The essence of memory organization is classification, relating new experiences to the old.
- William Estes
1. Concepts & Categorization - An Introduction
Think about this: You can easily recognize a pigeon when you see one, even though you may
have never seen that particular pigeon before. Moreover, having decided that it is a pigeon, you reason that it can fly, nest and like to eat grains [ category based induction ].
How are we able to quickly differentiate between a leaf and a flower; a female face from
a male; a praise from an insult; a sound reasoning from a ridiculous assertion; even
though sometimes we can be truly stumped. How do we build up concepts and categories in memory and utilize them when needed?
On the one hand, there is no simple answer yet that covers all aspects of human reasoning and recognition. On the other hand, some salient aspects have indeed been recognized,
over a period of time that stretches from ancient Greeks to the present, that can help understand cognition slightly better.
1.1 Classical Theory
The classical definition (Aristotle, Katz, Postal) is that natural concepts are characterized by simple sets of defining features that are singly necessary and jointly sufficient to determine category membership.
For example, the round thing in the sky that shines during the day is the sun.
However, during a solar eclipse it can be partially covered and yet we know that it is
the sun. Therefore, even if we do assume that a list of characteristics exist for a category, full compliance is usually not necessary to perform a classification. For instance, a three legged dog is still easily classifiable as a dog and not a horse.
The central problem with the classical view is that it assumes a sharp boundary between categories. With a necessary and sufficient list it will be always possible to say if
something did or did not belong to a category. But this does not reflect reality. When asked if a painting is a furniture, different people will give different answers and
justification. A person may even disagree with herself at times. Ever been happy and sad at the same time?
Also, studies by Rosch and Mervis revealed an interesting fact that categories are graded. Some members are more typical of a category than another. Most people
would immediately agree that a chair is a furniture. They would take longer to decide
if a carpet is or is not a furniture. This should not happen under the classical view
where one could run through a list to decide, with certainty, if something did or did not belong to a category. The findings basically sounded the death knoll for the classical view.
1.2 Examplar and Prototype Theory
Most natural concepts do not have a sharp necessary and sufficient boundary. It seems more likely that categories in our mind are defined by examplars(examples) or prototypes.
Categories tend to possess members that have features that are neither necessary
nor sufficient. - Wittgenstein, 1953.
Categories have a distribution of members, some more representative, some less.
- Posner and Keele, 1968.
Categories can be represented by the inter correlation between features or
relationship between features. - Medin,Estes 1985.
Such observations led to the development of prototype and examplar model.
Most of us have seen different types of birds. Depending on the region, the type of birds and the frequency of each could differ. From our experience, we might abstract out certain characteristics that seem to qualify something as a bird.
That is, as a result of experience with exemplars of a category, we abstract out a
central tendency of the category.
One could say that the salient features of the prototype is the list of attributes that defines the category, and in that respect that classical model is right. This is true.
However, where the classical model goes wrong is in claiming that each attribute is absolutely essential, or that the list is complete and the compliance has to be perfect.
A table may or may not have legs. A typical table has four legs but any other number need
not make it less of a table.
Not all the characteristics need to be equally important. Edibility is more central to the category food than the color. In other words, edibility provides the cue [validity] that it is a food item. Moreover, members - even typical ones - may not have all the charactertistics.
Now, the question is how do we judge whether a given object belongs to one category or another. This, of course, begs the question - how do we represent categories internally? The approach in the literature, is naturally, mathematical. The model in the literature may not eventually resemble how we, as humans, categorize. However, if the ultimate
results are same this is already a big step.
2. Modelling and Testing
We will look at some standard academic ways of testing categorization.
2.1 Typicality Test
Suppose we ask a group of subjects S1to prepare a list of characteristics for a beautiful face. Some of the expected items in the list are - tanned, big eyes, healthy look, happy or smiling, perfect teeth.
Next, we take this list and assign weights - if 50% of the people said happy or smiling we assign it a weight of 0.5. Next, we ask another large set of people S2 to look at a set of pictures (of say actresses) and mark against the features list prepared earlier. Multiply the ticks by the weights and after some averaging, you will have the list of typical beautiful faces (high scores) as judged jointly by S1 and S2.
This exercise can be done for any category. For instance, if done for birds one is likely to find sparrows as a typical example of bird rather than penguin. For a good joke, typical characteristics are - anxiety, a feeling of superiority and an element of surprise. For instance, consider the gag below:
A couple of New Jersey hunters are out in the woods when one of them falls to the ground.
He doesn't seem to be breathing, his eyes are rolled back in his head. The other guy
whips out his cell phone and calls the emergency services. He gasps to the operator: "My
friend is dead! What can I do?" The operator, in a calm soothing voice says: "Just take
it easy. I can help. First, let's make sure he's dead." There is a silence, then a shot
is heard. The guy's voice comes back on the line. He says: "OK, now what?"
- M. Gilligan
The notion of family resemblance must be mentioned in this context - There is no defining characteristic that all members of a family, or category, must share. However, similarity between them do exist. For example, in the category game, there is no single defining characteristic. However, badminton and tennis are similar. As is chess and checkers. Chess is similar (has family resemblance) to many other games because it
is a board game with strategy and competition. This makes chess a typical game.
Therefore, it can be said that examplars are more typical to the extent that they
bear a family resemblance (i.e. have attributes in common with) other members of the category.
The above statement brings home an important point in categorization - similarity and frequency. Suppose I have lived in a region fulll of penguins. I have also seen other birds in my life most of which are not like penguins. I saw these other types here and there and not too many samples of each. The question is: What is my typical bird?
Is it still a robin or a sparrow because most other birds are similar to it?
Or is my typical bird a penguin because most of my encounters were with penguins?
Mathematically, this translates to - in the similarity test: Do i give an equal weightage to penguin and sparrow?
As another interesting example to think about, most of the time we see one table and four to six chairs (in a typical house). Therefore, do we judge chairs are more typical of furniture than a table.
2.2 Conclusion from the Studies
Rosch and Mervis (1975), in their study on typicality, discovered that items with the
highest prototypicality were also those with the highest cue validity. Now, if prototypes
function cognitively as representative of a category, and if prototypes are also members
with the highest cue validity, then one can use the mechanism of matching a given item
to a pre-built prototype to determine category. This does not go against the cue validity
model which has already been seen to be highly true.
What seems to happen in cognition is that based on examplars we abstract out the central tendency of a category. The specific item information is usually rapidly forgotten.
The abstract category information (prototype), is however retained and used to perform
classification and induce properties of that category.
3. Within Category Structure of Semantic Concepts
Hypothesis: Exemplars are more typical to the extent that they bear a family resemblance
to - i.e. they have attributes in common with - other members of the category.
Excerpt: Categories have what I called a graded structure of better and worse examples, and many categories have unclear boundaries. It is often said to be the royal road to understanding cognition.If you're to identify true or false, an apple is a fruit, you're fast. A boysenberry is a fruit? A bit slower (for American norms). A kumquat is a fruit? Pause, uuuh I think so. A carrot is a vegetable? Yes! A pickle is a vegetable? Hmm, maybe.
The second part of the category work had to do with the principles by which categories are formed in the first place. Think about what determines the level of abstraction at which things will be categorized. My claim was that there is a basic level of abstractions which mirrors the correlational structure in the object's real world perception and use. For example, if somebody asked you what is that [points to a chair], what would you say? A chair? Yeah. Now, you wouldn't say right off, an office chair, but it is. You wouldn't say a piece of furniture right off, except in a special context. And you would not say a material object, again except in a certain context, although it certainly is all that.
4. The Context Model
The context model of Medin and Schaffer makes the following assumptions:
- Category judgements are made based on specific item information only
- Given two categories X and Y where x and y are stimulus in each category respectivley, the probability of classifying a test stimuli t into X is an increasing function of similarity of t to stored examplars of X and a decreasing function of similarity to stored examplars of contrast category Y
- Test stimuli act as retrieval cues to access similar stored examplars
- Cue dimensions combine in a multiplicative way to determine overall similarity
- Selective attention can be represented by changes in salience
- Retention loss can be represented by changes in similarity parameters.
5. Useful Literature available (Free) on the Web
- Bradley Love's web-site.This Prof has all the papers in pdf form freely available (God Bless Him).
- Komatsu - Recent Views on Conceptual Structures: A nice overview article.
- Choice, Similarity and the Context Theory of Classification
- Homepage of douglas Medin
- Categories are for Talking, Derek Edwards
- Cognitive Science by Robert Nosofsky
- Problem with Classical View
- An interesting reading list on Categorization