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Oh no, in-depth maths/marketing type stuff..
Today I learned about segmentation.. A fairly straightforward concept, but I don't think I entirely got it before..

Fundamentally, a number of nodes in N-dimensions can be grouped together based on proximity to one another (which I'd rather do as a squared euclidean distance rather than using taxicab geometry), it's then possible to construct a 'centre of gravity' if you will for that particular group, and then reasses the members of the group until you end up with a cohesive set of customers that don't differ by more than a certain margin from the established centre of gravity. The whole thing holds together because even though it's in N dimensions, each dimension has a causal relationship to the others (usually), so it works quite nicely.

So for example, your 25-30 year olds might be hungry for credit, and they all have a need for loans in common. They'll also have several other characteristics in common due to their age - average salary, marital status, etc. So you grab their centre of gravity, and then see who is still in close proximity. You might only end up with 26-28 year olds, because they're the group that deviate the least from the average (which in turn is based on all those other characteristics). So in effect, you can take a broad pot of customers, and boil it down into cohesive groups - it might be that your 29-30 year olds are in a transition phase, and the number of customers in your model is too small to accomodate their newly-varying needs.

So you end up with stepping stones, in effect, through the life of a customer. They start off as an impoverished student, 20 years old with an overdraft and few financial obligations. Your segmentation might not really concentrate much on your 21-24 year olds - it's not that they're not included, but they sit either in much smaller clusters that fall off the radar, or they're on the fringes of other large clusters. Then at 25, you have another segment, full of credit-hungry young professionals. And so on.

Now this is great, because by knowing either which stepping stone a customer is on, or which one they're heading towards, you can know how to treat them. But the more maths/logic part of my brain takes issue with some of the over-simplifications. You transition from Segment A to Segment B, and it takes you five years, and in the meantime you don't really fit anywhere. All I've seen in terms of work on this is that there's an arrow from A to B, and we're to accept that the customer is either in one of the segments, or just between them.

This fails to satisfy my brain. My brain seeks to identify loci in N-dimensional space that represent smaller segments, along with vectors between them that show the true path of the customer (or at the least, a good approximation). So for example, let's assume that there are two points, (x1,y1,z1) and (x2,y2,z2). Variable 1 is age, Variable 2 is annual income, Variable 3 is product holdings. So we have that:

x1 = 20
y1 = 4,000
z1 = 2

x2 = 25
y2 = 22,000
z2 = 5

So between ages 20 and 25, the customer has increased in salary from 4k to 22k, and now has five financial products instead of two. But how did they get from A to B? After all, you can plot the two points on a 3D graph, there's x,y,z coordinates for the start and the end. But what is a typical path between the two? At what rate does y change in relation to x (as in, do these customers enjoy a sudden rise in income at a particular age)? Do the product holdings seem to arise out of more complex financial needs as brought on by salary, or more complex life situations due to their increasing age, or is it something else?

Our current proposition, if you like, is "For the Journey". So while the segments are nice, the visual representations are never in sufficient dimensions (possibly because anything above 3 is rather difficult), and vectors between them don't actually show the true transitions. So now (in my spare time, of course), I have to come up with a way to calculate all of that. Should be fun!