Search has always been an integral part of any tagging system. Such systems need to make sense out of the abundant user generated metadata such that the documents/items can be ranked in some order. However, very little has been said or written openly about such ranking algorithms for tagging systems.
Most systems, that allow tag search, base their rankings on factors like simply the ‘number of unique users’ or on ratios like ‘number of unique users for tag t / number of unique users for all tags’ etc. These conventional algorithms do work, but not quite so well for large datasets where they can be exploited. They also often do not represent the true relevance. Reminds me often of the pre-PageRank era of information retrieval systems.
So, which relevance algorithm do I use?
Well, you can always use the conventional methods, but then you can always try the algorithm I devised. This algorithm seems to capture the true essence of relevance in tagging systems. I call it the WisdomRank as it is truly based on the ‘wisdom’ of the crowds, the fundamental part of any social system. Read along to understand it in detail (or download the pdf).
Inferring relevance for tag search
from user authority – Abstract
Tagging is an act of imparting human knowledge/wisdom to objects. Thus a tag, a one word interpretation/categorization of the object by the user, fundamentally represents the basic unit of human wisdom for any object. This wisdom is difficult to quantify as it is relative for every user. One approach to quantify this would be to use the wisdom of the other users to define this for us. This can be done by assuming that every tag corresponds to a topic for which every user has some authority. Also, every tag added to an object corresponds to a vote, similar to the Digg model, asserting that the object belongs to that topic (tag).
Let us consider a user Ui who has tagged object Oj with the tag Tk. Whenever other users in the system tag Oj with Tk, they are implicitly affirming Ui’s wisdom for tag Tk.
Thus, we define the function affirmation for the tuple(u, d, t) as the number of other users who have also tagged document d with tag t:
affirmation(u, d, t) = ∑i=All users except ‘u’ tagged(ui, d, t)
u – the user
d – the document/object
t – the tag
tagged – 1 if the user Ui has tagged d with t
- 0 otherwise
Hence, we can proceed to define the wisdom of the user for a topic (tag) t as the sum of all such assertions by other users,
wisdom(u, t) = ∑x=For all documents d tagged with tag t by U affirmation(u, d, t)
Likewise, we can now define the authority of a user for the topic t, as the ratio of the user’s wisdom to the collective wisdom for t. Hence,
authority(u, t) = wisdom(u, t) / ∑ wisdom(ui, t)
For example: Let us determine the authority of user u1 for tag t1
Object d1: Object d2: Object d3:
t1 by u1 t1 by u1 t1 by u2
t1 by u2 t3 by u1 t1 by u3
t1 by u3 t3 by u1
t2 by u1
affirmation(u1, d1, t1) = 2 affirmation(u1, d2, t1) = 0
Hence, wisdom(u1, t1) = 2
Likewise for other users,
wisdom(u2, t1) = 3
wisdom(u3, t1) = 3
Hence the authority of user u1 for t1 is as follows:
authority(u1, t1) = 2 / (2 + 3 + 3) = 2 / 8 = 0.25
Whenever a user tags an object with a tag, he does so with the authority he possesses for that tag. Thus as compared to conventional methods, where the objects are usually ranked on the number of instances of the tags, in this method the measure of the relevance of a tag for an object is equivalent to the sum of all such user authorities. Thus,
relevance_metric(d, t) = ∑i= all user who have tagged document d with t authority(u, t)
This relevance score, when calculated for every tag would provide an accurate measure for ranking the objects. As compared to the conventional methods where more number of instances of a tag for an object ensured a higher relevance for that tag, here the number of authoritative users counts.
Let us consider the following example:
Object d1: Object d2:
t1 by u1 t1 by u2
t2 by u5 t1 by u3
t1 by u4
Let us assume that u1 has a very high authority for tag t1. Hence in the above scenario, a search for tag t1 may rank d1 higher than d2, if
authority(u1, t1) > authority(u2, t1) + authority(u3, t1) + authority(u4, t1)
This result is with the assumption that u1’s authority is greater than those of u2,u3 and u4 combined.
On the other hand, d2 would be ranked higher than d1 if the combined authorities of u2, u3 and u4 exceed that of u1. If the majority of the users are suggesting something, it indicates that their suggestion is far more valuable than that of an individual user or a subset of users.
While calculating the user assertions this algorithm currently considers all such users as equal even though they may have varying authorities for the corresponding tag. As a future enhancement, I plan to incorporate the authorities of the users as well into the affirmation calculations.