> From: "Chan Dorothy" <DWYC195@psy.soton.ac.uk>
> Date: Fri, 3 May 1996 15:31:05 GMT
> Subject: Categorisation and Prototypes
>
> Could you please tell me what is the purpose for prototypes?
> What is the difference between [prototypes] and categorisation?
Before I can explain the role of prototypes, I have to explain
categorisation, and especially the "classical view" of categorisation,
according to which categorisation is accomplished on the basis of
features that are necessary and sufficient for deciding what belongs in
what category:
Categorisation is sorting things. Some things are members of a
particular category, some are not. For example, a sparrow is a member of
the category "bird"; so is a robin, a penguin and an ostrich. But a
platypus and a flying-fish are not members of the category "bird,"
That's categorisation. Categorisation is a task. It's something we DO.
Categories are just sets of things to which we DO the same thing; we
respond to them in the same way; for example, we eat all their members,
or we flee from all their members, or we call all their members by the
same name.
Now the classical view of categorisation is that the way things are
sorted into their proper categories is on the basis of features. For
example, mammals are creatures that (1) give birth to live young, and
(2) nurse them with milk. There are fish that give birth to live young,
but do not nurse them with milk. They are not mammals. There may be
creatures that nurse their young, but their young hatch from eggs
(platypuses? I'm not sure). Those aren't mammals either. Only creatures
that have both these features are mammals.
I'll switch to a completely imaginary example, in the mushroom world.
The mushroom world has only two categories of things: edible and
inedible. There are only mushrooms, but you've got to know which ones
are safe to eat and which ones aren't. So let's suppose that the safe
ones are (1) red AND (2) have white spots. Being red alone is necessary
for being edible, but not sufficient. Same for having white spots. (1)
and (2) are singly necessary but only jointly sufficient for being
edible.
That's the classical view. The work of Eleanor Rosch (see Rosch & Lloyd
1978) challenged it by showing that:
(1) When people categorise, they cannot tell you what features they are
using.
(2) When people categorise, they usually find some members of categories
more "typical" or "better" than others (e.g., a robin is a better member
of the category "bird" than an ostrich).
(3) When people categorise, they categorise more typical members more
quickly than less typical ones.
>From this evidence (as well as from some philosophical problems raised
by Ludwig Wittgentsein, 1953, who pointed out that no one can give the
features of the category "game," because the only thing its members
have in common is a vague "family resemblance"), Rosch concluded that the
classical view was wrong; features are not the basis on which people
categorise. Rather, they categorise on the basis of how close something
is to the "prototype" or ideal member of a category. A robin is closer
to the bird prototype than an ostrich is, but they are both closer to it
than they are to the protype of a fish, so we call them both birds, only
it takes longer to say an ostrich is a bird than it take to say a robin
is a bird, because the ostrich is further from the prototype.
So you see the opposition is not between categorisation and prototypes
but between the classical theory of how we categorise ("it's done
on the basis of features") and the prototype theory ("it's done on the
basis of distance from a prototype").
The classical theory would require that your brain learn the features
that are sufficient to categorise things, building up feature detectors
that are "tuned" to pick out the right features and ignore the others.
Inputs would be sorted by this feature detector on the basis of whether
or not they had the right features.
The prototype theory would require that your brain build up an image
or template of an idealised or prototypical member of the category.
Inputs would be sorted on the basis of whether they matched more closely
to the prototype of this category or to that of another category.
> Which one is better when explaining "how our minds work"?
Prototype matching works well for some things (for example, facial
expression categories), but for most things it does not, because there
is no prototype: There is no ideal "chair." Chairs must simply share
certain features. Prototype theories, which began as rivals to feature
theories, gradually turned into feature theories themselves: A prototype
was no longer an idealised member of a category, but a set of features.
The real problem with prototype theories of categorisation was that they
were not really categorical: Closeness to a prototype is a matter of
degree, it's not an all-or-none, categorical matter. This may work fine
for a category like "big," whose membership is indeed a matter of
degree. (Everything that has any size at all is "big" to some degree;
the rest is all relative, depending on the range of things you are
considering, and how big their extreme ends -- the prototypes -- are.
Even "little" things are "big," it's just that they're much less big
than big things are. Not so of "bird": A bird is not a bird merely as a
matter of degree (and a fish, to a lesser degree). A bird is ALL bird;
not "mostly" bird, because closer to the prototype of a bird than the
prototype of a fish.
So in the end, I would say the classical feature view provides a better
explanation of how our minds work than the prototype view (except in
a few special cases, such as faces).
> Have they got any thing to do with Neural Nets?
Neural nets are good at categorisation. Unsupervised nets with
competitive learning work more like prototype models, whereas supervised
nets like backpropagation can both memorise special cases and learn
features, rules and regularities, so are feature processing models.
Logically speaking though, even "distance from a prototype" is a
feature! So prototype models are really just special cases of feature
models -- and rather limited special cases at that.
> In the lecture, you used the example for distinguishing " mammal",
> could you use it again for explaining the terms "necessary" and
> "sufficient"?
Let me give some abstract examples first from symbolic logic. Here are
two propositions, followed by their truth conditions:
A AND B (True if both A and B are true, False in every other case).
In this case, the truth of A is necessary but not sufficient, the truth
of B is necessary but not sufficient, and the truth of both together is
both sufficient and necessary for the truth of the proposition as a whole.
A OR B (inclusive "or": True if either A alone or B alone or both together
are true, False if not)
In this case the truth of A alone is sufficient but not necessary, and
the truth of B alone is sufficient but not necessary for the truth of the
proposition as a whole. The truth of both together is also sufficient,
but not necessary.
A XOR B (exclusive "or": True if either A alone or B alone are true;
False if both are true; False if both are false)
In this case the truth of A alone is neither necessary nor sufficient;
neither is the truth of B alone. The truth of one with the falsity of
the other are sufficient and necessary for the truth of the proposition
as a whole.
(A category with features A XOR B cannot be learned by a perceptron, and
this is the basis of Minsky's critique of neural nets. A multilayered
net like backprop, however, can learn XOR too.)
The classical view of categorisation is that the members of a category
share a set of features that provide the necessary and sufficient
conditions for being a member of that category (depending on what
combination of ANDs and ORs they happen to be based on).
The mammal example is the same as A AND B: A creature is a mammal if and
only if (A) it gives birth to live young and (B) nurses its young.
A is necessary but not sufficient, B is necessary but not sufficient,
A and B together are necessary and sufficient.
You need not undertand the logic of necessity/sufficiency for this
course! So don't trouble your heads about this unless you are
interested:
A ONLY IF B (True if A and B are both True or if A is False; False only
if A is True and B is False)
Here, the truth of A is necessary but not sufficient and the truth of B
is sufficient but not necessary for the truth of the proposition as a
whole.
References
Rosch, E. & Lloyd, B. B. (1978) Cognition and categorization.
Hillsdale NJ: Erlbaum Associates
Wittgenstein, L. (1953) Philosophical investigations. New York: Macmillan
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