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 = [154, 181, 338]
# 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)
import seaborn as sns
percentiles_data = 100*data.rank(pct=True)
percentiles_samples = percentiles_data.iloc[indices]
sns.heatmap(percentiles_samples, annot=True)
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, delis, wholesale retailers, among many others. Avoid using names for establishments, such as saying "McDonalds" when describing a sample customer as a restaurant. You can use the mean values for reference to compare your samples with. The mean values are as follows:
- Fresh: 12000.2977
- Milk: 5796.2
- Grocery: 7951.3
- Frozen : 3071.9
- Detergents_paper: 2881.4
- Delicatessen: 1524.8
Knowing this, how do your samples compare? Does that help in driving your insight into what kind of establishments they might be?
Answer:
The establishment with indice 154 has an annual spending much lower than average belonging to the lower 25 percentile for all the features. This shows that it could be a rather small business. We also see that the majority of its annual spending covers "Fresh" products followed by "Grocery". This can be the indicator that the establishement is a small restaurant.
The establishment with indice 181 has an annual spending much higher than average in all of the features. It's in the upper 75 percentile for all category of products which makes me think that it might be a very big hotel or for a chain of hotels.
The establishment with indice 338 has an annual spending overall lower than the mean except for the products belonging to the "Frozen" category which is actually pretty high with an annual spending of 15601 and therefore belonging in the upper 75 percentile ot the dataset. Considering the Frozen feature, it is actually about 2 std away from the mean on the upper side although all the other features are rather low. This observation can lead us to believe that this establishment might be a market that sells frozen product.
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
def score_feature(data, feature):
from sklearn.model_selection import train_test_split
from sklearn.tree import DecisionTreeRegressor
new_data = data.drop([feature], axis=1)
# TODO: Split the data into training and testing sets(0.25) using the given feature as the target
# Set a random state.
all_scores = []
for i in range (100):
X_train, X_test, y_train, y_test = train_test_split(new_data, data[feature], test_size=0.25)
# TODO: Create a decision tree regressor and fit it to the training set
regressor = DecisionTreeRegressor()
regressor.fit(X_train, y_train)
# TODO: Report the score of the prediction using the testing set
all_scores.append(regressor.score(X_test, y_test))
score = np.mean(all_scores)
print "For feature \"{}\", the coefficient of determination is {}".format(feature, score)
for key in data:
score_feature(data, key)
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. If you get a low score for a particular feature, that lends us to beleive that that feature point is hard to predict using the other features, thereby making it an important feature to consider when considering relevance.
Answer: I didn't set the random state because the coefficient of determination varied greatly when I changed it so I instead calculated the mean of scores over 100 iterations to have a more general idea.
I first attempted to predict "Fresh" and the coefficient of determination was -0.708230948053. The score being negative, it shows that no correlation with the other features has been found and that the model fails to fit the data. This shows that "Fresh" provides unique information that cannot be predicted by other features, therefore the feature "Fresh" should be necessary for identifying customers' spending habits.
Visualize Feature Distributions¶
To get a better understanding of the dataset, we can construct a scatter matrix of each of the six product features present in the data. If you found that the feature you attempted to predict above is relevant for identifying a specific customer, then the scatter matrix below may not show any correlation between that feature and the others. Conversely, if you believe that feature is not relevant for identifying a specific customer, the scatter matrix might show a correlation between that feature and another feature in the data. Run the code block below to produce a scatter matrix.
# Produce a scatter matrix for each pair of features in the data
pd.plotting.scatter_matrix(data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');
import seaborn as sns; sns.set()
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, annot=True, fmt='+.3f')
Question 3¶
- Using the scatter matrix as a reference, discuss the distribution of the dataset, specifically talk about the normality, outliers, large number of data points near 0 among others. If you need to sepearate out some of the plots individually to further accentuate your point, you may do so as well.
- 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? You can use corr() to get the feature correlations and then visualize them using a heatmap(the data that would be fed into the heatmap would be the correlation values, for eg: data.corr()) to gain further insight.
Answer:
The data appears to have a highly positively skewed distribution with all the features, showing the presence of outliers with very high annual spendings for all features compared to the average. Indeed, most of the data points are near zero. This biais could impact the algorithm performance and therefore it is important to apply some kind of normalisation to make the features normally distributed.
We can see that "Grocery" and "Detergents_Paper" exhibit the highest correlation pair with 0.925. We also see some correlation between "Grocery" and "Milk" (0.728); "Milk" and "Detergents_Paper" (0.662) but the correlation is relatively mild. There are no obvious correlation pair with "Fresh", "Frozen" and "Delicatessen".
This confirms what we observed previously, the coefficient of determination for predicting "Fresh" with the other features was -0.708230948053. This score showed no obvious correlation with the other features which corroborates our observation in the scatter matrix where no clear pattern can be observed with any of the features.
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.plotting.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.
# 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 = 1.5*(Q3-Q1)
# Display the outliers
print "Data points considered outliers for the feature '{}':".format(feature)
display(log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))])
# OPTIONAL: Select the indices for data points you wish to remove
outliers = [65, 66, 75, 128, 154]
# Remove the outliers, if any were specified
good_data = log_data.drop(log_data.index[outliers]).reset_index(drop = True)
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
outlierslist to be removed, explain why.
Hint: If you have datapoints that are outliers in multiple categories think about why that may be and if they warrant removal. Also note how k-means is affected by outliers and whether or not this plays a factor in your analysis of whether or not to remove them.
Answer:
The following data points were found to be outliers in more than one feature based on the above definition [65, 66, 75, 128, 154]. I think those points should be removed from the dataset as they might induce wrong biaises to the model. Indeed because those are outliers for multiple feature this shows a specific spending behavior that is not representative of the masse. Therefore I added them to the outliers list above. I kept the data points that were flagged as outliers for only one feature because removing them all would mean taking out a consequent amount of data points (42 in total), representing 9.5% of the data this would generally not be recommended without a strong justification. One other possibility could have been to increase the step size in Tukey's method to find the extreme outliers.
Feature Transformation¶
In this section you will use principal component analysis (PCA) to draw conclusions about the underlying structure of the wholesale customer data. Since using PCA on a dataset calculates the dimensions which best maximize variance, we will find which compound combinations of features best describe customers.
Implementation: PCA¶
Now that the data has been scaled to a more normal distribution and has had any necessary outliers removed, we can now apply PCA to the good_data to discover which dimensions about the data best maximize the variance of features involved. In addition to finding these dimensions, PCA will also report the explained variance ratio of each dimension — how much variance within the data is explained by that dimension alone. Note that a component (dimension) from PCA can be considered a new "feature" of the space, however it is a composition of the original features present in the data.
In the code block below, you will need to implement the following:
- Import
sklearn.decomposition.PCAand assign the results of fitting PCA in six dimensions withgood_datatopca. - Apply a PCA transformation of
log_samplesusingpca.transform, and assign the results topca_samples.
# TODO: Apply PCA by fitting the good data with the same number of dimensions as features
from sklearn.decomposition import PCA
pca = PCA(n_components=6).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()
Question 5¶
- How much variance in the data is explained in total by the first and second principal component?
- How much variance in the data is explained by the first four principal components?
- Using the visualization provided above, talk about each dimension and the cumulative variance explained by each, stressing upon which features are well represented by each dimension(both in terms of positive and negative variance explained). 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 individual feature weights.
Answer:
| Dimension | Explained Variance | Cumulative Explained Variance | Discussion |
|---|---|---|---|
| 1 | 0.4430 | 0.4430 | Mainly "Detergents_Paper", "Milk" and "Grocery" together negatively-weighted. This corresponds to day-to-day household spendings which might represent retailers. |
| 2 | 0.2638 | 0.7068 | Mainly "Fresh", "Frozen" and "Delicatessen" together negatively-weighted. This corresponds to mainly food spendings which might represent restaurants, canteens. |
| 3 | 0.1231 | 0.8299 | Mainly "Fresh" being negatively-weighted and "Delicatessen" being positively-weighted. This corresponds mainly to fresh and ethnic food spendings which might represent small familial restaurants, organic/ethnic food shops. |
| 4 | 0.1012 | 0.9311 | Mainly "Frozen" being positively-weighted and "Delicatessen" being negatively-weighted. This corresponds mainly to frozen and ethnical food spendings which might represent convinient stores. |
| 5 | 0.0485 | 0.9796 | Mainly "Milk" being positively-weighted and "Detergent_Paper" being negatively-weighted. |
| 6 | 0.0204 | 1.0000 | Mainly "Grocery" being positively-weighted and "Milk"being negatively-weighted. |
- Variance explained in total by the first and second principal components : 0.7068
- Variance explained in total by the first four principal components : 0.9311
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 the log-transformed sample data
display(log_samples)
# 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).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?
- From the biplot, which of the original features are most strongly correlated with the first component?
"Detergents_Paper", "Grocery" and "Milk" are the features most strongly correlated with the first component because most of their magnitude can be described along the first component axis.
- What about those that are associated with the second component?
"Delicatessen", "Frozen" and "Fresh" are the features most strongly correlated with the second component because most of their magnitude can be described along the second component axis.
- Do these observations agree with the pca_results plot you obtained earlier?
We see that the observations support the results obtained in the pca_results plot for dimension 1 and dimension 2 as we can clearly see that the projection of the vectors onto each dimension correspond to the PC plane with original features projections.
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?
Hint: Think about the differences between hard clustering and soft clustering and which would be appropriate for our dataset.
Answer:
K-Means advantages:
- Fast and efficient: time complexity of K Means is linear while that of hierarchical clustering is quadratic1
- Produces tighter clusters than hierarchical clustering
Gaussian Mixture Model advantages:
- Results are more reproducible
- Don't need prior knowledge on the dataset compared to K-means
- Agnostic : Maximizes likelihood avoiding biaises
- a “soft” classification is available
The main criteria I would take into account to choose between these two algorithms are the speed VS second order information desired and the underlying structure of the data.
Since our dataset is quite small and scalability would not be an issue I would use the Gaussian Mixture Model because ranking the data points with their likelihood (soft classification) gives more flexibility and insight about the result than K-means (hard classification).
Implementation: Creating Clusters¶
Depending on the problem, the number of clusters that you expect to be in the data may already be known. When the number of clusters is not known a priori, there is no guarantee that a given number of clusters best segments the data, since it is unclear what structure exists in the data — if any. However, we can quantify the "goodness" of a clustering by calculating each data point's silhouette coefficient. The silhouette coefficient for a data point measures how similar it is to its assigned cluster from -1 (dissimilar) to 1 (similar). Calculating the mean silhouette coefficient provides for a simple scoring method of a given clustering.
In the code block below, you will need to implement the following:
- Fit a clustering algorithm to the
reduced_dataand assign it toclusterer. - Predict the cluster for each data point in
reduced_datausingclusterer.predictand assign them topreds. - Find the cluster centers using the algorithm's respective attribute and assign them to
centers. - Predict the cluster for each sample data point in
pca_samplesand assign themsample_preds. - Import
sklearn.metrics.silhouette_scoreand calculate the silhouette score ofreduced_dataagainstpreds.- Assign the silhouette score to
scoreand print the result.
- Assign the silhouette score to
# TODO: Apply your clustering algorithm of choice to the reduced data
from sklearn.mixture import GaussianMixture
from sklearn.metrics import silhouette_score
from sklearn.cluster import KMeans
'''
In the function, silhouette(i), you have hard-coded the value of n_components to be 2.
This is why you are getting approximately the same silhouette score in each iteration.
'''
def silhouette(i, n):
clusterer = GaussianMixture(n_components=n).fit(reduced_data)
# clusterer = KMeans(n_clusters=2).fit(reduced_data)
# TODO: Predict the cluster for each data point
preds = clusterer.predict(reduced_data)
# TODO: Find the cluster centers
centers = clusterer.means_
# 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)
print "- Silhouette coefficient for {} clusters: {}".format(n, score)
return preds, centers, sample_preds
n=10
for i in range(1,10):
preds, centers, sample_preds = silhouette (i, n)
i += 1
n -= 1
Question 7¶
- Report the silhouette score for several cluster numbers you tried.
- Of these, which number of clusters has the best silhouette score?
Answer:
- Silhouette coefficient for 10 clusters: 0.311496246584
- Silhouette coefficient for 9 clusters: 0.282552459146
- Silhouette coefficient for 8 clusters: 0.325530641623
- Silhouette coefficient for 7 clusters: 0.324359181668
- Silhouette coefficient for 6 clusters: 0.292962293977
- Silhouette coefficient for 5 clusters: 0.292587640.421916846463806
- Silhouette coefficient for 4 clusters: 0.345867137512
- Silhouette coefficient for 3 clusters: 0.404248738241
- Silhouette coefficient for 2 clusters: 0.422324682646
The best silhouette score is with 2 clusters : 0.422324682646
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)
display(np.exp(good_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(specifically looking at the mean values for the various feature points). 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'. Think about what each segment represents in terms their values for the feature points chosen. Reference these values with the mean values to get some perspective into what kind of establishment they represent.
Answer: The value for "Milk", "Grocery" and "Detergents_Paper" in segment 0 (cluster 0) belong to the upper percentile 75 of the dataset and could therefore help identify the establishments such as big and small shops/retailers reselling primarely groceries, dairies and household products.
The value for "Fresh" and "Frozen" in segment 1 (Cluster 1) are above the median of the dataset and could help identify the establishments such as restaurants/canteens needing primarely fresh products but also need some frozen food.
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:
The sample point 0 corresponds to the establishment index 154 and was estimated to be a small restaurant. It is indeed consistent with the classification in the Cluster 1 that I above described.
The sample point 1 corresponds to the establishment index 181. Unfortunately this data point was removed from the dataset because it was considered an outlier in a previous section. I estimated this customer to be a big Hotel or a chain of hotels as it was spending much more in all features than the average. It has been classified in the Cluster 0 that I described as representing mainly establishments being big and small shops/retailers. Being an outlier makes this categorization complicated to interpret without having a closer look to the data.
The sample point 2 corresponds to the establishment index 338 and was estimated to be a market that sells frozen product. It was classified in the Cluster 1. It is consistent with the observation that the Cluster 1 includes establishments with higher spendings on frozen products than the ones in 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:
We can run A/B tests separately for each segment where a certain percentage of customers are offered the 3 days a week option (group A) instead of the 5 days a week option (group B). A representative proportions of customers from each segments should be tested for the new option. This would allow to determine if there is a correlation between how well the new option is received. At the end of a defined period, it would be possible to compare the revenu made by the distributor and determine if customers reacted positively or negatively depending on segments and groups (A or B).
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:
Now that we have customer segments fairly well described, we can engineer those segments as new features for the data. Because there are only two segments, we can apply this to a binary supervised learner. We can consider the feature "segment" the target variable (labels), split the data into training and testing sets and train the supervised learner on the training set. The learner should be tested for its performance and if the performance is satisfying, then the learner should be able to predict with a known accuracy in which new customers should belong only with their features (which are the provided estimates for anticipated annual spending of each product category).
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:
- The distribution of segments found with the Gaussian Mixture Model is quite similar to the above distribution of Hotel/Restaurant/Cafe customers to Retailer customers. We can see that the centroids are very close although the frontier isn't as sharp. This confirms that the GMM was a good choice of algorithm, as the clusters do have a fair amount of overlap in reality. Soft clustering gives us confidence levels in our predictions, which would understandably be low at the boundary between two clusters.
- When looking at the data we see that their are parts of the segment that would be classified as purely Retailer for x-values < -3 and as purely Hotels/Restaurants/Cafes for x-values > 2. More complicated shapes could be described to better estimate those areas.
- My definition of the customer segments were:
Segment 0 (Cluster 0) could help identify the establishments such as big and small shops/retailers reselling primarely groceries, dairies and household products.
Segment 1 (Cluster 1) could help identify the establishments such as restaurants/canteens needing primarely fresh products but also need some frozen food, dairies and groceries.
Here segment 0 corresponds to "Retailer" and segment 1 corresponds to "Hotel/Restaurant/Cafe". Those classifications are consistent with the previous definition I gave of the customer segments.
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.