How do you take a log of transactional data from

your customers (or audience, users,

subscribers, citizens, etc.) and use it to understand them?

PROBLEM: Identifying customer similarities

Traditional methods of “blasting” customers with e-mail newsletters in an

all-or-nothing 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.

But

We need to take the customer base and find a happy medium between blasting everyone with

the same e-mail, 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.

Cluster analysis is the practice of gathering up a bunch of objects

and separating them into groups of similar objects.

SOLUTION: Exploratory data mining

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.

And

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K-Means ClusteringA 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 expectation-maximization 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).

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.

2. Determine what to measure

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.

3. Consolidate results (standardize data)

4. Determine number of clusters (k)

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.

Copy MATRIX tab and name new tab: 4MC

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 feetEuclidean 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!