Predicting Preferences

Posted: February 7th, 2009 | Author: David | Filed under: Computer Science | Tags: , , , , , , , | Comments Off

This post is a continuation of Good Recommendations, Using Set Theory to analyse Recommendation relationships and Variation within Preferences.

Does all of this just mean that the underlying rule is to pair the Advisee to the Advisor with biggest Preference Set? And how does that relate to what was concluded earlier about the similarity of the two sets; the Jaccard co-effient. Taking an extreme scenario illustrated here:

Advisor (A) has a Preference Set of a large order of magnitude greater than the Advisee (B). Assuming that there’s a similar variance within the two sets, and that the previous assertions were correct, then this would clearly be approaching a Utopian case.

In reality we would find it difficult to assume so much about such a small sample relative to the larger one. It would be much better if we could transform the smaller set in to a larger sample on the basis of predicted future recommendations. Such as in the following diagram, where the dashed line shows the expansion of the Advisee’s original Preference Set to the Advisee’s Predicted Preference Set (B).

However, this makes the assumption that growth would be uniformly distributed out from the current Preference Set, and that the coupling of Advisor (A) with Advisee (B) was a good one to begin with and one that holds throughout the introduction of future recommendations.

My assumption would be that the variation within the Preference Sets holds the solution for this. Taking the difference in variation in the Common Set (A∩B) and the Recommendation Set (A—B) as ‘pull’ factors towards the Advisor and the difference in variation between the Common Set (A∩B) and B—A as ‘push’ factors away from the Advisor, we could infer growth of the Common Set with a the centre weighted towards or away from the Advisee. A greater pull could be shown as in the following diagram:

Whilst a greater push could be illustrated as:

The Jaccard co-effient could then be applied to work out the predicted similarity between the two sets. And from this, predict whether the original relationship is likely to provide more interesting, average, or more obvious recommendations.

Formally this can be represented as:

A∩PPS(B) / A∪PPS(B)

where: PPS(X)  = weighted Predicted Preference Set of X

Summary: Between Obvious and Interesting

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