Monday, May 28, 2007

Semantic Vectors

In mathematics a vector space is a collection of objects called vectors. For our purpose, the interesting thing about vectors is that that each vector has a number of linearly independent dimensions and that there is a notion of distance between vectors that relates to the distance between values of each independent dimension.

Quite a while ago I introduced the notion of a semantic vector. A semantic vector is a way to model objects in the world as vectors such that similarities between objects can be computed via a distance metric. Equally relevant, changes to objects, such as those imparted by adjectives or verbs, can be molded as transformations of vectors in a semantic space.

Unlike mathematical vectors, semantic vectors are most useful when organized in hierarchies that model concepts such as whole-part.

Another interesting aspect of semantic vectors is that they need not be organized into a rigid inheritance or classification hierarchies. Such hierarchies can be synthesized dynamically by concentrating on similarities and differences along specific dimensions.

Finally, the uniform mathematical representation across all dimensions is suggestive of a method for analogy, simile and metaphor.

A good portion of this blog will be dedicated to the elaboration and development of the idea of a semantic vector space.

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