PROBLEM: Identifying customer
similarities
How do you take a log of
transactional data from your
customers (or audience,
users, subscribers, citizens,
etc.) and use it to
understand them
Traditional methods of
“blasting” customers with email newsletters in an all-ornothing send is less and less
effective.
It’s hard to understand each
customer personally,
especially if they’ve all had
their own different ways of
engaging with you.
We need to take the customer base
and find a happy medium between
blasting everyone with the same email, and understanding everything
about everyone for an individualized
email newsletter.
One way to find a balance is to use
clustering to create a market segmentation
of customers so that you can market to
segments of customers with targeted
content, deals, etc.
SOLUTION: Exploratory data mining
Cluster analysis is the practice of
gathering up a bunch of objects and
separating them into groups of similar
objects.
Clustering techniques help tease
out relationships in large
datasets that are too hard to
identify by eye.
Relationships between customers is
useful across industries - whether it’s
film recommendations based on the
viewing habits of people in a cluster, or
identifying crime hot spots in urban
areas.
The most common type of clustering is
called k-means clustering - the go-to
clustering technique for knowledge
discovery in databases across industries
and governments.
K-means isn’t the most rigorous of techniques,
but more often than not it hits the spot. It
requires analyst intuition, which is part of its
attraction: it’s not an unsupervised machine
learning technique.
The goal of k-means clustering is to take
some points in space and put them into k
groups (where k is any number you want to
pick).
The k-groups are defined by a point
in the centre that says: “Join me if
you are closer to this point than any
other.”
Just to be technical, the group centre is
called the cluster centroid - the mean
from which k-means gets its name. And
this creates a Voronoi Diagram, named
after, you guessed it, Voronoi.
Grade 8Grade
Grad
Dance
8 graduation
dance
Text
Song List
Led Zeppelin: Stairway to Heaven
Deep Purple: Smoke on the Water
Alice Cooper: Elected
Queen: Bohemian Rhapsody
Sweet: Ballroom Blitz
Wings: Band on the Run
K-Means Clustering
A method of unsupervised machine learning that provides a way to
classify a given data set around a certain number of clusters. The most
well-known clustering algorithm is the k-means, an iterative expectationmaximization type approach, which attempts to address the following
objective: given a set of points in a Euclidean space and a positive
integer k (the number of clusters), split the points into k clusters so that
the total sum of the (squared Euclidean) distances of each point to its
nearest cluster centre is minimized.
In our example we are working with customer data
obtained through an email marketing campaign.
This would work equally well with retail purchase
data, ad conversion data, social media data, and
so on.
Goal
Segment the list of customer into groups based on their
interest in specific wine offerings. Then, you could
customize the newsletter to each segment and maybe
drum up some more business.
Which ever deal you thought matched up better with the
segment could go in the subject line and would come first
in the newsletter. That type of targeting can result in a
bump in sales.
Method
1.
Look at what data we have.
OrderInformation: Worksheet of wine deals last year (32).
Transactions: Worksheet of which customer bought what
deals (324 purchases).
2. Determine what to measure
Pivot table from transaction tab: Offers (row),
Customers (column), Count of Customers
(values).
This gives us purchases by customer in
matrix form. We know what deal each
customer took, and what they didn’t take.
3. Consolidate results (standardize data)
Copy orderInformation tab
and name new tab: Matrix
Then paste the values from the Pivot
table starting at column H
End up with a fleshed out version of the
matrix with consolidated deal descriptions
with purchase data.
4. Determine number of clusters (k)
Copy MATRIX tab and name new tab: 4MC
Insert four columns after Past Peak in columns H through K that
will be the cluster centers. Label these clusters Cluster 1 through
Cluster 4. You can also place some conditional formatting on them
so that whenever each cluster center is set you can see how they
differ.
What you’d like to see is that they, like in the middle school dance, distribute
themselves to minimize the distances between each customer and their
closest cluster center.
Obviously then, these centers will have values between 0 and 1 for each deal
since all the customer vectors are binary.
5a.
Measuring distances between customers
and deals: Euclidean Distance
These two points are 8 – 4 = 4 feet apart in the vertical direction.
They’re 4 – 2 = 2 feet apart in the horizontal direction. By the
Pythagorean theorem then, the squared distance between these
two points is 4^2 + 2^2 = 16 + 4 = 20 feet. So the distance between
them is the square root of 20, which is approximately 4.47 feet
Euclidean distance is the square root of the sum of squared
distances in each single direction
5b.
Measuring distances between customers
and deals: Euclidean Distance
In the context of the newsletter subscribers, you have more than two dimensions, but
the same concept applies. Distance between a customer and a cluster center is
calculated by taking the difference between the two points for each deal, squaring
them, summing them up, and taking the square root.
Starting in cell L34, below Adams’ purchases, you can take the difference of Adams’ vector and
the cluster center, square it, sum it, and square root the sum, using the following array formula
(note the absolute references that allow you to drag this formula to the right or down without the
cluster center reference changing):
{=SQRT(SUM((L$2:L$33-$H$2:$H$33)^2))}
{=SQRT(SUM((L$2:L$33-$I$2:$I$33)^2))}
{=SQRT(SUM((L$2:L$33-$J$2:$J$33)^2))}
{=SQRT(SUM((L$2:L$33-$K$2:$K$33)^2))}
The end result is a single number: 1.732. This makes sense because
Adams took three deals, but the initial cluster center is all 0s, and the
square root of 3 is 1.732.
5c.
Measuring distances between customers
and deals: Euclidean Distance
For each customer then, you know their distance to all four cluster centers. Their
cluster assignment is to the nearest one, which you can calculate in two steps.
Going back to customer Adams in column L, let’s calculate the minimum
distance to a cluster center in cell L38. That’s just:
=MIN(L34:L37)
And then to determine which cluster center matches that minimum distance, you
can use the MATCH formula:
=MATCH(L38,L34:L37,0)
Labels for cells G34 – G39:
Distance to Cluster 1
Distance to Cluster 2
Distance to Cluster 3
Distance to Cluster 4
Minimum Cluster Distance
Assigned Cluster
6. Solving for Cluster Distances
You now have distance calculations and cluster assignments in the
spreadsheet. To set the cluster centers to their best locations, you need
to find the values in columns H through K that minimize the total
distance between the customers and their assigned clusters denoted on
row 39 beneath each customer.
This is an optimization step, and an optimization step means using Solver.
In order to use Solver, you need an objective cell, so in cell
A36, let’s sum up all the distances between customers and
their cluster assignments:
=SUM(L38:DG38)
7a.
Running Solver
This sum of customers’ distances from their closest cluster center is
exactly the objective function encountered earlier when clustering on the
McAcne Middle School dance floor. But Euclidean distance with its
squares and square roots is crazy non-linear, so you need to use the
evolutionary solving method instead of the simplex method to set the
cluster centers.
You have everything you need to set up a problem in Solver:
Objective: Minimize the total distances of customers from their cluster centers (A36).
• Decision variables: The deal values of each row within the cluster center (H2:K33).
•
Constraints: Cluster centers should have values somewhere between 0 and 1. (H2:K33 <= 1)
•
7b.
Solution Method
The Simplex LP engine solves linear optimization problems. A linear optimization problem
is one in which the target cell and constraints are all created by adding terms of the
(changing cell)*(constant) form.
The GRG nonlinear engine solves optimization problems in which the target cell or some
of the constraints are not linear and are computed by using common mathematical
operations such as multiplying or dividing changing cells, raising changing cells to a
power, exponential or trigonometric functions involving changing cells, and so on. The
GRG engine includes a powerful Multistart option that enables you to solve many
problems that were solved incorrectly with previous versions of Excel.
The Evolutionary Solver engine is used when your target cell or constraints contain non- smooth
functions that reference changing cells. A nonsmooth function is one whose slope abruptly
changes. For example, when x = 0, the slope of the absolute value of x abruptly changes from –
1 to 1. If your target cell or constraints contain IF, SUMIF, COUNTIF, SUMIFS, COUNTIFS,
AVERAGEIF, AVERAGEIFS, ABS, MAX, or MIN functions that reference the changing cells,
you are using nonsmooth functions, and the Evolutionary Solver engine probably has the best
shot at finding a good solution to your optimization problem.
8. Interpreting the results
Once Solver gives you the optimal cluster
centers, you get to mine the groups for insight!