Categorization

Anderson applies his rational analysis to the problem of categorization to show that its signature data can be explained by analysis of the task alone:
  1. To a degree, people extract central tendency of a set of instances.
  2. To a degree, people extract tendency of a set of instances from particular exemplars.
  3. Subjects pick up the existence of multiple central tendencies.
  4. Categorization is nonlinear in the size of the relevant feature space.
  5. There is an effect of category size.
  6. In some cases there are basic level categories.
  7. Feedback is necessary for categories to emerge.
  8. Category formation is positively correlated with predictive utility of the category.
The optimal algorithm Anderson asserts for categorization is Bayes's theorem which he subsequently simplifies since the theorem assumes that all information about the items to be characterized are known. On the basis of Bayesian analysis all of the eight signatures are justified.

Assumptions

Some of the following assumptions in the analysis were discussed in class, some proposed by Simon, and some asserted by members of the group:
  1. Feature space is fixed
  2. Features are independent
  3. Features naturally form disjoint partitions.
  4. Feature list is static.
  5. The probability that a new category is needed to characterize an object is known.

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