Machine Learning Engineer Nanodegree

Unsupervised Learning

Project: 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 [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?")
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 [2]:
# 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 [3]:
# TODO: Select three indices of your choice you wish to sample from the dataset
indices = [0, 200, 360]

# 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)
Chosen samples of wholesale customers dataset:
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
0 12669 9656 7561 214 2674 1338
1 3067 13240 23127 3941 9959 731
2 19746 2872 2006 2601 468 503

Question 1

Consider the total purchase cost of each product category and the statistical description of the dataset above for your sample customers.

  • What kind of establishment (customer) could each of the three samples you've chosen represent?

Hint: Examples of establishments include places like markets, cafes, delis, wholesale retailers, among many others. Avoid using names for establishments, such as saying "McDonalds" when describing a sample customer as a restaurant. You can use the mean values for reference to compare your samples with. The mean values are as follows:

  • Fresh: 12000.2977
  • Milk: 5796.2
  • Grocery: 7951.3
  • Frozen: 3071.9318
  • Detergents_paper: 2881.4
  • Delicatessen: 1524.8

Knowing this, how do your samples compare? Does that help in driving your insight into what kind of establishments they might be?

Answer:

  • The first sample is clearly sort of restaurant that sell a lot of cooking foods to customers because they spend money on fresh category more than that of the mean scale. Besides, milk is a very great ingredient for cooking and many restaurants love to use milk as their main ingredient for drink like coffee.
  • The second sample must be retail store/supermarket. 23127 on Grocery category and 9959 on Detergents paper category are the excellent signals here: retail store loves to stock a lot of cleaning stuff.
  • The third sample spend tremendously on Fresh category and a little on Frozen. This should be market that sell fresh foods from farms with some frozen meats.

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 [4]:
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestRegressor

# TODO: Make a copy of the DataFrame, using the 'drop' function to drop the given feature
new_data = data.copy()

target = 'Grocery'

X = new_data.drop(target, axis=1)
y = new_data[target]

# TODO: Split the data into training and testing sets(0.25) using the given feature as the target
# Set a random state.
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=123)

# TODO: Create a decision tree regressor and fit it to the training set
regressor = RandomForestRegressor(n_estimators=1000, n_jobs=-1 ,random_state=123)
regressor.fit(X_train, y_train)

# TODO: Report the score of the prediction using the testing set
score = regressor.score(X_test, y_test)

print(score)
0.9160162890682477

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 am trying to predict the Grocery category.
  • R^2 score is significantly high, 0.9160.
  • I think the R^2 is pretty high because random forrest can capture some behaviours of grocery stores/retailers. Most of grocery stores tend to spend heavily on every category, to stock a lot of goods for customers. Thus, random forrest see this patterns and can predict annual spending amounts on grocery very accurately.
  • However, this feature "Grocery" may not be neccesary for indentifying customers' spending habits much because it means this feature is highly correlated with each others and "Grocery" may give us just a very little information to the model.
  • In many cases, most data scientists tend to drop highly correlated features to prevent 'multicolinearlity' of linear model and curse of dimensionality. The idea behind here is to keep your model simple as much as possible. However, this is also depended on which models you use, some models can handle this by themselves such as tree/ random forrest.

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 [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');
/home/john/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: FutureWarning: pandas.scatter_matrix is deprecated. Use pandas.plotting.scatter_matrix instead
  

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.

In [6]:
import matplotlib.pyplot as plt
import seaborn as sns

sns.heatmap(data.corr())
plt.show()
In [7]:
fig, ax = plt.subplots(figsize=(10, 5))

for col in data.columns:
    sns.kdeplot(data[col], shade=True, ax=ax)
In [8]:
data.describe()
Out[8]:
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

Answer:

  • Detergents paper and Grocery is highly correlated. This supports my analysis in question 1 that retail store tends to stock a lot of detergents paper.
  • Grocery also has the most correlated values with others. This supports my analysis in question 2 that retail store tends to purchase a bulk of other categories, and this could explain why R2 score in question 2 are pretty damn high - highly strong correlation.

  • All of the features have the mean value greater than the median meaning they are positively skewed and have long tail distribution. The mean of each feature clearly affected by the very large value in the distribution (outliers). It's a good idea to do some transformation such as log transformation to make hightly skewed distribution less skewed.

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 logarithmic scaling. Use the np.log function for this.
  • Assign a copy of the sample data to log_samples after applying logarithmic scaling. Again, use np.log.
In [9]:
# TODO: Scale the data using the natural logarithm
log_data = np.log(new_data)

# TODO: Scale the sample data using the natural logarithm
log_samples = np.log(samples)

# Produce a scatter matrix for each pair of newly-transformed features
pd.scatter_matrix(log_data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');
/home/john/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:8: FutureWarning: pandas.scatter_matrix is deprecated. Use pandas.plotting.scatter_matrix instead
  

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 [10]:
# Display the log-transformed sample data
display(log_samples)
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
0 9.446913 9.175335 8.930759 5.365976 7.891331 7.198931
1 8.028455 9.490998 10.048756 8.279190 9.206232 6.594413
2 9.890706 7.962764 7.603898 7.863651 6.148468 6.220590

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 [11]:
outliers  = []

# For each feature find the data points with extreme high or low values
for feature in log_data.keys():
    
    # TODO: Calculate Q1 (25th percentile of the data) for the given feature
    Q1 = np.percentile(log_data[feature], 25)
    
    # TODO: Calculate Q3 (75th percentile of the data) for the given feature
    Q3 = np.percentile(log_data[feature], 75)
    
    # TODO: Use the interquartile range to calculate an outlier step (1.5 times the interquartile range)
    step = 1.5 * (Q3 - Q1)
    
    # Display the outliers
    print("Data points considered outliers for the feature '{}':".format(feature))
    outliers_df = log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))]
    display(outliers_df)
    outliers.extend(outliers_df.index.values)
    
# OPTIONAL: Select the indices for data points you wish to remove
outliers = list(sorted(set([i for i in outliers if outliers.count(i) > 1])))
print(outliers)

# 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
[65, 66, 75, 128, 154]

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 outliers list 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:

  • Based on my code, there are a lot of data points that appear as outliers more than one features in data.
  • There are 65, 66, 75, 128, 154 index values.
  • If the data points are shown as the outliers more than one time, it should be considered as outliers because it is highly risk to be collected wrongly or record mistakenly.
  • However, appearing one time is acceptable. They might spend much truly on that category. This is a very valuable information and should not be removed.
  • Another reason to remove outliers here is because the way k-means works is to calculate the distances and measure the centroids(mean). Suspicious outliers impact directly on this method and should be removed whenever you can.

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 log_samples using pca.transform, and assign the results to pca_samples.
In [12]:
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=good_data.shape[1]).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)

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:

  • The first and second principal component explain 0.4430 + 0.2638 = 0.7068 variance in the data.
  • The first four principal componentes explain 0.4430 + 0.2638 + 0.1231 + 0.1012 = 0.9311 variance in the data.
  • The first dimension explain 0.4430 variance in the data. The visualization tells us that detergents_paper has the largest impacact on this dimension. Besides, milk and grocery have also the large impact here. Because of grocery, detergents_paper and milk, I strongly believe that this represent a retail store customers like my second sample in question 1.
  • The second dimension explain 0.2638 variance in the data. Now, you can see that this dimension has covered other features like Fresh and Frozen into negative values like others. This represents much more on fresh market/restaurants customers (my third sample in question 1) and also retailers.
  • The third dimension explain 0.1231 variance in the data. Fresh and delicatessen play a big contrast here. This would represents markets and a much small retail store than previous pc.
  • The forth dimension explain 0.1012 in the data. This is the first time that Frozen has the largest impact. In my opinion, I think this pc is sort of like the complementary of the third dimension. It just represents markets and a small retail store in a different way.
  • The fifth dimension explain 0.0485 in the data. Note that in most case, we tend to drop this and last component because the cumulative sums of 1-4 principals is 0.9311 which could keep most information in this dataset. Analyising this principal component is harder because it mostly capture a lot of noise. The largest impact is milk so this could represent the retailer customers again.
  • The sixth dimension explain 0.0204 in the data. It is super small and may not give much valuable information here.

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 [13]:
# 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 -1.7580 0.0097 -0.9590 -1.6824 0.2680 -0.3891
1 -2.9903 -0.3645 0.2521 1.5653 0.1922 0.1244
2 1.2858 -0.6909 -0.7416 0.2645 0.0180 -0.4601

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 results to reduced_data.
  • Apply a PCA transformation of log_samples using pca.transform, and assign the results to pca_samples.
In [14]:
# TODO: Apply PCA by fitting the good data with only two dimensions
pca = PCA(n_components=2).fit(good_data)

# TODO: Transform the good data using the PCA fit above
reduced_data = pca.transform(good_data)

# TODO: Transform log_samples using the PCA fit above
pca_samples = pca.transform(log_samples)

# Create a DataFrame for the reduced data
reduced_data = pd.DataFrame(reduced_data, columns = ['Dimension 1', 'Dimension 2'])

Observation

Run the code below to see how the log-transformed sample data has changed after having a PCA transformation applied to it using only two dimensions. Observe how the values for the first two dimensions remains unchanged when compared to a PCA transformation in six dimensions.

In [15]:
# 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 -1.7580 0.0097
1 -2.9903 -0.3645
2 1.2858 -0.6909

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.

In [16]:
# Create a biplot
vs.biplot(good_data, reduced_data, pca)
Out[16]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f3047b642e8>

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 can compute very fast and it is very easy to write an algorithm from scratch. Also, it converges to the optimum very fast with just a few iterations.
  • Gaussian Mixture Model performs much better on soft clustering. When you are not sure about the boundaries region, GMM should be used as it's much more flexible and handle much better on data points overlapping in multiple regions.
  • According to reduced dimension scatter plot of this data, the data points cannot be grouped with naked eyes and the clear boundaries region for each customers are not there. In this case, soft clustering, meaning that the data point can be assigned to more than one group, should be picked and implemented here.

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 [17]:
from sklearn.mixture import GaussianMixture
from sklearn.metrics import silhouette_score

# Choose n components
for i in range(2, 11):
    # TODO: Apply your clustering algorithm of choice to the reduced data 
    clusterer = GaussianMixture(n_components=i).fit(reduced_data)

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

    # TODO: Find the cluster centers
    centers = clusterer.means_

    # TODO: Predict the cluster for each transformed sample data point
    sample_preds = clusterer.predict(pca_samples)

    # TODO: Calculate the meGaussianMixtureGaussianMixturean silhouette coefficient for the number of clusters chosen
    score = silhouette_score(reduced_data, preds)
    print(f'{i} clusters: silhouette score is {score}')
2 clusters: silhouette score is 0.4223246826459388
3 clusters: silhouette score is 0.39442078175032197
4 clusters: silhouette score is 0.2883915968747593
5 clusters: silhouette score is 0.3159596455918114
6 clusters: silhouette score is 0.25327286978208724
7 clusters: silhouette score is 0.2709596561369201
8 clusters: silhouette score is 0.2578888877471003
9 clusters: silhouette score is 0.2957182912690238
10 clusters: silhouette score is 0.3252330223691048
In [18]:
# TODO: Apply your clustering algorithm of choice to the reduced data 
clusterer = GaussianMixture(n_components=2).fit(reduced_data)

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

# TODO: Find the cluster centers
centers = clusterer.means_

# TODO: Predict the cluster for each transformed sample data point
sample_preds = clusterer.predict(pca_samples)

# TODO: Calculate the mean silhouette coefficient for the number of clusters chosen
score = silhouette_score(reduced_data, preds)
print(f'silhouette_score:{score}')
silhouette_score:0.4219168464626149

Question 7

  • Report the silhouette score for several cluster numbers you tried.
  • Of these, which number of clusters has the best silhouette score?

Answer:

  • 2 clusters: silhouette score is 0.4223246826459388
  • 3 clusters: silhouette score is 0.37553218893793083
  • 4 clusters: silhouette score is 0.3012335184138044
  • 5 clusters: silhouette score is 0.2887287136765808
  • 6 clusters: silhouette score is 0.29919288343704986
  • 7 clusters: silhouette score is 0.33528795634914194
  • 8 clusters: silhouette score is 0.3264498908364276
  • 9 clusters: silhouette score is 0.29238384528328487
  • 10 clusters: silhouette score is 0.3214341260690378

The best sihouette score is from 2 clusters : 0.422.. score

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 [19]:
# Display the results of the clustering from implementation
vs.cluster_results(reduced_data, preds, centers, pca_samples)

Implementation: Data Recovery

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

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

  • Apply the inverse transform to 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 [20]:
# 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)
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
Segment 0 3552.0 7837.0 12219.0 870.0 4696.0 962.0
Segment 1 8953.0 2114.0 2765.0 2075.0 353.0 732.0

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.

  • Fresh: 12000.2977
  • Milk: 5796.2
  • Grocery: 7951.3
  • Frozen: 3071.9318
  • Detergents_paper: 2881.4
  • Delicatessen: 1524.8

Answer: </br> When we are dealing with clustering or segments groups, it is always worth looking at the average of each category and compare that with our clustering point.

  • The segment 0 has 3 most important features that can distinguish the customer group easily. These 3 features are Milk, Grocery and Detergents_Paper. Noticing that these 3 features has their values above averages on each of them. This segment is customer group of retail store/supermarkets.
  • The segment 1 represents food market/restaurant customer. Milk, Grocery and detergents_paper cateogry has below average. You can see clearly the large gap of frozen and fresh category between these 2 segments.

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 [21]:
# Display the predictions
for i, pred in enumerate(sample_preds):
    print("Sample point", i, "predicted to be in Cluster", pred)
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:

  • According to prediction in question 8: First and second sample is retail store customers. third sample is the market/restaurant customer.

  • At the beginning of this journey, I think first sample is sort of restaurant because of the very high values of fresh. Unfortunately, I might be wrong here because our prediction say it is in retail store segment. The possible explanation here is that I blindly ignore to look grocery value. In addition, milk is an important signal for the retail store customer.

  • Second and third sample prediction are sastified and reasonable. Second sample clearly is a big retail store that match my explanation in question 8. Third sample's prediction does make a lot of sense here because they spend a lot of money on fresh like I've explained in question 8.

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:

  • The motivation behind wholesale distributor doing this is to make their customers happier, reduce and optimize costs of delivery/storage, and store stocks/products much more effeicent and effective.

  • Firstly, before proceeding to whatever you're going to do, let understand the different between segment 0 and segment 1.

  • Segment 0 is the customers who love to purchase products that could be stored for weeks. Think of it as retail stores selling tissue papers, housewares.
  • Segment 1 is the customers who really love to purcahse fresh foods. Obviously, those cannot be stored for a long time. Think of it as restaurants selling foods or fresh markets selling raw materials to chefs.
  • Thus, the difference is 'Fresh' and Not 'Fresh'.

  • Wholesale distributor, thus, decides to do some A/B tests experiment. The hypothesis is to expect the positive reaction from segment 0 and negative reaction from segment 1.

  • segment 0 may be sastified. That means they have to pay much less on delivery costs and their inventory would not be flooded by tissue papers anymore.
  • However, segment 1 may be dissapointed because they love 'fresh'. Delivering much less means no 'fresh' food like before and also encounter with "out of stocks" fresh food problem.

  • So, we setup the test group and control group by assigning random samples into each group. Changing delivery days in test group but do nothing in control group.

  • Now, we can compare each segment group independently. For example, segment 0 in control group vs segment 0 in test group.
  • With these setup, now we can measure the difference, reaction of each segment (positve or negative reaction) and improvement of tweaking the delivery days.

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:

  • Just use the clustering group labels as the target variable and total spending on each category as the input features.
  • Use any supervised learner (knn, svm, tree) to fit and train the model.
  • Now, we can easily predict and do a customer segment to our new customers by using our supervised learner.

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.

In [22]:
# Display the clustering results based on 'Channel' data
vs.channel_results(reduced_data, outliers, pca_samples)

Question 12

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

Answer:

  • It does a pretty good job!. We can easily intrepret the result and clearly draw a boundaries region between hotel/restaurant/cafe and retailer customers.
  • According to the visualization, higher dimension 1 means customers in hotel/restaurant/cafe segment while lower dimension 1 is retail stores.
  • However, they still have no 100% clear line to separate them. There are some data points lying randomly across the scatter plot.
  • I am not surprised now why my first sample analysis in question 1 and 8 is wrong. the graph shows that the closest data point of my first sample is classified as Restaurants customers which match my initial analysis.
  • I would consider these classifications as consistent with my previous analysis throughout this notebook. Notice that even my first sample has a proper explanation now.

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.