, 154]
#outliers=[]
# Remove the outliers, if any were specified
good_data = log_data.drop(log_data.index[outliers]).reset_index(drop = True)
Answer: 5 data points can be considered as outliers for more than one feature based on the definition above. These may either be the results of erronous entries or of very peculiar type of shop not representative of the rest of the population. I therefore decided to remove them from the dataset.
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:
sklearn.decomposition.PCA and assign the results of fitting PCA in six dimensions with good_data to pca.log_samples using pca.transform, and assign the results to pca_samples.
In [177]:
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)
print pca_results['Explained Variance'].cumsum()
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: 70.68% of the variance in the data is explained in total by the first and second principal component. This percentage increases to 93.11% when including the first four principal components.
The first four dimensions could represent different types of customer spending behaviors. Dimension 1 represents a relatively diversified basket with strong positive correlation (larger weights) with milk, grocery and detergents_paper. This may represent a retail store. Dimension 2 has large positive weights (strong positive correlation) on fresh, frozen and delicatessen and could correspond to a restaurant or food market. Dimension 3 represents outlets purchasing almost exclusively delicatessen and frozen products, and purchase much less fresh produce and to a lesser extent detergents_paper (negative weights/correlations for these products). Dimension 4 has a strong positive correlation with frozen food purchase and a heavy negative one with delicatessen (and to a lesser extent on fresh). This could represent retail outlets.
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.
In [178]:
# Display sample log-data after having a PCA transformation applied
display(pd.DataFrame(np.round(pca_samples, 4), columns = pca_results.index.values))
0 and 2 to match initial intuition. 0 was identified as a potential restaurant, and indeed has a high value for dimension 2. 2 was potentially identified as a retail store, which matches the large value for dimension 1. New values along these 6 dimensions for 1 are however non trivial to interpret.
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:
good_data to pca.good_data using pca.transform, and assign the results to reduced_data.log_samples using pca.transform, and assign the results to pca_samples.
In [179]:
# 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'])
In [180]:
# 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.
In [181]:
# Create a biplot
vs.biplot(good_data, reduced_data, pca)
Out[181]:
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?
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.
Answer: K-means clustering aims to segment the data into a given number of groups such that each point is as close to the center of its group as possible. The objective is to find the right number of groups, and the right centers, so that this is achieved. K-means clustering performs a ‘clear-cut’ allocation, whereby each data point is assigned to a single group. On the contrary, a Gaussian Mixture Model (GMM) clustering algorithm performs a soft assignment, with each point having a probability to belong to each group, and with a possibility to obtain density estimation for each group/cluster.
K-means is relatively fast to train and easy to visualize in 2D or 3D. It however suffers from the curse of dimensionality.
In our case, we want to separate customers in customer groups that correspond to different types of establishment, and therefore would not benefit from a soft assignment. The dimensionality is also small and therefore a k-means clustering should perform well.
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:
reduced_data and assign it to clusterer.reduced_data using clusterer.predict and assign them to preds.centers.pca_samples and assign them sample_preds.sklearn.metrics.silhouette_score and calculate the silhouette score of reduced_data against preds.score and print the result.
In [182]:
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
# TODO: Apply your clustering algorithm of choice to the reduced data
clusterer = KMeans(n_clusters=2, random_state=0).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
labels = clusterer.labels_
score = silhouette_score(reduced_data, labels)
print score
Answer: The silouhette scores for 2, 3, 4, 5 and 6 clusters are respectively equal to 0.43, 0.40, 0.33, 0.35, and 0.37. The best silouhette score is achieved for 2 clusters.
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.
In [183]:
# 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:
centers using pca.inverse_transform and assign the new centers to log_centers.np.log to log_centers using np.exp and assign the true centers to true_centers.
In [184]:
# 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)
In [185]:
true_centers = true_centers.append(data.describe().ix['50%'])
true_centers.plot(kind = 'bar', figsize = (16, 4))
Out[185]:
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: The representative data point for Segment 0 corresponds to purchases of fresh food around the average, of milk, grocery, detergents and delicatessen just above the first quartile threashold. Purchases of frozen food is however above average (3rd quartile). <br> The representative data point for Segment 1 corresponds to puchases of milk, grocery and detergents well above the respective sample averages (values in top quartile of the distributions). Purchase values for delicatessen is around the sample average, while the ones for fresh and frozen fall below average (both in 2nd quartile). <br> Segment 0 could represent retaurants whereas Segment 1 could represent the customer segment of retailers.
In [186]:
# Display the predictions
for i, pred in enumerate(sample_preds):
print "Sample point", i, "predicted to be in Cluster", pred
Answer: We initially noted the following prior to doing any analysis:
Sample point 0: This sample has a purchases of Fresh produce, Frozen and Delicatessen in the top quartile. However, puchase of Milk is below average, and purchase of grocery and detergents are in the first quartile. This could indicate that this is a Restaurant.
Sample point 1: Sample 1 has purchase quantities for all product types well below the first quartile cut-off. This is therefore a small establishment. The ratios of frozen, grocery and fresh food are relatively high, which could indicate that it is a small cafe for instance
Sample point 2: The quantities purchased by Sample 2 are in the top quartile for the all categories apart from Frozen food. It has a relatively diversified basket and could be a retailer / supermarket.
The predictions for 0 and 2 are consistent with this. For instance, we can note that Cluster 0 has purchases of milk, grocery and detergents just above the first quartile threshold, while these values are below average (milk) and in the first quartile (grocery and detergents) for Sample Point 1. Sample Point 2, similar to the representative data point for segment 1 has purchases for milk, grocery and detergents in the top quartiles. Prediction for 1 are less straightforward to comment on, since the absolute values are very small. The metrics of interest are more the ratios as opposed to the absolute purchases. With ratios of frozen, grocery and fresh it is consistent that sample point 1 be associated with cluster/segment 0.
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: For each customer segment, the distributor can change its delivery service from 5 to 3 days for a sub-sample of customers. In effect, the customer segment is used to stratify the sample prior to A/B testing. One can then estimate the impact of the change for each group separately and determine in particular which group of customers is the most affected (based on changes in purchase behavior). Intuitively, given that their purchase volume across the different categories of products are different, we woul expect the effect to be different between the two groups. For instance, reducing delivery frequency is not likely to affect purchase for non-perishable products, but could affect purchases for milk, fresh produce for instance.
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 distributor could train its clustering based on actual purchase of other customers and estimate the segment for each new client using their estimated spending as opposed to actual purchase.
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.
In [187]:
# Display the results of the clustering from implementation
vs.cluster_results(reduced_data, preds, centers, pca_samples)
In [188]:
# 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: The clustering algorithm performs pretty well, with 2 groups identified and a relatively good performance for allocation. There are however a number of customers who fall close to the boundary between the 2 segments and for which the identified segment does not match the channel from the data. There is therefore likely no strict equivalence between the customer segment and the channel as defined in the dataset.
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.