Partitioning and categorization

by Neil Rickert

I discussed the idea of partitioning the world in an earlier post.  Categorization is an old idea, dating back to Plato or earlier.  In this post, I want to compare and contrast the ideas of partitioning and of categorization.

It is widely believed that categorization is cognitively important.  However, heretic that I am, I disagree.  I believe that it is partitioning that is cognitively important, and I suspect that the results of partitioning are often being mischaracterized as due to categorization.

Categorization is usually described as grouping things into categories.  Either one groups things that are similar, or one groups things that are similar to a presumed stereotypical model.  The result is a hierarchical organization of the world, with larger categories composed of smaller categories.  So your pet dog might be an entity.  This, along with other dogs, is grouped into the categories of dogs.  Then dogs, cats and other critters are grouped into the category of mammals, etc.  Partitioning results in a similar hierarchical organization.  The difference is that, with partitioning, one starts at the top (the world as a whole), and looks for reliable ways of dividing that large group into small groups.  So partitioning and categorization can both be said to structure the world, with the structuring being done top-down with partitioning or bottom up with categorization.

The trouble with categorization, is that you cannot even start unless you have solved the problem of object recognition, and unless you have a way of deciding questions of similarity.  By contrast, partitioning does not require any prior ability at object recognition, nor at determining similarity.  Rather, partitioning can be seen as a method toward accomplishing object recognition and toward developing a way of deciding questions of similarity.  For if the hierarchical organization can be built without relying on a prior ability at object recognition or a prior way of determining similarity, then we can use that hierarchical organization in recognition and judgments of similarity.

An important advantage of partitioning, is that it solves a problem of vision.  There’s a difficulty for an animal in that, as the animal moves around, the light received by a particular retinal sensor depends on the location and orientation of the animal as well as on what is present in the environment.  The animal can, of course, try to subtract off the effects of motion and orientation.  But, in order to do that, it has to already be able to tell what is its motion and orientation.  And that would seem to require that it has achieved vision as a prerequisite to being able to pick up the information required to achieve vision.  If partitioning is used, then a different approach is possible.  Instead of using a retinal sensor to get information about a specific location in the environment, the sensor can instead be used to scan across the environment.  The scanning would be looking for abrupt transitions in signal, as the line of vision crossed an edge or boundary.  A moving animal can use this method to detect the boundaries or edges with a pretty good degree of reliability and accuracy, even when the animal is moving relative to the environment.  So the idea is to find these edges, and use them as part of the partitioning.  That then provides a basis for the animal to determine its relative motion and orientation, and to use the edges in its scheme of partitioning the world.  Proceeding with partitioning and then repartitioning the parts, the animal can then begin to fill in the details of what is in the environment.  And, with sufficient partitioning, it will be able to achieve object recognition, based on the details of the partitioning steps used.

If vision is achieved as I have suggested, then this would be consistent with the views of J.J. Gibson on direct perception.  This is in contrast with indirect perception, which claims that we form an internal image or representation as a pixel map, and then achieve perception by analysis of that internal representation.

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