Appendix B: K-Means customer segmentation case study#

import os
import random
import sys
import time

import numpy as np
import pandas as pd

sys.path.append("code/.")
import matplotlib.pyplot as plt
import seaborn as sns

from plotting_functions import *
from sklearn import cluster, datasets, metrics
from sklearn.compose import ColumnTransformer, make_column_transformer
from sklearn.datasets import make_blobs
from sklearn.decomposition import PCA
from sklearn.pipeline import Pipeline, make_pipeline
from sklearn.preprocessing import StandardScaler
# from support_functions import *
from yellowbrick.cluster import KElbowVisualizer, SilhouetteVisualizer

#plt.style.use("seaborn")

plt.rcParams["font.size"] = 16

What is customer segmentation?#

  • Understand landscape of the market in businesses and craft targeted business or marketing strategies tailored for each group.

source

Check out this interesting talk by Malcom Gladwell. Humans are diverse and there is no single spaghetti sauce that would make all of them happy!

Often it’s beneficial to businesses to explore the landscape of the market and tailor their services and products offered to each group. This is called customer segmentation. It’s usually applied when the dataset contains some of the following features.

  • Demographic information such as gender, age, marital status, income, education, and occupation

  • Geographical information such as specific towns or counties or a customer’s city, state, or even country of residence (in case of big global companies)

  • Psychographics such as social class, lifestyle, and personality traits

  • Behavioral data such as spending and consumption habits, product/service usage, and desired benefits

Business problem#

  • Imagine that you are hired as a data scientist at a bank. They provide some data of their credit card customers to you.

  • Their goal is to develop customized marketing campaigns and they ask you to group customers based on the given information.

  • Now that you know about K-Means clustering, let’s apply it to the dataset to group customers.

Data#

  • We will use the Credit Card Dataset for clustering from Kaggle.

  • Download the data and save the CSV under the data folder.

  • I encourage you to work through this case study on your own.

creditcard_df = pd.read_csv("data/CC General.csv")
creditcard_df.shape

---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
Cell In[2], line 1
----> 1 creditcard_df = pd.read_csv("data/CC General.csv")
      2 creditcard_df.shape

File ~/miniconda3/envs/cpsc330/lib/python3.10/site-packages/pandas/io/parsers/readers.py:948, in read_csv(filepath_or_buffer, sep, delimiter, header, names, index_col, usecols, dtype, engine, converters, true_values, false_values, skipinitialspace, skiprows, skipfooter, nrows, na_values, keep_default_na, na_filter, verbose, skip_blank_lines, parse_dates, infer_datetime_format, keep_date_col, date_parser, date_format, dayfirst, cache_dates, iterator, chunksize, compression, thousands, decimal, lineterminator, quotechar, quoting, doublequote, escapechar, comment, encoding, encoding_errors, dialect, on_bad_lines, delim_whitespace, low_memory, memory_map, float_precision, storage_options, dtype_backend)
    935 kwds_defaults = _refine_defaults_read(
    936     dialect,
    937     delimiter,
   (...)
    944     dtype_backend=dtype_backend,
    945 )
    946 kwds.update(kwds_defaults)
--> 948 return _read(filepath_or_buffer, kwds)

File ~/miniconda3/envs/cpsc330/lib/python3.10/site-packages/pandas/io/parsers/readers.py:611, in _read(filepath_or_buffer, kwds)
    608 _validate_names(kwds.get("names", None))
    610 # Create the parser.
--> 611 parser = TextFileReader(filepath_or_buffer, **kwds)
    613 if chunksize or iterator:
    614     return parser

File ~/miniconda3/envs/cpsc330/lib/python3.10/site-packages/pandas/io/parsers/readers.py:1448, in TextFileReader.__init__(self, f, engine, **kwds)
   1445     self.options["has_index_names"] = kwds["has_index_names"]
   1447 self.handles: IOHandles | None = None
-> 1448 self._engine = self._make_engine(f, self.engine)

File ~/miniconda3/envs/cpsc330/lib/python3.10/site-packages/pandas/io/parsers/readers.py:1705, in TextFileReader._make_engine(self, f, engine)
   1703     if "b" not in mode:
   1704         mode += "b"
-> 1705 self.handles = get_handle(
   1706     f,
   1707     mode,
   1708     encoding=self.options.get("encoding", None),
   1709     compression=self.options.get("compression", None),
   1710     memory_map=self.options.get("memory_map", False),
   1711     is_text=is_text,
   1712     errors=self.options.get("encoding_errors", "strict"),
   1713     storage_options=self.options.get("storage_options", None),
   1714 )
   1715 assert self.handles is not None
   1716 f = self.handles.handle

File ~/miniconda3/envs/cpsc330/lib/python3.10/site-packages/pandas/io/common.py:863, in get_handle(path_or_buf, mode, encoding, compression, memory_map, is_text, errors, storage_options)
    858 elif isinstance(handle, str):
    859     # Check whether the filename is to be opened in binary mode.
    860     # Binary mode does not support 'encoding' and 'newline'.
    861     if ioargs.encoding and "b" not in ioargs.mode:
    862         # Encoding
--> 863         handle = open(
    864             handle,
    865             ioargs.mode,
    866             encoding=ioargs.encoding,
    867             errors=errors,
    868             newline="",
    869         )
    870     else:
    871         # Binary mode
    872         handle = open(handle, ioargs.mode)

FileNotFoundError: [Errno 2] No such file or directory: 'data/CC General.csv'

Information of the dataset#

We have behavioral data.

  • CUSTID: Identification of Credit Card holder

  • BALANCE: Balance amount left in customer’s account to make purchases

  • BALANCE_FREQUENCY: How frequently the Balance is updated, score between 0 and 1 (1 = frequently updated, 0 = not frequently updated)

  • PURCHASES: Amount of purchases made from account

  • ONEOFFPURCHASES: Maximum purchase amount done in one-go

  • INSTALLMENTS_PURCHASES: Amount of purchase done in installment

  • CASH_ADVANCE: Cash in advance given by the user

  • PURCHASES_FREQUENCY: How frequently the Purchases are being made, score between 0 and 1 (1 = frequently purchased, 0 = not frequently purchased)

  • ONEOFF_PURCHASES_FREQUENCY: How frequently Purchases are happening in one-go (1 = frequently purchased, 0 = not frequently purchased)

  • PURCHASES_INSTALLMENTS_FREQUENCY: How frequently purchases in installments are being done (1 = frequently done, 0 = not frequently done)

  • CASH_ADVANCE_FREQUENCY: How frequently the cash in advance being paid

  • CASH_ADVANCE_TRX: Number of Transactions made with “Cash in Advance”

  • PURCHASES_TRX: Number of purchase transactions made

  • CREDIT_LIMIT: Limit of Credit Card for user

  • PAYMENTS: Amount of Payment done by user

  • MINIMUM_PAYMENTS: Minimum amount of payments made by user

  • PRC_FULL_PAYMENT: Percent of full payment paid by user

  • TENURE: Tenure of credit card service for user

Preliminary EDA#

creditcard_df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 8950 entries, 0 to 8949
Data columns (total 18 columns):
 #   Column                            Non-Null Count  Dtype  
---  ------                            --------------  -----  
 0   CUST_ID                           8950 non-null   object 
 1   BALANCE                           8950 non-null   float64
 2   BALANCE_FREQUENCY                 8950 non-null   float64
 3   PURCHASES                         8950 non-null   float64
 4   ONEOFF_PURCHASES                  8950 non-null   float64
 5   INSTALLMENTS_PURCHASES            8950 non-null   float64
 6   CASH_ADVANCE                      8950 non-null   float64
 7   PURCHASES_FREQUENCY               8950 non-null   float64
 8   ONEOFF_PURCHASES_FREQUENCY        8950 non-null   float64
 9   PURCHASES_INSTALLMENTS_FREQUENCY  8950 non-null   float64
 10  CASH_ADVANCE_FREQUENCY            8950 non-null   float64
 11  CASH_ADVANCE_TRX                  8950 non-null   int64  
 12  PURCHASES_TRX                     8950 non-null   int64  
 13  CREDIT_LIMIT                      8949 non-null   float64
 14  PAYMENTS                          8950 non-null   float64
 15  MINIMUM_PAYMENTS                  8637 non-null   float64
 16  PRC_FULL_PAYMENT                  8950 non-null   float64
 17  TENURE                            8950 non-null   int64  
dtypes: float64(14), int64(3), object(1)
memory usage: 1.2+ MB

  • All numeric features

  • Some missing values

creditcard_df.describe()
BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
count 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8950.000000 8949.000000 8950.000000 8637.000000 8950.000000 8950.000000
mean 1564.474828 0.877271 1003.204834 592.437371 411.067645 978.871112 0.490351 0.202458 0.364437 0.135144 3.248827 14.709832 4494.449450 1733.143852 864.206542 0.153715 11.517318
std 2081.531879 0.236904 2136.634782 1659.887917 904.338115 2097.163877 0.401371 0.298336 0.397448 0.200121 6.824647 24.857649 3638.815725 2895.063757 2372.446607 0.292499 1.338331
min 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 50.000000 0.000000 0.019163 0.000000 6.000000
25% 128.281915 0.888889 39.635000 0.000000 0.000000 0.000000 0.083333 0.000000 0.000000 0.000000 0.000000 1.000000 1600.000000 383.276166 169.123707 0.000000 12.000000
50% 873.385231 1.000000 361.280000 38.000000 89.000000 0.000000 0.500000 0.083333 0.166667 0.000000 0.000000 7.000000 3000.000000 856.901546 312.343947 0.000000 12.000000
75% 2054.140036 1.000000 1110.130000 577.405000 468.637500 1113.821139 0.916667 0.300000 0.750000 0.222222 4.000000 17.000000 6500.000000 1901.134317 825.485459 0.142857 12.000000
max 19043.138560 1.000000 49039.570000 40761.250000 22500.000000 47137.211760 1.000000 1.000000 1.000000 1.500000 123.000000 358.000000 30000.000000 50721.483360 76406.207520 1.000000 12.000000

Practice exercises for you#

  1. What is the average BALANCE amount?

  2. How often the BALANCE_FREQUENCY is updated on average?

  3. Obtain the row the customer who made the maximum cash advance transaction.





Mini exercises for you (Answers)#

  1. What is the average BALANCE amount? 1564.47

  2. How often the BALANCE_FREQUENCY is updated on average? 0.877 (pretty often)

  3. Obtain the row of the customer who made the maximum cash advance transaction.

# Answer 3.
max_cash_advance = creditcard_df["CASH_ADVANCE"].max()
creditcard_df[creditcard_df["CASH_ADVANCE"] == max_cash_advance]
CUST_ID BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
2159 C12226 10905.05381 1.0 431.93 133.5 298.43 47137.21176 0.583333 0.25 0.5 1.0 123 21 19600.0 39048.59762 5394.173671 0.0 12

Let’s examine correlations between features.

cor = creditcard_df.corr()
plt.figure(figsize=(20, 10))
sns.set(font_scale=1)
sns.heatmap(cor, annot=True, cmap=plt.cm.Blues);

/var/folders/b3/g26r0dcx4b35vf3nk31216hc0000gr/T/ipykernel_6151/4232743610.py:1: FutureWarning: The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.
  cor = creditcard_df.corr()
../_images/26db054514c34f27e74fe82d516415367c201467b6d55b379a16001bf05fe8b4.png 
corr_df = (creditcard_df.corr('spearman').round(2))
corr_df.style.background_gradient().set_precision(2)

/var/folders/b3/g26r0dcx4b35vf3nk31216hc0000gr/T/ipykernel_6151/2227010425.py:1: FutureWarning: The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.
  corr_df = (creditcard_df.corr('spearman').round(2))
/var/folders/b3/g26r0dcx4b35vf3nk31216hc0000gr/T/ipykernel_6151/2227010425.py:2: FutureWarning: this method is deprecated in favour of `Styler.format(precision=..)`
  corr_df.style.background_gradient().set_precision(2)
  BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
BALANCE 1.00 0.54 0.01 0.15 -0.09 0.57 -0.15 0.12 -0.14 0.54 0.55 -0.05 0.37 0.43 0.90 -0.48 0.07
BALANCE_FREQUENCY 0.54 1.00 0.15 0.13 0.13 0.14 0.20 0.16 0.15 0.18 0.18 0.20 0.11 0.21 0.50 -0.17 0.23
PURCHASES 0.01 0.15 1.00 0.75 0.71 -0.38 0.79 0.69 0.61 -0.39 -0.38 0.89 0.26 0.39 -0.01 0.24 0.13
ONEOFF_PURCHASES 0.15 0.13 0.75 1.00 0.20 -0.18 0.42 0.95 0.12 -0.18 -0.18 0.59 0.30 0.36 0.07 0.05 0.10
INSTALLMENTS_PURCHASES -0.09 0.13 0.71 0.20 1.00 -0.36 0.79 0.19 0.92 -0.37 -0.36 0.78 0.12 0.24 -0.05 0.28 0.12
CASH_ADVANCE 0.57 0.14 -0.38 -0.18 -0.36 1.00 -0.45 -0.19 -0.38 0.94 0.95 -0.41 0.16 0.26 0.48 -0.27 -0.11
PURCHASES_FREQUENCY -0.15 0.20 0.79 0.42 0.79 -0.45 1.00 0.46 0.85 -0.45 -0.45 0.92 0.10 0.17 -0.10 0.29 0.10
ONEOFF_PURCHASES_FREQUENCY 0.12 0.16 0.69 0.95 0.19 -0.19 0.46 1.00 0.11 -0.18 -0.17 0.61 0.28 0.32 0.05 0.06 0.08
PURCHASES_INSTALLMENTS_FREQUENCY -0.14 0.15 0.61 0.12 0.92 -0.38 0.85 0.11 1.00 -0.38 -0.37 0.78 0.05 0.12 -0.08 0.26 0.11
CASH_ADVANCE_FREQUENCY 0.54 0.18 -0.39 -0.18 -0.37 0.94 -0.45 -0.18 -0.38 1.00 0.98 -0.41 0.09 0.20 0.46 -0.29 -0.13
CASH_ADVANCE_TRX 0.55 0.18 -0.38 -0.18 -0.36 0.95 -0.45 -0.17 -0.37 0.98 1.00 -0.40 0.10 0.21 0.47 -0.28 -0.10
PURCHASES_TRX -0.05 0.20 0.89 0.59 0.78 -0.41 0.92 0.61 0.78 -0.41 -0.40 1.00 0.19 0.28 -0.03 0.25 0.17
CREDIT_LIMIT 0.37 0.11 0.26 0.30 0.12 0.16 0.10 0.28 0.05 0.09 0.10 0.19 1.00 0.45 0.26 0.02 0.17
PAYMENTS 0.43 0.21 0.39 0.36 0.24 0.26 0.17 0.32 0.12 0.20 0.21 0.28 0.45 1.00 0.37 0.19 0.21
MINIMUM_PAYMENTS 0.90 0.50 -0.01 0.07 -0.05 0.48 -0.10 0.05 -0.08 0.46 0.47 -0.03 0.26 0.37 1.00 -0.48 0.14
PRC_FULL_PAYMENT -0.48 -0.17 0.24 0.05 0.28 -0.27 0.29 0.06 0.26 -0.29 -0.28 0.25 0.02 0.19 -0.48 1.00 0.02
TENURE 0.07 0.23 0.13 0.10 0.12 -0.11 0.10 0.08 0.11 -0.13 -0.10 0.17 0.17 0.21 0.14 0.02 1.00

Feature types and preprocessing#

Let’s identify different feature types and transformations

creditcard_df.columns

Index(['CUST_ID', 'BALANCE', 'BALANCE_FREQUENCY', 'PURCHASES',
       'ONEOFF_PURCHASES', 'INSTALLMENTS_PURCHASES', 'CASH_ADVANCE',
       'PURCHASES_FREQUENCY', 'ONEOFF_PURCHASES_FREQUENCY',
       'PURCHASES_INSTALLMENTS_FREQUENCY', 'CASH_ADVANCE_FREQUENCY',
       'CASH_ADVANCE_TRX', 'PURCHASES_TRX', 'CREDIT_LIMIT', 'PAYMENTS',
       'MINIMUM_PAYMENTS', 'PRC_FULL_PAYMENT', 'TENURE'],
      dtype='object')

drop_features = ["CUST_ID"]
numeric_features = list(set(creditcard_df.columns) - set(drop_features))

from sklearn.impute import SimpleImputer

numeric_transformer = make_pipeline(SimpleImputer(), StandardScaler())

preprocessor = make_column_transformer(
    (numeric_transformer, numeric_features), ("drop", drop_features)
)

transformed_df = pd.DataFrame(
    data=preprocessor.fit_transform(creditcard_df), columns=numeric_features
)

transformed_df
CASH_ADVANCE PURCHASES INSTALLMENTS_PURCHASES BALANCE PURCHASES_FREQUENCY PRC_FULL_PAYMENT TENURE ONEOFF_PURCHASES ONEOFF_PURCHASES_FREQUENCY PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS BALANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY
0 -0.466786 -0.424900 -0.349079 -0.731989 -0.806490 -0.525551 0.360680 -0.356934 -0.678661 -0.511333 -0.960433 -0.528979 -3.109675e-01 -0.249434 -0.476070 -0.707313 -0.675349
1 2.605605 -0.469552 -0.454576 0.786961 -1.221758 0.234227 0.360680 -0.356934 -0.678661 -0.591796 0.688639 0.818642 8.931021e-02 0.134325 0.110074 -0.916995 0.573963
2 -0.466786 -0.107668 -0.454576 0.447135 1.269843 -0.525551 0.360680 0.108889 2.673451 -0.109020 0.826062 -0.383805 -1.016632e-01 0.518084 -0.476070 -0.916995 -0.675349
3 -0.368653 0.232058 -0.454576 0.049099 -1.014125 -0.525551 0.360680 0.546189 -0.399319 -0.551565 0.826062 -0.598688 4.878305e-17 -1.016953 -0.329534 -0.916995 -0.258913
4 -0.466786 -0.462063 -0.454576 -0.358775 -1.014125 -0.525551 0.360680 -0.347294 -0.399319 -0.551565 -0.905464 -0.364368 -2.657913e-01 0.518084 -0.476070 -0.916995 -0.675349
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
8945 -0.466786 -0.333293 -0.132643 -0.737950 1.269843 1.183951 -4.122768 -0.356934 -0.678661 -0.350408 -0.960433 -0.486217 -3.498541e-01 0.518084 -0.476070 1.179833 -0.675349
8946 -0.466786 -0.329136 -0.122823 -0.742423 1.269843 -0.525551 -4.122768 -0.356934 -0.678661 -0.350408 -0.960433 -0.503396 4.878305e-17 0.518084 -0.476070 1.179833 -0.675349
8947 -0.466786 -0.401965 -0.294893 -0.740398 0.854576 0.329200 -4.122768 -0.356934 -0.678661 -0.390639 -0.960433 -0.570615 -3.354655e-01 -0.185477 -0.476070 0.760469 -0.675349
8948 -0.449352 -0.469552 -0.454576 -0.745174 -1.221758 0.329200 -4.122768 -0.356934 -0.678661 -0.591796 -1.097856 -0.580536 -3.469065e-01 -0.185477 -0.182998 -0.916995 0.157527
8949 -0.406205 0.042146 -0.454576 -0.572575 0.439310 -0.525551 -4.122768 0.301732 1.556082 0.333524 -0.905464 -0.576869 -3.329464e-01 -0.889033 -0.182998 -0.916995 0.990398

8950 rows × 17 columns

Now that we have transformed the data, we are ready to run K-Means to cluster credit card customers.

Choosing n_clusters#

  • There is no definitive method to find the optimal number of clusters.

  • Let’s try different approaches.

The Elbow method#

model = KMeans(random_state=42, n_init='auto')
visualizer = KElbowVisualizer(model, k=(1, 20))

visualizer.fit(transformed_df)  # Fit the data to the visualizer
visualizer.show();
../_images/2a3d5244a84dbe4b1f2e02cdf61a5fc261fbb072fd5c51bd395b0c8157739cce.png

  • The optimal number of clusters is not as clear as it was in our toy example.

  • Let’s examine Silhouette scores.

for k in range(3, 6):
    model = KMeans(k, random_state=42)
    visualizer = SilhouetteVisualizer(model, colors="yellowbrick")
    visualizer.fit(transformed_df)  # Fit the data to the visualizer
    visualizer.show()

/Users/kvarada/opt/miniconda3/envs/563/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(
../_images/143d1dea456b63df31137176a8c887b84e64b2d7776dbf78c0958b14572932b5.png 
/Users/kvarada/opt/miniconda3/envs/563/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(
../_images/db849c3f26be159a7dec5855ae2c6b41372e72826b92163414f8092765a88739.png 
/Users/kvarada/opt/miniconda3/envs/563/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(
../_images/bb741803e22767afac7b32368acce956a6c4f4f5a8b64577e5492eeb32023588.png

  • I’m going to run KMeans with n_clusters = 4.

  • You can try out n_clusters = 5 and n_clusters = 6 on your own.

Visualizing clusters#

  • Can we visualize the clusters?

  • We have a high dimensional data and we need to reduce the dimensionality in order to visualize it.

  • Let’s reduce the dimensionality using a technique called UMAP.

I forgot to put this package in the course environment file. So to run the code below, you’ll have to install the umap-learn package in the course conda environment either with conda or pip, as described in the documentation.

> conda activate 563
> conda install -c conda-forge umap-learn

or

> conda activate 563
> pip install umap-learn

import umap

def plot_umap_clusters(
    data,
    cluster_labels,
    size=50,
    n_neighbors=15,
    title="UMAP visualization",
):
    """
    Carry out dimensionality reduction using UMAP and plot 2-dimensional clusters.

    Parameters
    -----------
    data : numpy array
        data as a numpy array
    cluster_labels : list
        cluster labels for each row in the dataset
    size : int
        size of points in the scatterplot
    n_neighbors : int
        n_neighbors hyperparameter of UMAP. See the documentation.
    title : str
        title for the visualization plot

    Returns
    -----------
    None. Shows the clusters.
    """

    reducer = umap.UMAP(n_neighbors=n_neighbors)
    Z = reducer.fit_transform(data)  # reduce dimensionality
    umap_df = pd.DataFrame(data=Z, columns=["dim1", "dim2"])
    umap_df["cluster"] = cluster_labels

    labels = np.unique(umap_df["cluster"])

    fig, ax = plt.subplots(figsize=(10, 7))
    ax.set_title(title)

    scatter = ax.scatter(
        umap_df["dim1"],
        umap_df["dim2"],
        c=umap_df["cluster"],
        cmap="tab20b",
        s=size,
        edgecolors="k",
        linewidths=0.1,
    )

    legend = ax.legend(*scatter.legend_elements(), loc="best", title="Clusters")
    ax.add_artist(legend)

    plt.show()

for k in range(3, 7):
    kmeans = KMeans(n_clusters=k, random_state=42)
    kmeans.fit(transformed_df)
    labels = kmeans.labels_
    plot_umap_clusters(transformed_df, kmeans.labels_, title=f"K-Means with k = {k}")

/Users/kvarada/opt/miniconda3/envs/563/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(
../_images/d56aa4507dfe17cbd2de3d8a9ef45313985a808dc6c87ba75579f4bb340cf96b.png 
/Users/kvarada/opt/miniconda3/envs/563/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(
../_images/4ebecb53a176b66d79e7fcf29edf15517efbf1c0b0fc33894a18f1feaf8e197f.png 
/Users/kvarada/opt/miniconda3/envs/563/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(
../_images/c07a8d5049cf5390fcf12d5f39d81712d6c2e099145a62a1927cd321ec76048e.png 
/Users/kvarada/opt/miniconda3/envs/563/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(
../_images/4a2f4b3ce9c88e71ff28cb7035026ce7e69d1827757ca11a211e537aaa496d34.png

  • The clusters above look reasonably well separated.

  • This might not always be the case.

Cluster interpretation#

  • Let’s examine the cluster centers for k=4 and identify types of customers.

reasonable_k = 4
kmeans = KMeans(n_clusters=reasonable_k, random_state=42)
kmeans.fit(transformed_df)
labels = kmeans.labels_

/Users/kvarada/opt/miniconda3/envs/563/lib/python3.10/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
  warnings.warn(

cluster_centers = pd.DataFrame(
    data=kmeans.cluster_centers_, columns=[transformed_df.columns]
)
cluster_centers
CASH_ADVANCE PURCHASES INSTALLMENTS_PURCHASES BALANCE PURCHASES_FREQUENCY PRC_FULL_PAYMENT TENURE ONEOFF_PURCHASES ONEOFF_PURCHASES_FREQUENCY PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS BALANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY
0 -0.366373 0.109044 0.255904 -0.321688 0.983721 0.395041 0.057744 0.000926 0.317153 0.296985 -0.077298 -0.138502 -0.091844 0.242574 -0.360303 0.874138 -0.462599
1 1.688972 -0.234638 -0.253747 1.459578 -0.504848 -0.406367 -0.097146 -0.163914 -0.212939 -0.283580 0.838968 0.603821 0.490910 0.384753 1.617143 -0.450201 1.745948
2 -0.182691 -0.343190 -0.387798 -0.265552 -0.797823 -0.258866 -0.052972 -0.230500 -0.389437 -0.474987 -0.334417 -0.262060 -0.119249 -0.368944 -0.164607 -0.714246 -0.101500
3 -0.155091 3.125845 2.406470 0.954485 1.136338 0.454703 0.324140 2.713251 1.798653 3.003251 1.429882 1.919096 0.477421 0.462694 -0.170458 1.065918 -0.319096

  • Recall that we have applied imputation and scaling on the dataset.

  • But we would be able to interpret these clusters better if the centers are in the original scale.

  • So let’s apply inverse transformations to get the cluster center values in the original scale.

data = (
    preprocessor.named_transformers_["pipeline"]
    .named_steps["standardscaler"]
    .inverse_transform(cluster_centers[numeric_features])
)

org_cluster_centers = pd.DataFrame(data=data, columns=numeric_features)
org_cluster_centers = org_cluster_centers.reindex(
    sorted(org_cluster_centers.columns), axis=1
)
org_cluster_centers
BALANCE BALANCE_FREQUENCY CASH_ADVANCE CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX CREDIT_LIMIT INSTALLMENTS_PURCHASES MINIMUM_PAYMENTS ONEOFF_PURCHASES ONEOFF_PURCHASES_FREQUENCY PAYMENTS PRC_FULL_PAYMENT PURCHASES PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY PURCHASES_TRX TENURE
0 894.907458 0.934734 210.570626 0.042573 0.790021 4213.207678 642.478274 650.167072 593.974874 0.297070 1332.194205 0.269258 1236.178934 0.885165 0.711842 22.091773 11.594595
1 4602.462714 0.968415 4520.724309 0.484526 14.284641 7546.957050 181.607404 2008.251157 320.373681 0.138934 3481.145990 0.034859 501.896219 0.287731 0.185516 7.661102 11.387312
2 1011.751528 0.789871 595.759339 0.114833 2.125503 3277.703165 60.386625 586.301239 209.853863 0.086281 974.505090 0.078001 269.973466 0.170146 0.080578 2.903421 11.446429
3 3551.153761 0.986879 653.638891 0.071290 2.085575 9696.943765 2587.208264 1976.815179 5095.878826 0.739031 7288.739497 0.286707 7681.620098 0.946418 0.788060 89.359413 11.951100 
cluster_labels = {0: "Transactors", 1: "Revolvers", 2: "Low activity", 3: "VIP/Prime"}
org_cluster_centers["cluster_labels"] = list(cluster_labels.values())

relevant_cols = [
    "cluster_labels",
    "BALANCE",
    "CREDIT_LIMIT",
    "PRC_FULL_PAYMENT",
    "PURCHASES_FREQUENCY",
    "CASH_ADVANCE",
    "CASH_ADVANCE_FREQUENCY",
    "CASH_ADVANCE_TRX",
]
org_cluster_centers[relevant_cols]
cluster_labels BALANCE CREDIT_LIMIT PRC_FULL_PAYMENT PURCHASES_FREQUENCY CASH_ADVANCE CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX
0 Transactors 894.907458 4213.207678 0.269258 0.885165 210.570626 0.042573 0.790021
1 Revolvers 4602.462714 7546.957050 0.034859 0.287731 4520.724309 0.484526 14.284641
2 Low activity 1011.751528 3277.703165 0.078001 0.170146 595.759339 0.114833 2.125503
3 VIP/Prime 3551.153761 9696.943765 0.286707 0.946418 653.638891 0.071290 2.085575

One way to interpret and label the clusters above is as follows.

Transactors#

  • Credit card users who pay off their balance every month with least amount of interest charges.

  • They are careful with their money.

  • They have lowest balance and cash advance

Revolvers#

  • Credit card users who pay off only part of their monthly balance. They use credit card as a loan.

  • They have highest balance and cash advance, high cash advance frequency, low purchase frequency, high cash advance transactions, low percentage of full payment

  • Their credit limit is also high. (Lucrative group for banks 😟.)

Low activity#

  • There is not much activity in the account. It has low balance and not many purchases.

  • Credit card users who have low credit limit.

VIP/Prime#

  • Credit card users who have high credit limit.

  • They have high one-off purchases frequency, high number of purchase transactions.

  • They have high balance but they also have higher percentage of full payment, similar to transactors

  • Target for increase credit limit (and increase spending habits)

More on interpretation of clusters#

  • In real life, you’ll look through all features in detail before assigning meaning to clusters.

  • This is not that easy, especially when you have a large number of features and clusters.

  • One way to approach this would be visualizing the distribution of feature values for each cluster.

  • Some domain knowledge would definitely help at this stage.

creditcard_df['cluster'] = labels

Let’s check the cluster assignment for the customer who made the maximum cash advance transaction.

creditcard_df[creditcard_df["CASH_ADVANCE"] == max_cash_advance]
CUST_ID BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE cluster
2159 C12226 10905.05381 1.0 431.93 133.5 298.43 47137.21176 0.583333 0.25 0.5 1.0 123 21 19600.0 39048.59762 5394.173671 0.0 12 1 
def show_hists(df=creditcard_df, cols=["BALANCE", "CASH_ADVANCE"]):
    for i in cols:
        plt.figure(figsize=(35, 5))
        for j in range(4):
            plt.subplot(1, 4, j + 1)
            cluster = df[df["cluster"] == j]
            cluster[i].hist(bins=20)
            plt.title(f"{i}    \nCluster: {cluster_labels[j]} ")

        plt.show()

show_hists() # Examining clusters for two features.
../_images/d5f82cf8db32768ae31b29a5a489d25fd101bab40a26e080247406565ffe7029.png ../_images/f6b3984730e85a4f795dfe0d40c3e0d589c9efc2230733ba296c37b89ed712e6.png 
# Uncomment the code below to show histograms for all features. 
# cols = creditcard_df_cluster.columns.to_list()
# cols.remove('CUST_ID')
# cols.remove('cluster')
# show_hists(creditcard_df_cluster, cols)

Practice exercise for you#

  • Try out different values for n_clusters in KMeans and examine the clusters.

  • If you are feeling adventurous, you may try customer segmentation on All Lending Club loan data.