Wikipedia says:

An expert is someone widely recognized as a reliable source of technique or skill whose faculty for judging or deciding rightly, justly, or wisely is accorded authority and status by their peers or the public. An expert, more generally, is a person with extensive knowledge or ability in a particular area of study.

Definitions:

• rating: personal meaning, liking (e.g. "I like this song.", "I don't like this feature.")
• opinion: personal view (e.g. "I think this song has sad lyrics.", "I don't think that this has breathing female vocals.")

Content-based recommendation:

• goal: find rating function, that predicts the user's rating based on the features of an item
• rating function is highly personalized, different for each user
• in SkipForward, the feature annotation depends on the user, too
• conclusion: perfect rating function could still be wrong, because the features may be inaccurate
• goal: find similarity function, that calculates the similarity between user's opinions
• => expert: someone with the same opinion like me

Problem:

• hierarchical feature space
• subclass-of relation has no well-defined semantic

Examples

Example 1:

• SongArtist (links to an artist)
  • RemixedBy
  • SongAlsoArtist
  • SongMainArtist

Let there be the following opinions

• User A says that song S has the feature SongAlsoArtist artist Z.
• User B says that song S has the feature SongMainArtist artist Z.

In a strict sense, they share no opinion because they have expressed opinions on different features. But one could infer that both users think that artist Z is some kind of SongArtist of song S. So in some way, the opinions of user A and B and more similar than to some user C who says that artist Z is NOT a SongArtist of song S.

Example 2:

• Electric_Guitar_Riffs
  • Dirty_Electric_Guitar_Riffs
  • Layered_Electric_Guitar_Riffs

Let there be the following opinions

• User A says that song S has the feature Dirty_Electric_Guitar_Riffs.
• User B says that song S has the feature Layered_Electric_Guitar_Riffs.
• User C says that song S has the feature Electric_Guitar_Riffs.
• User D says that song S does NOT have the feature Layered_Electric_Guitar_Riffs.

Again, the only two opinions directly comparable are the ones of users B and D, as they are oppositional. Users A and B are similar, because they both think that the song has some sort of Electric_Guitar_Riffs, but the have a dissens in the special type of guitar riffs. But does this mean, that user A and C are more similar than A and B?

It gets worse, because the opinion of user D does NOT state that the song has no Electric_Guitar_Riffs at all, just that is has no Layered_Electric_Guitar_Riffs.

Idea

We postpone the problem of calculating an overall similarity between users by looking at each feature class individually. For this, we take advantage of a method widely used^{[citation needed]} in collaborative filtering/recommendation. The ​Pearson Produkt-Moment Correlation Coefficient (or Pearson-correlation for short) "indicates the strength and direction of a linear relationship between two random variables".

In Collaborative Filtering (CF), the ratings of user X and user Y represent these two random variables and a (positive) linear relationship between these two is equivalent to both users rating items in the same way (but not necessarily identical). The Pearson-correlation normalizes both random variables to their respective mean value, meaning that two random variables are considered positively correlated if both differ from their respective mean in the same direction. (TODO: example needed)

Our approach is to look at one feature class at a time and interpret the opinion of a user as rating. The applicability represents the rating value whereas the confidence acts as a weight of this rating, therefor needing a more generalized formula for the Pearson-correlation allowing weighted ratings. (TODO: include formula)

The resulting correlation coefficient always is in range [-1;+1] and indicated how similar two users opinions are regarding only this specific feature class. Users with a high correlation are then called experts regarding this feature class. This correlation can also be used to add an additional weight to this users opinion about an item. (TODO: example)