In the optimization problem, we assumed
the compatibility scores were data
that we could input directly into the optimization model.
But where do these scores come from?
In the words of the founder-- Neil Clark Warren --opposites
attract, then they attack.
eHarmony's compatibility match score
is based on similarity between users' answers
to the questionnaire.
Let us attempt to demonstrate an approach
to develop compatibility scores.
We utilize public data from eHarmony containing features
for 275,000 users and binary compatibility.
Feature names and exact values are
masked to protect users' privacy.
Correspondingly we won't be able to directly interpret
which features are important as we do not
know the identity of these features.
We used logistic regression on pairs of users' differences
to predict compatibility.
To reduce the size of the problem,
we filtered the data to include only users in the Boston area
who have compatibility scores listed in the data set.
We computed absolute difference in features for these 1,475
pairs and trained a logistic regression model
on these differences.
Let us observe the results of this experiment.
If we use a low threshold in the logistic regression model,
we predict more false positives but also get
more true positives.
For example, the classification matrix
for threshold equal to 0.2 is as follows.
Note that we found 1,030 pairs that are not compatible
and 92 pairs that are compatible correctly.
Note that 92 out of 319-- which is 227 plus 92 --of these
were correctly identified.
That is, 29% percent of the matches we recommend
would be successful, a very high success rate for online dating.
Clearly, there is a potential for using
many other analytic methods.
Specifically trees, which are especially
useful for predicting compatibility
if there are nonlinear relationships
between variables.
Clustering is another potential approach
with the idea of segmenting the users.
Finally, text analytics is yet another approach
with the idea of analyzing the text of users' profiles.
Of course, many other techniques are possible.
To give some intuition of various features,
let us see how the probability of a match
changes with the distance between the two adults.
It is interesting to note that the probability drops
with distance, and then for a very long distance,
the probability increases again.
Also interesting is this graph that
shows that if the attractiveness is too high or too low,
the probability of a successful match decreases.
Finally, if the difference in height is too high or too low,
the probability of the match also drops.
It seems the sweet spot is a difference in height
between four and eight inches.