Categories and Concepts
Categories versus Concepts
Category: A category is a collection of instances which are treated as if they were the same.
- Natural kinds
Concept: A concept refers to all the knowledge that one has about a category.
- Some kind of identification procedure
- Inferences which can be made either strongly or weakly.
Categories and Computational Complexity
- 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
Classical View of categories
- 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 Prototype Model
- 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.
Exemplar Models of categories
- 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
Knowledge based categorization
- 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)
The Basic Level
- The existence of categories decreases computational complexity, but it raises some computational complexity questions of its own.
a b c d
(a)(b)(c)(d), (ab)(c)(d), (a)(bc)(d), (a)(b)(cd), (a)(bd)(c), (abc)(d),
(a)(bcd), (acd)(b), (abd)(c), (ab)(cd), (ad)(bd), (ac)(bd), (abcd)
100,000 possible groupings
What is this?
Animal that lays eggs
Two legged animal
Not a library book
Bird or piece of cheese
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
- Experts may tend to categorize at lower levels
- Atypical category members tend to be categorized at the subordinate level