Machine Learning Engineer Nanodegree

Unsupervised Learning

Project 3: Creating Customer Segments

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.


In [2]:
# Import libraries necessary for this project
import numpy as np
import pandas as pd
import renders as rs
from IPython.display import display # Allows the use of display() for DataFrames

# Show matplotlib plots inline (nicely formatted in the notebook)
%matplotlib inline

# Load the wholesale customers dataset
try:
    data = pd.read_csv("customers.csv")
    data.drop(['Region', 'Channel'], axis = 1, inplace = True)
    print "Wholesale customers dataset has {} samples with {} features each.".format(*data.shape)
except:
    print "Dataset could not be loaded. Is the dataset missing?"


/Users/karataev/anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.
  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')
Wholesale customers dataset has 440 samples with 6 features each.

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.


In [3]:
# Display a description of the dataset
display(data.describe())


Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
count 440.000000 440.000000 440.000000 440.000000 440.000000 440.000000
mean 12000.297727 5796.265909 7951.277273 3071.931818 2881.493182 1524.870455
std 12647.328865 7380.377175 9503.162829 4854.673333 4767.854448 2820.105937
min 3.000000 55.000000 3.000000 25.000000 3.000000 3.000000
25% 3127.750000 1533.000000 2153.000000 742.250000 256.750000 408.250000
50% 8504.000000 3627.000000 4755.500000 1526.000000 816.500000 965.500000
75% 16933.750000 7190.250000 10655.750000 3554.250000 3922.000000 1820.250000
max 112151.000000 73498.000000 92780.000000 60869.000000 40827.000000 47943.000000

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.


In [11]:
# Select three indices of your choice you wish to sample from the dataset
indices = [4, 81, 390]

# 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)

print "Diff with the mean of the dataset"
display(samples - data.mean().round())

print "Diff with the median of the dataset"
display(samples - data.median().round())

print "Quartile Visualization"

# Import Seaborn, a very powerful library for Data Visualisation
import seaborn as sns
perc = data.rank(pct=True)
perc = 100 * perc.round(decimals=3)
perc = perc.iloc[indices]
sns.heatmap(perc, vmin=1, vmax=99, annot=True)

samples_bar = samples.append(data.describe().loc['mean'])
samples_bar.index = indices + ['mean']
_ = samples_bar.plot(kind='bar', figsize=(14,6))


Chosen samples of wholesale customers dataset:
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
0 22615 5410 7198 3915 1777 5185
1 219 9540 14403 283 7818 156
2 3352 1181 1328 5502 311 1000
Diff with the mean of the dataset
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
0 10615.0 -386.0 -753.0 843.0 -1104.0 3660.0
1 -11781.0 3744.0 6452.0 -2789.0 4937.0 -1369.0
2 -8648.0 -4615.0 -6623.0 2430.0 -2570.0 -525.0
Diff with the median of the dataset
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
0 14111.0 1783.0 2442.0 2389.0 961.0 4219.0
1 -8285.0 5913.0 9647.0 -1243.0 7002.0 -810.0
2 -5152.0 -2446.0 -3428.0 3976.0 -505.0 34.0
Quartile Visualization

Question 1

Consider the total purchase cost of each product category and the statistical description of the dataset above for your sample customers.
What kind of establishment (customer) could each of the three samples you've chosen represent?
Hint: Examples of establishments include places like markets, cafes, and retailers, among many others. Avoid using names for establishments, such as saying "McDonalds" when describing a sample customer as a restaurant.

Answer:

I've chosen three different indices which represent three completely different types of establishments:

  1. Index 4: Probably a big supermarket in a good neighbourhood. All spendings are well above the median for each category, which means that the scale is large. Sales of Fresh and Delicatessen are in 86% and 97% respectively, which probably makes it almost an outlier in the data.
  2. Index 81: A shop near a poor neighbourhood (taking into account the amount of Fresh and Delicatessen sales). This point of sales is focused on sales of Milk, Groceries and Detergents, with all sales in 80+ percentile (their sales are much higher than the mean and the median).
  3. Index 390: considering low sales of Milk, Grocery and Detergents - probably a fast food of some kind with a focus on saled of Frozen (84 percentile).

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_data a copy of the data by removing a feature of your choice using the DataFrame.drop function.
  • Use sklearn.cross_validation.train_test_split to split the dataset into training and testing sets.
    • Use the removed feature as your target label. Set a test_size of 0.25 and set a random_state.
  • 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 score function.

In [13]:
# Make a copy of the DataFrame, using the 'drop' function to drop the given feature
features = data.columns

for feature in features:
    new_data = data.drop(feature, axis = 1)
    target = data[feature]

    # Split the data into training and testing sets using the given feature as the target
    from sklearn import cross_validation

    X_train, X_test, y_train, y_test = cross_validation.train_test_split(
        new_data, target, test_size = 0.25, random_state = 0)

    # Create a decision tree regressor and fit it to the training set
    from sklearn.tree import DecisionTreeRegressor

    regressor = DecisionTreeRegressor(random_state = 0)
    regressor.fit(X_train, y_train)
    # Report the score of the prediction using the testing set
    score = regressor.score(X_test, y_test)

    print feature, score


Fresh -0.252469807688
Milk 0.365725292736
Grocery 0.602801978878
Frozen 0.253973446697
Detergents_Paper 0.728655181254
Delicatessen -11.6636871594

Question 2

Which feature did you attempt to predict? What was the reported prediction score? Is this feature is necessary for identifying customers' spending habits?
Hint: The coefficient of determination, R^2, is scored between 0 and 1, with 1 being a perfect fit. A negative R^2 implies the model fails to fit the data.

Answer: I've tried to predict each feature of the set to understand if we have some features with a high r^2. The highest prediction score was 0.73 with Detergents_Paper. I don't think this feature is necessary for identifying customer habits, as we have a limited number of samples and that's why we shouldn't use highly correlated features in the dataset. And also we can get the same information from other features.

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.


In [16]:
# Correlations between segments
corr = data.corr()
mask = np.zeros_like(corr)
mask[np.triu_indices_from(mask)] = True
with sns.axes_style("white"):
    ax = sns.heatmap(corr, mask=mask, square=True, annot=True, cmap='RdBu')

# 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

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 several pairs of features: Milk - Detergents, Milk - Grocery, Grocery - Detergents.

The biggest correlation is between Grocery and Detergents_Paper features. This picture confirmed my suspicions about the relevance of the Groceries feature. In each case the data is skewed to the right.

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_data after applying a logarithm scaling. Use the np.log function for this.
  • Assign a copy of the sample data to log_samples after applying a logrithm scaling. Again, use np.log.

In [18]:
# 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')

## Checked the difference between data and cleaned data (with 1 deleted outlier)
## pd.scatter_matrix(good_data, alpha = 0.3, figsize = (14,8), diagonal = 'kde')


Out[18]:
array([[<matplotlib.axes._subplots.AxesSubplot object at 0x126a39690>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12b24d850>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x125c40990>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x129f2f350>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1268db0d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1269ce350>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x12b0f58d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12a81e2d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12864d950>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x126948a90>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x124e7fe10>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x124e6d110>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x1285c4910>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12adb0bd0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12b41eb50>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x125757bd0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1245e2890>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12458dd10>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x12460cd50>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x124619e10>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x124038710>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x125aca910>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1250d5d50>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1281de3d0>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x12b29e650>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x124577bd0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x124581a10>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1242c76d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x1281fc690>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12b463d50>],
       [<matplotlib.axes._subplots.AxesSubplot object at 0x12b2b3c10>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12ad98250>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12ac54310>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12b4f4b10>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x124ed62d0>,
        <matplotlib.axes._subplots.AxesSubplot object at 0x12bb10fd0>]], dtype=object)

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.


In [19]:
# Display the log-transformed sample data
display(log_samples)


Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
0 10.026369 8.596004 8.881558 8.272571 7.482682 8.553525
1 5.389072 9.163249 9.575192 5.645447 8.964184 5.049856
2 8.117312 7.074117 7.191429 8.612867 5.739793 6.907755

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. Use np.percentile for this.
  • Assign the value of the 75th percentile for the given feature to Q3. Again, use np.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 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 [22]:
# 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)
    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  = [75]

# Remove the outliers, if any were specified
good_data = log_data.drop(log_data.index[outliers]).reset_index(drop = True)


Data points considered outliers for the feature 'Fresh':
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
65 4.442651 9.950323 10.732651 3.583519 10.095388 7.260523
66 2.197225 7.335634 8.911530 5.164786 8.151333 3.295837
81 5.389072 9.163249 9.575192 5.645447 8.964184 5.049856
95 1.098612 7.979339 8.740657 6.086775 5.407172 6.563856
96 3.135494 7.869402 9.001839 4.976734 8.262043 5.379897
128 4.941642 9.087834 8.248791 4.955827 6.967909 1.098612
171 5.298317 10.160530 9.894245 6.478510 9.079434 8.740337
193 5.192957 8.156223 9.917982 6.865891 8.633731 6.501290
218 2.890372 8.923191 9.629380 7.158514 8.475746 8.759669
304 5.081404 8.917311 10.117510 6.424869 9.374413 7.787382
305 5.493061 9.468001 9.088399 6.683361 8.271037 5.351858
338 1.098612 5.808142 8.856661 9.655090 2.708050 6.309918
353 4.762174 8.742574 9.961898 5.429346 9.069007 7.013016
355 5.247024 6.588926 7.606885 5.501258 5.214936 4.844187
357 3.610918 7.150701 10.011086 4.919981 8.816853 4.700480
412 4.574711 8.190077 9.425452 4.584967 7.996317 4.127134
Data points considered outliers for the feature 'Milk':
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
86 10.039983 11.205013 10.377047 6.894670 9.906981 6.805723
98 6.220590 4.718499 6.656727 6.796824 4.025352 4.882802
154 6.432940 4.007333 4.919981 4.317488 1.945910 2.079442
356 10.029503 4.897840 5.384495 8.057377 2.197225 6.306275
Data points considered outliers for the feature 'Grocery':
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
75 9.923192 7.036148 1.098612 8.390949 1.098612 6.882437
154 6.432940 4.007333 4.919981 4.317488 1.945910 2.079442
Data points considered outliers for the feature 'Frozen':
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
38 8.431853 9.663261 9.723703 3.496508 8.847360 6.070738
57 8.597297 9.203618 9.257892 3.637586 8.932213 7.156177
65 4.442651 9.950323 10.732651 3.583519 10.095388 7.260523
145 10.000569 9.034080 10.457143 3.737670 9.440738 8.396155
175 7.759187 8.967632 9.382106 3.951244 8.341887 7.436617
264 6.978214 9.177714 9.645041 4.110874 8.696176 7.142827
325 10.395650 9.728181 9.519735 11.016479 7.148346 8.632128
420 8.402007 8.569026 9.490015 3.218876 8.827321 7.239215
429 9.060331 7.467371 8.183118 3.850148 4.430817 7.824446
439 7.932721 7.437206 7.828038 4.174387 6.167516 3.951244
Data points considered outliers for the feature 'Detergents_Paper':
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
75 9.923192 7.036148 1.098612 8.390949 1.098612 6.882437
161 9.428190 6.291569 5.645447 6.995766 1.098612 7.711101
Data points considered outliers for the feature 'Delicatessen':
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
66 2.197225 7.335634 8.911530 5.164786 8.151333 3.295837
109 7.248504 9.724899 10.274568 6.511745 6.728629 1.098612
128 4.941642 9.087834 8.248791 4.955827 6.967909 1.098612
137 8.034955 8.997147 9.021840 6.493754 6.580639 3.583519
142 10.519646 8.875147 9.018332 8.004700 2.995732 1.098612
154 6.432940 4.007333 4.919981 4.317488 1.945910 2.079442
183 10.514529 10.690808 9.911952 10.505999 5.476464 10.777768
184 5.789960 6.822197 8.457443 4.304065 5.811141 2.397895
187 7.798933 8.987447 9.192075 8.743372 8.148735 1.098612
203 6.368187 6.529419 7.703459 6.150603 6.860664 2.890372
233 6.871091 8.513988 8.106515 6.842683 6.013715 1.945910
285 10.602965 6.461468 8.188689 6.948897 6.077642 2.890372
289 10.663966 5.655992 6.154858 7.235619 3.465736 3.091042
343 7.431892 8.848509 10.177932 7.283448 9.646593 3.610918

Question 4

Are there any data points considered outliers for more than one feature? Should these data points be removed from the dataset? If any data points were added to the outliers list to be removed, explain why.

Answer:

There are several points, which are outliers for more than 1 feature: 65, 66, 75, 128, 154.

I think, only point 75 should be removed as it really changes the trend in the data and it is very far from the rest of data points. Probably, it is a recording error. After deleting we can see a better picture of the data.

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.PCA and assign the results of fitting PCA in six dimensions with good_data to pca.
  • Apply a PCA transformation of the sample log-data log_samples using pca.transform, and assign the results to pca_samples.

In [9]:
# Apply PCA to the good data with the same number of dimensions as features
from sklearn.decomposition import PCA

pca = PCA(n_components=len(good_data.columns))
pca.fit(good_data)

# Apply a PCA transformation to the sample log-data
pca_samples = pca.transform(log_samples)

# Generate PCA results plot
pca_results = rs.pca_results(good_data, pca)


Question 5

How much variance in the data is explained in total by the first and second principal component? What about the first four principal components? Using the visualization provided above, discuss what the first four dimensions best represent in terms of customer spending.
Hint: A positive increase in a specific dimension corresponds with an increase of the positive-weighted features and a decrease of the negative-weighted features. The rate of increase or decrease is based on the indivdual feature weights.

Answer:

  1. ~72% of data explained by 1 and 2 principal components.
  2. 93.4% of data explained by 1-4 components.

The first dimension has the biggest positive weight on Detergents and slightly lower weights on Groceries and Milk, which are the 3 features with the highest correlation (based on the plots). It also shows that these customers are buying Fresh and Frozen products in a much lesser proportion.

  • type of a customer: modern trade store (supermarket type) with a variety of products, probably with a smaller assortment (to maintain larger sales per meter from a shelf and to keep prices lower).
  • customers with a high value are buying Detergents more than any other product, sligthly less Milk and Groceries, while sales of Fresh and Frozen are low.
  • customers with a negative value are the opposite: they almost do not buy Detergents, Groceries and Milk.

The second dimension probably is orthogonal to the first, reducing the impact of Milk, Grocery, and Detergents, and instead puting high weights on sales of Fresh, Frozen and Delicatessen items.

  • type of a customer: HoReCa point of sales due to the prevalence of sales of foods which are needed to be cooked (Fresh, Frozen, Delicatessen).
  • customers with a positive value are buying Fresh, Frozen and Delicatessen products.
  • customers with a negative value almost aren't buying Fresh, Frozen and Delicatessen products.

The third dimension has a high Fresh weight and a very negative Delicatessen weight.

  • type of a customer: looks like an open market to me (farmers market for example) as it sells Fresh products more than anything else.
  • customers with a high positive value are buying a lot Fresh products.
  • customers with a negative value are buying primarily Delicatessen products with a slight increase in Frozen.

The 4th dimension is mostly focused on Frozen with a high weight and with a very low Delicatessen weight.

  • type of a customer: could be a place which sells frozen meat (but the Frozen category can be anything: ice cream, meat, etc - I don't know for sure). Considering the fact that this data is from Portugal, I would argue that this is a stall type of a client selling frozen meat products.
  • customers with a positive value buy Frozen and spend very little on Delicatessen.
  • customers with a negative value buy Delicatessen with a slight increase in Fresh products.

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.


In [10]:
# Display sample log-data after having a PCA transformation applied
display(pd.DataFrame(np.round(pca_samples, 4), columns = pca_results.index.values))


Dimension 1 Dimension 2 Dimension 3 Dimension 4 Dimension 5 Dimension 6
0 0.7965 2.4568 -0.4670 -0.3007 0.3025 0.0465
1 3.1348 -3.5991 -0.2480 0.7339 -0.3028 -0.1850
2 -1.8544 0.0541 -1.1964 0.7421 0.6962 -0.2770

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_data to pca.
  • Apply a PCA transformation of good_data using pca.transform, and assign the reuslts to reduced_data.
  • Apply a PCA transformation of the sample log-data log_samples using pca.transform, and assign the results to pca_samples.

In [11]:
# Fit PCA to the good data using only two dimensions
pca = PCA(n_components=2)
pca.fit(good_data)

# Apply a PCA transformation the good data
reduced_data = pca.transform(good_data)

# Apply a PCA transformation to the sample log-data
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.


In [12]:
# Display sample log-data after applying PCA transformation in two dimensions
display(pd.DataFrame(np.round(pca_samples, 4), columns = ['Dimension 1', 'Dimension 2']))


Dimension 1 Dimension 2
0 0.7965 2.4568
1 3.1348 -3.5991
2 -1.8544 0.0541

Clustering

In this section, you will choose to use either a K-Means clustering algorithm or a Gaussian Mixture Model clustering algorithm to identify the various customer segments hidden in the data. You will then recover specific data points from the clusters to understand their significance by transforming them back into their original dimension and scale.

Question 6

What are the advantages to using a K-Means clustering algorithm?

What are the advantages to using a Gaussian Mixture Model clustering algorithm?

Given your observations about the wholesale customer data so far, which of the two algorithms will you use and why?

Answer:

K-Means clustering:

  • It uses a hard assignment of points to clusters.
  • In practice, the k-means algorithm is very fast (one of the fastest clustering algorithms available) and scalable.
  • Gives best result when data set are distinct or well separated from each other.

Gaussian Mixture Model clustering:

  • The GMM algorithm is a good algorithm to use for the classification of static postures and non-temporal pattern recognition.
  • The fastest algorithm for learning mixture models, but it is slower than the K-Means due to using information about the data distribution — e.g., probabilities of points belonging to clusters.
  • It uses a soft classification, which means a sample will not be classified fully to one class but it will have different probabilities in several classes.

I will start with the K-Means, as I don't have a complete understanding of the dataset and K-means is usually used as a first algorithm to use for clustering.

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_data and assign it to clusterer.
  • Predict the cluster for each data point in reduced_data using clusterer.predict and assign them to preds.
  • 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_samples and assign them sample_preds.
  • Import sklearn.metrics.silhouette_score and calculate the silhouette score of reduced_data against preds.
    • Assign the silhouette score to score and print the result.

In [13]:
# Apply your clustering algorithm of choice to the reduced data 
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

clusters = range(2, 11)
best = (0, 0.0)

for each in clusters:
    clusterer = KMeans(n_clusters=each, random_state=0).fit(reduced_data)

    # Predict the cluster for each data point
    preds = clusterer.predict(reduced_data)

    # Find the cluster centers
    centers = clusterer.cluster_centers_

    # 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 "Clusters:", each, "score:", score
    if score > best[1]:
        best = (each, score)

clusterer = KMeans(n_clusters=best[0], random_state=0).fit(reduced_data)

# Predict the cluster for each data point
preds = clusterer.predict(reduced_data)

# Find the cluster centers
centers = clusterer.cluster_centers_

# 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 "The best n of Clusters:", best[0], "\nScore:", best[1]


Clusters: 2 score: 0.420795773671
Clusters: 3 score: 0.396034911432
Clusters: 4 score: 0.331704488262
Clusters: 5 score: 0.349383709753
Clusters: 6 score: 0.361735087656
Clusters: 7 score: 0.363059697196
Clusters: 8 score: 0.360593881403
Clusters: 9 score: 0.354722206188
Clusters: 10 score: 0.349422838857
The best n of Clusters: 2 
Score: 0.420795773671

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've tried 9 different numbers of clusters:

  • Clusters: 2 score: 0.420795773671
  • Clusters: 3 score: 0.396034911432
  • Clusters: 4 score: 0.331704488262
  • Clusters: 5 score: 0.349383709753
  • Clusters: 6 score: 0.361735087656
  • Clusters: 7 score: 0.363059697196
  • Clusters: 8 score: 0.360593881403
  • Clusters: 9 score: 0.354722206188
  • Clusters: 10 score: 0.349422838857

The best number of Clusters: 2 with a score: 0.420795773671

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.


In [14]:
# Display the results of the clustering from implementation
rs.cluster_results(reduced_data, preds, centers, pca_samples)


Implementation: Data Recovery

Each cluster present in the visualization above has a central point. These centers (or means) are not specifically data points from the data, but rather the averages of all the data points predicted in the respective clusters. For the problem of creating customer segments, a cluster's center point corresponds to the average customer of that segment. Since the data is currently reduced in dimension and scaled by a logarithm, we can recover the representative customer spending from these data points by applying the inverse transformations.

In the code block below, you will need to implement the following:

  • Apply the inverse transform to centers using pca.inverse_transform and assign the new centers to log_centers.
  • Apply the inverse function of np.log to log_centers using np.exp and assign the true centers to true_centers.

In [15]:
# 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(data.describe())
print samples


Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
Segment 0 3532.0 7893.0 12189.0 892.0 4611.0 977.0
Segment 1 8999.0 1899.0 2480.0 2081.0 297.0 676.0
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
count 440.000000 440.000000 440.000000 440.000000 440.000000 440.000000
mean 12000.297727 5796.265909 7951.277273 3071.931818 2881.493182 1524.870455
std 12647.328865 7380.377175 9503.162829 4854.673333 4767.854448 2820.105937
min 3.000000 55.000000 3.000000 25.000000 3.000000 3.000000
25% 3127.750000 1533.000000 2153.000000 742.250000 256.750000 408.250000
50% 8504.000000 3627.000000 4755.500000 1526.000000 816.500000 965.500000
75% 16933.750000 7190.250000 10655.750000 3554.250000 3922.000000 1820.250000
max 112151.000000 73498.000000 92780.000000 60869.000000 40827.000000 47943.000000
   Fresh  Milk  Grocery  Frozen  Detergents_Paper  Delicatessen
0  22615  5410     7198    3915              1777          5185
1    219  9540    14403     283              7818           156
2   3352  1181     1328    5502               311          1000

Question 8

Consider the total purchase cost of each product category for the representative data points above, and reference the statistical description of the dataset at the beginning of this project. What set of establishments could each of the customer segments represent?
Hint: A customer who is assigned to 'Cluster X' should best identify with the establishments represented by the feature set of 'Segment X'.

Answer:

Cluster 0: considering the sales of Milk, Groceries and Detergents which are much higher than mean we can think of this cluster as a retailers channel.

Cluster 1: high sales of Fresh products - probably so-called HoReCa channel: hotels, restaraunts, cafes.

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.


In [16]:
# Display the predictions
for i, pred in enumerate(sample_preds):
    print "Sample point", i, "predicted to be in Cluster", pred
    
import matplotlib.pyplot as plt

# check if samples' spending closer to segment 0 or 1
df_diffs = (np.abs(samples-true_centers.iloc[0]) < np.abs(samples-true_centers.iloc[1])).applymap(lambda x: 0 if x else 1)

# see how cluster predictions align with similariy of spending in each category
df_preds = pd.concat([df_diffs, pd.Series(sample_preds, name='PREDICTION')], axis=1)
sns.heatmap(df_preds, annot=True, cbar=False, yticklabels=['sample 0', 'sample 1', 'sample 2'], square=True)
plt.title('Samples closer to\ncluster 0 or 1?')
plt.xticks(rotation=45, ha='center')
plt.yticks(rotation=0);


Sample point 0 predicted to be in Cluster 0
Sample point 1 predicted to be in Cluster 0
Sample point 2 predicted to be in Cluster 1

Answer:

Point 0 is consistent with the predictions. Almost every product is selling in high volumes, including Detergents.

Point 1 is also consistent because of the high sales of both Groceries and Detergents.

Point 2 consistent, sales in Fresh are the most important.

Conclusion

Question 10

Companies often run A/B tests when making small changes to their products or services. If the wholesale distributor wanted to change its delivery service from 5 days a week to 3 days a week, how would you use the structure of the data to help them decide on a group of customers to test?
Hint: Would such a change in the delivery service affect all customers equally? How could the distributor identify who it affects the most?

Answer:

I would choose some percentage of customers from both of the clusters (let's say 5%) and I would test both methods of deliveries on them, for example:

Pick 22 customers from the segment 0: 11 - 5 days/week, 11 - 3 days/week. Gather feedback, make a decision. Repeat the same for the segment 1.

Question 11

Assume the wholesale distributor wanted to predict a new feature for each customer based on the purchasing information available. How could the wholesale distributor use the structure of the clustering data you've found to assist a supervised learning analysis?
Hint: What other input feature could the supervised learner use besides the six product features to help make a prediction?

Answer:

Supervised learner coud have used numbers of segments predicted by the K-means algorithm.

Visualizing Underlying Distributions

At the beginning of this project, it was discussed that the 'Channel' and 'Region' features would be excluded from the dataset so that the customer product categories were emphasized in the analysis. By reintroducing the 'Channel' feature to the dataset, an interesting structure emerges when considering the same PCA dimensionality reduction applied earlier on to the original dataset.

Run the code block below to see how each data point is labeled either 'HoReCa' (Hotel/Restaurant/Cafe) or 'Retail' the reduced space. In addition, you will find the sample points are circled in the plot, which will identify their labeling.


In [17]:
# Display the clustering results based on 'Channel' data
rs.channel_results(reduced_data, outliers, pca_samples)


Question 12

How well does the clustering algorithm and number of clusters you've chosen compare to this underlying distribution of Hotel/Restaurant/Cafe customers to Retailer customers? Are there customer segments that would be classified as purely 'Retailers' or 'Hotels/Restaurants/Cafes' by this distribution? Would you consider these classifications as consistent with your previous definition of the customer segments?

Answer:

I would say that the clustering algorithm and the number of clusters are extremely similar to the real distribution of the clients and did a good job of separating customers. I would probably argue, that the algorithm did a better job of separating clients and could've been used in the real life to adjust delivery model, because we clearly saw a division by products sold in each of the segment: Fresh products should be delivered more often, other products - doesn't really matter.

There is some overlap between the segments, but it's not as critical and happens all the time in the real life. Some HoReCa customers can have a similar model of sales to retailers (for example, they can have a store inside a hotel, so the sales could be comparable to those of a small retailer).

I think that my definition of customer segments is consistent with the classification.

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.