Previous: Comparing Performance for Different Color Spaces Up: From Color Space to Color Names
A Sketch of a Developmental Model
Learning might very well be a domain where angels fear to tread, so my
brief remarks on the subject in this section should not be taken as having
any relevance for, or being encumbered by any knowledge of, the subject at
large.
The fitting of the category model to the color naming data as discussed in
Section 
might be considered as an optimization
problem, or perhaps a problem of parameter setting in a prior structure, to
use the terminology of [Brown 1994], but probably not as a learning
approach. Another distinction that [Brown 1994] makes is the one between
experience-expectant and experience-dependent processes. The
former would depend on species-specific experience that might have (had)
evolutionary importance, and might be described as ``biased learning'' or
development, while the latter would depend on individual-specific
experience, and would be closer to what is generally understood by
learning. Biased learning is also related to Edelman's Theory of Neuronal
Group Selection [G. Edelman 1989][G. Edelman 1992], in which the concept of
selection plays an important role, as opposed to recognition. In a
nutshell, the idea is that categorization (and, by extension, cognition)
may be a matter of the selection of certain neuronal groups by certain
stimuli, rather than the recognition of a stimulus by a general
categorization mechanism.
The connection I see
between biased learning and selection is that one might consider each of
the neuronal groups to ``implement'' a different bias (or ``attractor'')
for the feature/parameter space over which development and/or learning
takes place.
Bringing the discussion back to color categorization, one might consider
the foci of the Basic Color categories to represent biases or attractors of
this kind. Indeed, Berlin and Kay suggest that the 11 basic color
categories represent a universal inventory out of which particular
languages choose to lexicalize some number up to 11, presumably dependent
on their environment and needs (Section ). I have not been able to relate the location of
the foci to any particular neurophysiological phenomena, but let's assume
that they are indeed universal, for the purpose of the
discussion. Given that we know the locations of the foci in
(a particular) color space, a simple developmental or experience-expectant
algorithm for determining both the extent and the labels (names) of the
categories might go like this:
- Given: a stimulus, represented as a point
in color
space
optional: a label 
, represented as a symbol or a string
- collect the membership values
of 
for every
category in the set 
of known categories: 
- select the best candidate category:
- if necessary, adjust the width parameter
of
such that 
, without changing the categorization
of any other stimulus not belonging to the null category
- if a label was provided :
- if no label
is associated with , associate with it:
- if a label is associated with , and , do nothing
- if a label is associated with , and
, shake.
Step 4 could be implemented by keeping a list of examples of each
category on hand, and doing a minimization as described in
equation , with the appropriately chosen other-category
representatives, or such a list could be generated as needed each time
around by selecting for each other category 
, the point 
that is
closest to the focus of the best candidate category , such that
. This list has to be recomputed every time because
the 
may change in the course of development. Step 5.3 is a
somewhat complicated case, which could either be due to contradictory
input, to a problem with the category model itself, or to a previously
overgeneralized category. In any of these circumstances, the system has to
be ``shaken up'' or relaxed into a new maximally consistent state, but I
have not considered any algorithms for doing this. The sketched algorithm
also needs the 
associated with each category to be initialized
to some default value, which has an effect on the categorization behavior
in its initial stages: choosing the initial 
to be small will
result in categories that are the smallest possible to contain all examples
``seen'' to date, while choosing it to be large will result in the largest
possible categories that do not conflict with any examples seen to date.
These two possibilities may converge to the same state eventually after
seeing sufficiently many examples, but I have not investigated that.