Learning relationships based on profiles

Jochen WALZ - 1998-02-19

A profile is a group of attributes assigned to an object describing its characteristics or preferences. Attributes may be of different types (as described subsequently).

The congruence of two attributes or two profiles is a number between 0 and 1 (or 0% and 100%) indicating their degree of similarity. The calculation of two attributes' congruence is type specific and only possible for attributes of the same type.

The congruence of two profiles results as the weightened average of the congruences of all common attributes. Any attribute may be declared must forcing the whole profile congruence to 0 if this attribute's congruence becomes 0 (KO-condition).

Note that calculating congruences is not necessarily a commutative operation, thus:

congruence(attribute₁,attribute₂) # congruence(attribute₂,attribute₁)
congruence(profile₁,profile₂) # congruence(profile₂,profile₁)

Unlike entered profiles, a learning profile is calculated out of a sample of other profiles. Again the attributes are handeled seperately. I. e. merging the profiles of all my CDs allows to conclude to my musical preferences. Learning profiles change with every element of the underlieing sample. They can be compared with other profiles just like normal ones.

Types of attributes

The attribute type set

Set attributes represent a selection of one or several elements out of a predefined list. For example: The languages spoken (= attribute) as one of the skills (= profile) of a person (= object).

The congruence of two set attributes is 1 if they have at least one element in common, or 0 otherwise:

congruence(set₁,set₂) = ( ( set₁ ř set₂ ) # { } )

Thus the congruence of someone speaking Spanish and English is 1 with Canada (English, French) and 0 with Switzerland (German, French, Italian).

A merged set attribute contains those elements, which appear in a minimum quota of sets in the sample.

The attribute type grade

Grade attributes measure how much a quality applies to an object: You might for instance enjoy ice-cream a lot (1), more or less (0.5) or not at all (0). Any value between 0 and 1 is possible.

For a congruence of 1 two grade attributes must be equal, whereas 0 means they are maximally different (one of them is 1 and the other one is 0). The proper formula is:

congruence(grade₁,grade₂) = 1 - | grade₁ - grade₂ |

The handling of grades other than 0 and 1 causes additional problems, as a value of 0.5 might signify "exactly half of it" (which is a precise statement) or "don't know" (containing no information at all). Both cases make sense within the appropriate context. To cover this a correction factor allows to continuously reduce the congruence of intermediate grades - for two 0.5 values for instance from 1 (with a correction of 0) to 0 (with a correction of 1) - leading to an improved formula:

The following graphs demonstrate the correction's influence (congruence as function of two grades for different corrections):

0% correction 50% correction 100% correction

Grade attributes are merged building the average of all values:

grade_L = ( grade₁ + grade₂ + ... + grade_n ) / n

The attribute type keyword

Keyword attributes may contain all kind of unstructured, textual information.

If one keyword is part of another ignoring their capitalization, both have a congruence of 1 (or 0 else).

This type of attributes cannot be merged - learning profiles therefore never contain keyword attributes.

About the author

Jochen WALZ holds a Master of Information Engineering and Management from Federal Institute of Technology (ETH), Zurich, Switzerland since 1986.

To contact please send your e-mail to walz_20100905@from.ch.

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