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 [1]:
# 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 [2]:
# 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 [3]:
# TODO: Select three indices of your choice you wish to sample from the dataset
indices = [11, 100 ,200]
# Create a DataFrame of the chosen samples
samples = pd.DataFrame(data.loc[indices], columns = data.keys()).reset_index(drop = True)
print "Chosen samples of wholesale customers dataset:"
display(samples)
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:
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 [4]:
from sklearn.cross_validation import train_test_split
from sklearn.tree import DecisionTreeRegressor
def feature_relevance(selected_feature):
# TODO: Make a copy of the DataFrame, using the 'drop' function to drop the given feature
new_data = data.copy()
new_data.drop([selected_feature], axis = 1, inplace = True)
# TODO: Split the data into training and testing sets using the given feature as the target
X_train, X_test, y_train, y_test = train_test_split(new_data, data[selected_feature], 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)
return score
for feature in data.columns:
score = feature_relevance(feature)
print('The score for {} is {}.'.format(feature, score))
Which feature did you attempt to predict? What was the reported prediction score? Is this feature necessary for identifying customers' spending habits?
Hint: The coefficient of determination, R^2, is scored between 0 and 1, with 1 being a perfect fit. A negative R^2 implies the model fails to fit the data.
Answer:
I tried a few features.
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 [5]:
# 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:
There are pairs of features which exhibit some degree of correlation. For example, Detergents_Paper has a positive correlation with Milk and Grocery respectively. This result agrees with the high R^2 score.
The data is skewed right. Most of the data points are on the left side.
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 [6]:
# TODO: Scale the data using the natural logarithm
log_data = data.apply(np.log)
# TODO: Scale the sample data using the natural logarithm
log_samples = samples.apply(np.log)
# 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 [7]:
# 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 [8]:
# For each feature find the data points with extreme high or low values
# Returns a dict to hold (feature, outlier_index_list)
def find_outliers():
feature_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)
outlier = ~(log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step)
display(log_data[outlier])
outlier_idx = log_data[outlier].index.tolist()
feature_outliers[feature] = outlier_idx
return feature_outliers
# OPTIONAL: Select the indices for data points you wish to remove
# If an index appears more than twice in any features, add it to outliers
outliers_set = set()
seen = []
feature_outliers = find_outliers()
for k1, v1 in feature_outliers.iteritems():
for k2, v2 in feature_outliers.iteritems():
if k1 != k2 and not (k2 in seen):
same = set(v1).intersection(set(v2))
if len(same) > 0:
print('{} are in {} and {}'.format(same, k1, k2))
outliers_set.update(same)
seen.append(k1)
outliers = list(outliers_set)
print('Outlier indexes {} '.format(outliers))
# Remove the outliers, if any were specified
good_data = log_data.drop(log_data.index[outliers]).reset_index(drop = True)
Answer:
There are 5 data points that appears in more than one feature list. These data points should be removed because they don't represent the data well and tend to make the analysis inaccurately.
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 [9]:
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)
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 individual feature weights.
In [10]:
print('First two {}'.format(0.4430 + 0.2638))
print('First four {}'.format(0.4430 + 0.2638 + 0.1231 + 0.1012))
Answer:
The variance by the first and second PCs is 0.7068 and that by the first four PCs is 0.9311.
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 [11]:
# Display sample log-data after having a PCA transformation applied
display(pd.DataFrame(np.round(pca_samples, 4), columns = pca_results.index.values))
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 [12]:
# 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 [13]:
# 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 [14]:
# Create a biplot
vs.biplot(good_data, reduced_data, pca)
Out[14]:
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:
Referred to This Answer
At the beginning I chose Gaussian Mixture Model because the dimensions aren't high, the shape of the clusters are unknown and hard assignment may not be proper as the customer data showed a mixture of different categories.
But after compared the result of the two models, I found K-Means has better score. Also after compared the result of the hidden variables, I found K-Means is still better. So I guess I'd better choose the simple one to start with.
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 [15]:
# TODO: Apply your clustering algorithm of choice to the reduced data
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
def kmeans_clustering(n_classes):
clusterer = KMeans(n_clusters=n_classes, random_state=0)
clusterer.fit(reduced_data)
# TODO: Predict the cluster for each data point
preds = clusterer.predict(reduced_data)
# TODO: Find the cluster centers
centers = clusterer.cluster_centers_
# TODO: Predict the cluster for each transformed sample data point
sample_preds = clusterer.predict(pca_samples)
# TODO: Calculate the mean silhouette coefficient for the number of clusters chosen
score = silhouette_score(reduced_data, preds, metric='euclidean', random_state=0)
return (score, reduced_data, preds, centers, pca_samples, sample_preds)
for i in range(2,7):
score = kmeans_clustering(i)[0]
print('n_classes={}, score={}'.format(i, score))
Answer:
From the above data, the best silhouette score occurs when there are two 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 [16]:
# Display the results of the clustering from implementation
_, reduced_data, preds, centers, pca_samples, _ = kmeans_clustering(2)
vs.cluster_results(reduced_data, preds, centers, pca_samples)
In [17]:
from sklearn.mixture import GMM
from sklearn.metrics import silhouette_score
def gmm_clustering(n_classes):
clusterer = GMM(n_components=n_classes, covariance_type='full', random_state=0)
clusterer.fit(reduced_data)
preds = clusterer.predict(reduced_data)
centers = clusterer.means_
sample_preds = clusterer.predict(pca_samples)
score = silhouette_score(reduced_data, preds, metric='euclidean', random_state=0)
return (score, reduced_data, preds, centers, pca_samples, sample_preds)
for i in range(2,7):
score = gmm_clustering(i)[0]
print('n_classes={}, score={}'.format(i, score))
_, reduced_data, preds, centers, pca_samples, _ = gmm_clustering(2)
vs.cluster_results(reduced_data, preds, centers, pca_samples)
Since the result of K-Means is better, I use the result of K-Mean in the following exercise.
In [18]:
_, reduced_data, preds, centers, pca_samples, sample_preds = kmeans_clustering(2)
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 [19]:
# 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)
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:
Segment0: Restaurant. The amount of spending of all categories are lower than the average, meaning the size of the customer isn't big. The customer spends mostly on Fresh, Milk, Grocery and Frozen.
Segment1: Retailer. The customer spends more than average on Milk, Grocery, Detergents_Paper, meaning the size of the customer is large. It also spends good amount of Fresh and Delicatessen.
In [20]:
# Display the predictions
for i, pred in enumerate(sample_preds):
print "Sample point", i, "predicted to be in Cluster", pred
Answer:
Although the last two data points are both retailers, they sell products that focus on different categories.
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:
The change will affect customers differently. More frequent delivery is import for customer 1) who spend a lot on Fresh, Milk and Delicatessen; and 2) whose size is small that doesn't stock too much.
For the two segments, the segment 0 will react more positively than segment 1.
In the PCA analysis, the dimension 2 puts more weights on Fresh, Frozen and Delicatessen. We should definitely include this dimension when doing the analysis.
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 steps of labeling the new customers are as follows.
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 [21]:
# 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:
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.