Variation within Preferences

Posted: February 7th, 2009 | Author: David | Filed under: Computer Science | Tags: analysis, classification, information retrieval, preferences, Project, recommendations, set theory, variation | Comments Off

This post is a continuation of Good Recommendations and Using Set Theory to analyse Recommendation Relationships.

Until now, I’ve kept the assumption that both the Advisor’s and Advisee’s Preference Sets exhibit a similar level of variation within the Domain. That is to say that any member of the Recommendation Set would be as likely to be as good a recommendation as any other member, which is clearly unrealistic. The following diagram shows quadrants on a cartesian plane that show the relationships between increasing variety of a Preference Set within a Domain (from specialist to generalist), and the size of a preference set.

A more specialist Preference Set is one that contains more elements from within a particular sub division (e.g. Genre or sub-Domain) of the Domain than a more generalist Preference Set.

I am interested in the influence that each of these groupings is likely to have on the other, assuming a constant proportion of commonality between them. I would offer that a specialist Preference Set is less likely to receive good recommendations from a generalist Preference Set, but a smaller specialist Preference Set is more likely to receive good recommendations from a larger Preference Set of the same specialism.

I would also suggest that a larger generalist Preference Set would be more likely to receive a good recommendation from a specialist Preference Set of any size, than a smaller generalist Preference Set.

The following matrix summarises my assumptions about the suitability of each group to produce a good recommendation to another. (• indicates a good match between groups).

		Advisor (A)
		Niche Expert	Niche Novice	Domain Expert	Domain Novice
Advisee (B)	Niche Expert	•	-	-	-
	Niche Novice	•	•	-	-
	Domain Expert	•	•	•	-
	Domain Novice	•	•	•	•

From this, a good recommendation is more likely in the case where the following holds true:

v(B) ≥ v(A) and n(A) ≥ n(B)

where:

v(X) = variation of set X

n(X) = number of members of set X

That is to say the recommendation will be better received when the Advisee is more flexible about what he likes within the Domain, and the Advisor knows more about the Domain than the Advisee. Which also seems a bit of a no brainer when put like that.

Calculating Variation

Variation needs to indicate the range of member groupings within a set. This is problematic as we don’t necessarily know what all the groups are, how their boundaries lie, and where to allocate members as there may be many levels of sub-Domains or Genres within a Domain. I will make an assumption that there is some method of calculating variation within a set through some other means of set member classification (e.g. Naive Bayes, k-Nearest Neighbour, or otherwise).

In the next post, I’ll examine the possibility of predicting Preference Sets as a method to normalize preferences for comparative analysis.

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