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 = [7, 65, 190]
# 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, 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
- 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:
Sample 0: This composure feels like a supermarket, as the sales are spread across all the sections. With groceries, milk, delicatessen and fresh being above mean.
| Sample 0 | Fresh | Milk | Grocery | Frozen | Detergent_Paper | Delicatessen |
|---|---|---|---|---|---|---|
| Gross | 7579 | 4956 | 9426 | 1669 | 3321 | 2566 |
| Mean | 12000.30 | 5796.27 | 7951.28 | 3071.94 | 2881.49 | 2566 |
Sample 1: This may be a cafe, because frequent / high purchases of Milk, Grocery and Detergents_Paper are usually significant in cafes. The data shows that Fresh, Frozen are substantially on the lower side of mean / average. Deli is not very far from mean, Milk, Grocery and Detergent_Paper are on the higher side or very high compared to the mean / average values this pattern resembles with the nautre of transactions in a cafe.
| Sample 1 | Fresh | Milk | Grocery | Frozen | Detergent_Paper | Delicatessen |
|---|---|---|---|---|---|---|
| Gross | 85 | 20959 | 45828 | 36 | 24231 | 1423 |
| Mean | 12000.30 | 5796.27 | 7951.28 | 3071.94 | 2881.49 | 2566 |
Sample 2: This would be a restaurant with very high fresh, frozen, milk sections and low delicatessen. Also, the level of detergent_paper, delicatessen, grocery are lower than most and very far from their mean. While Fresh, Frozen are well above mean values and milk is not very far from mean value.
| Sample 2 | Fresh | Milk | Grocery | Frozen | Detergent_Paper | Delicatessen |
|---|---|---|---|---|---|---|
| Gross | 16936 | 6250 | 1981 | 7332 | 118 | 64 |
| Mean | 12000.30 | 5796.27 | 7951.28 | 3071.94 | 2881.49 | 2566 |
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.
from sklearn.tree import DecisionTreeRegressor
from sklearn.cross_validation import train_test_split
features = list(data)
for feature in features:
fresh = data[feature]
new_data = data.drop([feature],axis=1)
# Split the data into training and testing sets using the given feature as the target
X_train, X_test, y_train, y_test = train_test_split(new_data, fresh, test_size=0.25, random_state=1)
# Create a decision tree regressor and fit it to the training set
regressor = DecisionTreeRegressor(random_state=1)
regressor.fit(X_train, y_train)
r2_score = regressor.score(X_test, y_test)
# Report the score of the prediction using the testing set
print (feature,r2_score)
Question 2¶
- Which feature did you attempt to predict?
- What was the reported prediction score?
- Is this feature necessary for identifying customers' spending habits?
Hint: The coefficient of determination, R^2, is scored between 0 and 1, with 1 being a perfect fit. A negative R^2 implies the model fails to fit the data. 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 had iterated over all the features to get the R^2 score for when a feature is dropped.
R^2, score lies in between 0 and 1, with 1 being a perfect fit.
If a feature with weak usefulness is removed, R^2 would still remain closer to 1. Which, means that the feature is strongly predictable by all other categroies.
In laymans terms, we can say that the dropped feature will have strong correlation with the other categories and will not be necessary.
From above stats, we can conclude that dropping "Detergents_Paper" had the least impact on lowering the R^2 score followed by Grocery. Given, the figures above I think "Detergents_Paper" may not 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.scatter_matrix(data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');
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 most visible correlation is between Grocery and Detergents_Paper. In the previous answer, I had identified them to be most predictable when dropped.
Correlation between Grocery and Milk, Milk and Detergents_Paper is significant too.
The data does not appear to be normally distributed and most of the datapoints are lying around low values. Due to this skewedness, we need to normalize the features, as the algorithms we use assume that the data / features are roughly normally distributed.
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.
# Scale the data using the natural logarithm
log_data = np.log(data)
# Scale the sample data using the natural logarithm
log_samples = np.log(samples)
# Produce a scatter matrix for each pair of newly-transformed features
pd.scatter_matrix(log_data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');
Observation¶
After applying a natural logarithm scaling to the data, the distribution of each feature should appear much more normal. For any pairs of features you may have identified earlier as being correlated, observe here whether that correlation is still present (and whether it is now stronger or weaker than before).
Run the code below to see how the sample data has changed after having the natural logarithm applied to it.
# Display the log-transformed sample data
display(log_samples)
Implementation: Outlier Detection¶
Detecting outliers in the data is extremely important in the data preprocessing step of any analysis. The presence of outliers can often skew results which take into consideration these data points. There are many "rules of thumb" for what constitutes an outlier in a dataset. Here, we will use Tukey's Method for identfying outliers: An outlier step is calculated as 1.5 times the interquartile range (IQR). A data point with a feature that is beyond an outlier step outside of the IQR for that feature is considered abnormal.
In the code block below, you will need to implement the following:
- Assign the value of the 25th percentile for the given feature to
Q1. Usenp.percentilefor this. - Assign the value of the 75th percentile for the given feature to
Q3. Again, usenp.percentile. - Assign the calculation of an outlier step for the given feature to
step. - Optionally remove data points from the dataset by adding indices to the
outlierslist.
NOTE: If you choose to remove any outliers, ensure that the sample data does not contain any of these points!
Once you have performed this implementation, the dataset will be stored in the variable good_data.
remove_outliers = []
# For each feature find the data points with extreme high or low values
for feature in log_data.keys():
# Calculate Q1 (25th percentile of the data) for the given feature
Q1 = np.percentile(log_data[feature], 25)
# Calculate Q3 (75th percentile of the data) for the given feature
Q3 = np.percentile(log_data[feature], 75)
# Use the interquartile range to calculate an outlier step (1.5 times the interquartile range)
step = 1.5 * (Q3-Q1)
# Display the outliers
print ("Data points considered outliers for the feature '{}':".format(feature))
outliers = log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))]
display(outliers)
# Select the indices for data points you wish to remove
remove_outliers.extend(outliers.index.tolist())
#print throw_away
# Remove the outliers, if any were specified
remove_outliers = set(remove_outliers)
print ('Toss these: ', sorted(remove_outliers))
good_data = log_data.drop(log_data.index[list(remove_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:
There are 5 datapoints, identified as outliers in more than one feature. They are, data point number 65, 66, 75, 128 and 154.
These data points are not representative of the set and can probably be removed without causing any issues. Because, we want to cluster like-minded customers, it seems unlikely that these datapoints would help us in acheiving that.
I chose to remove all the outliers with the intent to attain a very simplified and generic conclusion.
Feature Transformation¶
In this section you will use principal component analysis (PCA) to draw conclusions about the underlying structure of the wholesale customer data. Since using PCA on a dataset calculates the dimensions which best maximize variance, we will find which compound combinations of features best describe customers.
Implementation: PCA¶
Now that the data has been scaled to a more normal distribution and has had any necessary outliers removed, we can now apply PCA to the good_data to discover which dimensions about the data best maximize the variance of features involved. In addition to finding these dimensions, PCA will also report the explained variance ratio of each dimension — how much variance within the data is explained by that dimension alone. Note that a component (dimension) from PCA can be considered a new "feature" of the space, however it is a composition of the original features present in the data.
In the code block below, you will need to implement the following:
- Import
sklearn.decomposition.PCAand assign the results of fitting PCA in six dimensions withgood_datatopca. - Apply a PCA transformation of
log_samplesusingpca.transform, and assign the results topca_samples.
from sklearn.decomposition import PCA
# Apply PCA by fitting the good data with the same number of dimensions as features
pca = PCA(n_components=6).fit(good_data)
# Transform log_samples using the PCA fit above
pca_samples = pca.transform(log_samples)
# Generate PCA results plot
pca_results = vs.pca_results(good_data, pca)
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:
Variance covered by first component :- 49.93%
Variance covered by second component: 22.59%
Total variance covered by PCAs one and two : 72.52%
Total variance covered by the first four PCAs : 92.75%
Dimension 1: The largest variance is explained by a customer buying mostly Detergens_Paper, but also Grocery and Milk. This might be a type of supermarket, where customers tend to buy necesseties.
Dimension 2: This dimension explains variance where a customer is purchasing a large amount of Fresh, Frozen, and Deli which make way for this to most probably a type of restaurant.
Dimension 3: This principal component describes a spending pattern where there is a lot of purchase of Delicatessen, frozen, moderate amount of Milk. But, large (I would say, significant) amount of avoidance in terms of purchase of fresh and detergents_paper.
Dimension 4: A high Delicatessen spending, followed by Fresh, Milk and moderate amounts of Grocery. And large amount of avoidance in Frozen and Detergents_Paper this could be a sandwich making vendor.
Observation¶
Run the code below to see how the log-transformed sample data has changed after having a PCA transformation applied to it in six dimensions. Observe the numerical value for the first four dimensions of the sample points. Consider if this is consistent with your initial interpretation of the sample points.
# Display sample log-data after having a PCA transformation applied
display(pd.DataFrame(np.round(pca_samples, 4), columns = pca_results.index.values))
Implementation: Dimensionality Reduction¶
When using principal component analysis, one of the main goals is to reduce the dimensionality of the data — in effect, reducing the complexity of the problem. Dimensionality reduction comes at a cost: Fewer dimensions used implies less of the total variance in the data is being explained. Because of this, the cumulative explained variance ratio is extremely important for knowing how many dimensions are necessary for the problem. Additionally, if a signifiant amount of variance is explained by only two or three dimensions, the reduced data can be visualized afterwards.
In the code block below, you will need to implement the following:
- Assign the results of fitting PCA in two dimensions with
good_datatopca. - Apply a PCA transformation of
good_datausingpca.transform, and assign the results toreduced_data. - Apply a PCA transformation of
log_samplesusingpca.transform, and assign the results topca_samples.
from sklearn.decomposition import PCA
# Apply PCA by fitting the good data with only two dimensions
pca = PCA(n_components=2).fit(good_data)
# Transform the good data using the PCA fit above
reduced_data = pca.transform(good_data)
# Transform log_samples using the PCA fit above
pca_samples = pca.transform(log_samples)
# Create a DataFrame for the reduced data
reduced_data = pd.DataFrame(reduced_data, columns = ['Dimension 1', 'Dimension 2'])
Observation¶
Run the code below to see how the log-transformed sample data has changed after having a PCA transformation applied to it using only two dimensions. Observe how the values for the first two dimensions remains unchanged when compared to a PCA transformation in six dimensions.
# Display sample log-data after applying PCA transformation in two dimensions
display(pd.DataFrame(np.round(pca_samples, 4), columns = ['Dimension 1', 'Dimension 2']))
Visualizing a Biplot¶
A biplot is a scatterplot where each data point is represented by its scores along the principal components. The axes are the principal components (in this case Dimension 1 and Dimension 2). In addition, the biplot shows the projection of the original features along the components. A biplot can help us interpret the reduced dimensions of the data, and discover relationships between the principal components and original features.
Run the code cell below to produce a biplot of the reduced-dimension data.
# Create a biplot
vs.biplot(good_data, reduced_data, pca)
Observation¶
Once we have the original feature projections (in red), it is easier to interpret the relative position of each data point in the scatterplot. For instance, a point the lower right corner of the figure will likely correspond to a customer that spends a lot on 'Milk', 'Grocery' and 'Detergents_Paper', but not so much on the other product categories.
From the biplot, which of the original features are most strongly correlated with the first component? What about those that are associated with the second component? Do these observations agree with the pca_results plot you obtained earlier?
Clustering¶
In this section, you will choose to use either a K-Means clustering algorithm or a Gaussian Mixture Model clustering algorithm to identify the various customer segments hidden in the data. You will then recover specific data points from the clusters to understand their significance by transforming them back into their original dimension and scale.
Question 6¶
- What are the advantages to using a K-Means clustering algorithm?
- What are the advantages to using a Gaussian Mixture Model clustering algorithm?
- Given your observations about the wholesale customer data so far, which of the two algorithms will you use and why?
Hint: Think about the differences between hard clustering and soft clustering and which would be appropriate for our dataset.
Answer:
K-Means clustering algorithm is simple to its core, fast and more scalable. It is fast because of the lower number of parameters and is well suited towards situations with lots of data, and where clusters are clearly seperable and non-uniform. The algorithm takes mean of data points and they rigidly belong to one cluster or another.
The advantage to this is that it provides more information about a data point based on where its located and what points are arround it.
The disadvantage of K-Means clustering is, it determines for 'certain' that a data point belongs in a region using / based on the distance metric between other points.
Gaussian Mixture Models have many more parameters than K-Means and it performs soft clustering. Using Gaussian distributions and probabilities, data points do not necessarilly have to be assigned rigidly and ones with lower probability can be assigned to multiple clusters at once. GMMs can assign non-spherical clusters. Moreover, it can be used to predict probabilities of events rather than rigid features.
The Guassian Mixture Model is very similar to KNN except that it will take into account that uncertainty, variance into consideration when measuring the distance between the points, give a better metric for how likely it is that the cluster assignment is correct.
Provided, the scatter plot appears to be quite uniform, most of the data points may be belonging to one or more clusters and the uncertaintyin the data set up until now, I would choose GMM to cluster the data.
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
from sklearn.mixture import GaussianMixture
from sklearn.metrics import silhouette_score
results = []
for x in range(2,20):
# Apply your clustering algorithm of choice to the reduced data
clusterer = GaussianMixture(n_components=x, random_state=0)
clusterer.fit(reduced_data)
# Predict the cluster for each data point
preds = clusterer.predict(reduced_data)
# Find the cluster centers
centers = clusterer.means_
# Predict the cluster for each transformed sample data point
sample_preds = clusterer.predict(pca_samples)
# Calculate the mean silhouette coefficient for the number of clusters chosen
score = silhouette_score(reduced_data,preds)
print (x, score)
Question 7¶
- Report the silhouette score for several cluster numbers you tried.
- Of these, which number of clusters has the best silhouette score?
Answer: I had calculated silhoutte scores for clusters from between 2 to 20, the best score achieved is with two clusters.
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
clusterer = GaussianMixture(n_components=2, random_state=0)
clusterer.fit(reduced_data)
preds = clusterer.predict(reduced_data)
centers = clusterer.means_
sample_preds = clusterer.predict(pca_samples)
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.
# Inverse transform the centers
log_centers = pca.inverse_transform(centers)
# Exponentiate the centers
true_centers = np.exp(log_centers)
# Display the true centers
segments = ['Segment {}'.format(i) for i in range(0,len(centers))]
true_centers = pd.DataFrame(np.round(true_centers), columns = data.keys())
true_centers.index = segments
display(true_centers)
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.
import matplotlib.pyplot as plt
import seaborn as sns
display(np.exp(good_data).describe())
plt.figure()
plt.axes().set_title("Segment 0")
sns.barplot(x=true_centers.columns.values,y=true_centers.iloc[0].values)
plt.figure()
plt.axes().set_title("Segment 1")
sns.barplot(x=true_centers.columns.values,y=true_centers.iloc[1].values)
Answer:
Segment 0: This segment represents customers purchasing significantly large quantities of fresh, frozen products. Accounting to more than 50th percentile of the data. These customers are purchasing in bulk from markets to reduce their expenses.
Segment 1: This segment represents customers with large purchases in grocery, milk and detergents_paper. Accounting to more than 75th percentile of the data. This could most possibly represent cafe/restaurants.
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.
print ("true centers :")
display(true_centers)
print ("samples :")
display(samples)
# Display the predictions
for i, pred in enumerate(sample_preds):
print("Sample point", i, "predicted to be in Cluster", pred)
Answer:
My initial assumptions / predictions were:
- Sample point 0: Super Market - Fresh Foods, Groceries, Frozen foods are usually high in markets.
- Sample point 1: Cafe - The purchases of Milk, Grocery and Detergents_Paper is high usually in cafes.
- Sample point 2: Restaurant - restaurants usually / tend to have very high fresh, frozen, milk sections and low delicatessen sections.
Yeah, the predictions are almost consistent with my initial intuitive assumptions / guesses.
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:
Using the classification we have deteremined, the wholesaler could take sample customers from each segment and experiment with offering 3 deliveries a week. Based on the response from each segment, they could extrapolate which segment would react more positively in general.
Intuitively we could probably say that segment 0 (probably from restaurants group) would be less flexible to reduced delivery days as they buy more from the Fresh catagory.
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:
A supervised model such as logistic regression could be used to classify these new customers as either Segment 0 or Segment 1. It should have no trouble being able to classify the new customers after being trained on the old customers. We could use the customer_segment variable with a boolean value to record the prediction.
The benefit of using a model like logistic regression would be that it could give us a confidence interval for the prediction as well.
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, list(remove_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:
Actual data correlates with our predicted clusters. The number of clusters we decided using silhouette score is the same as the number of actual classes in the dataset (i.e. 2).
Although, HoReCa seems to be wildly variant, as we see some HoReCa points in the Retailer space and the distribution of retailers and HoReCa is more mixed than predicted using GMM.
Overall, the data looks to fit the prediction pretty well and reasonable predictions on new data can be made with good confidence. I would consider that the classification is consistent with my expectations.