Categories and Concepts

Categories versus Concepts

Category: A category is a collection of instances which are treated as if they were the same.

Concept: A concept refers to all the knowledge that one has about a category.

Without categories we'd have to treat each new instance as if it were one of a kind
Categories allow for prediction
Categories allow for communication
Categories allow for abstract thought

Basically says that categories membership is determined by matching a definition
Category membership is defined by a set of features which are
- Wholly necessary (each feature must be present)
- Jointly sufficient (If each feature is present that's all you need)
Examples of classical categories
- Triangle: A closed figure with three sides.
- Even number: Any whole number which when divided by 2 does not leave a remainder.
- Bachelor: An adult male who has never been married.
Problems for the classical view.
- For most concepts it is difficult to specify a complete set of necessary and sufficient features.
- Categories show grade structure
  - When people are provided with examples of a category some examples are judged to be more typical than other examples.
  - For instance, a robin is more typical of the category bird than is ostrich.
  - People identify typical instances more quickly than atypical instances too.
- Unclear cases: Should a rug be considered furniture, clock radio. Subjects disagree with each other about these examples and even disagree with themselves on different occasions.
- Even classical categories show graded structure and unclear cases. Should a priest be considered a bachelor?

The claims of the Prototype account
- There are no necessary and sufficient features for categories
- Instead categories are defined in terms of a set of typical or likely features.
- Category members share a family resemblance.
- Category membership is determined by comparing the instance to a category Prototype.
- The view assumes that prototypes are pre-stored in memory***
Two ways the term Prototype is used
- Prototype as the most typical member of the group.
- Prototype as a kind of average of all the group members. The prototype does not correspond to any actual group member but is a summary of all the group members.*
Problems with the prototype view
- Typicality is influenced by context: Subjects who view a farm scene give chicken a higher typicality rating as a member of the bird category than if they are asked while viewing a city scene.
- People have knowledge of not just central tendency but also variability:
  - Subjects are told that an object is round and two inches in diameter and they are asked do you think its a pizza or a quarter?
  - Subjects overwhelming pick quarter.
  - Why is this a problem for the prototype view? 2 inches is closer to the size of a typical quarter than it is to the size of a typical pizza.
  - Why do people pick pizza rather than quarter: Because they know pizzas come in a variety of sizes but that quarters do not.

Assumptions of the Exemplar Models
- Every instance of a category is stored in memory. These instances are called exemplars of the category
- There is no pre-stored prototype.
- To decide if something is a member of a category, you retrieve (some number--perhaps all) of exemplars of that category from memory.
- To determine if the item is a member of the category you (depending on the model)
  - Determine how similar the item is to each of the exemplars retrieved and then compute the average similarity.
  - Compute the similarity to the exemplar that is closest--most similar-- to the item (Nearest Neighbor rule)
How does that solve the problems of the prototype model?
- Context influences which exemplars are retrieved.
- Can use exemplars to determine variability as well as central tendency.

The relationship between a example and a category is like that between a theory and data.
Classification is not simply a matter of matching attributes but instead requires that the example have the right explanatory relationship to the theory organizing the concept.
If we are at a party and someone dives into a swimming pool with his clothes on we're likely to think that he's drunk. Its unlikely that jumping into a swimming pool with one's clothes on is a feature in our representation of drunkenness. Rather its likely that we have a theory of the effects that alcohol can have on people including decreasing inhibitions and that we reason from that theory to the conclusion that the person is drunk.
Ad Hoc categories: Ad hoc categories demonstrate the theory based nature of categorization. Ad hoc categories are categories which are just created and are not pre-stored in memory.
Wisniewski & Medin (1991)

How do we constrain this computational Complexity?

People prefer to categorize at an intermediate level--The basic level
- First level learned
- Most common level named
- Most general level where shape is maintained
- Most bang for the buck. Feature listing experiments.
Why the basic level
- Within category similarity: We want categories in which each member of the category is a similar as possible to other members of the category (Prediction)
- Between category similarity: We want categories which are as different as possible from contrasting categories. We want categories to be distinctive
- The basic level is a compromise between the need for high within category similarity and low between category similarity
Exceptions
- Experts may tend to categorize at lower levels
- Atypical category members tend to be categorized at the subordinate level


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