On Fri, 6 Nov 1998, Nicholas Gessler wrote:
>I am looking to a departure from the classical taxonomic schemes that try to
>fit each artifact into a single taxon. Certainly this has advantages for
>the numerical comparison of assemblages but it tends to obscure the fact
>that each artifact may simultaneously participate in several different
>functions (or processes). [I consider function or process to include
>informational as well as material-energenetic action.] In plain English, an
>assemblage of artifacts may be classified in various ways depending upon the
>perceptions and goals of the potential user, and we may wish to capture
>these variations in some representational scheme. One such scheme might be
>(logically) to consider the primitive foundation of an assemblage as a
>collection of artifacts with a high number of attributes. How the creators
>of that assemblage, and we as its analyzers, might view or use it at any
>particular time, could be defined as the imposition of some structure to
>that data. More abstractly, a type (for a particular purpose) could then be
>defined as a cluster in some high dimensional hyperspace. This might make
>the comparison of assemblages more difficult, but it capture the practices
>of multiple-use and re-use. e.g. I can pound my tent-stakes in with a
>hammer, a rock, a piece of firewood, or my copy of Sokal and Sneath.)
>
>I am considering building a computational model of such a system and I'm
>looking for other references to the problem, both critical and theoretical.
Nick,
How to do it:
a. Choose a set of attributes.
[How you motivate the selection is up to you,
however, you it may help to think of attributes
as an alternative notation for set or class memberships.]
Let the description of each artifact be expressed
as a binary vector (1s & 0s) in which each attribute
in your scheme has an assigned position in the vector.
You may find it useful to use unary features (attributes).
This means that binary oppositions will NOT be implied
by the presence or absence of a 1 or 0 in a particular
feature. [Binary oppositions between two different
attributes (or features) would be marked by the fact that
in all tabulated artificats, if a given Attribute, Ai
always has a value opposite that of another specific
Attribute, Aj. [This can lead to the discovery of
binary oppositions among pairs of attributes; also,
the use of unary features makes it possible to represent
cases in which a single attribute occurs in different
opposition sets.]
If you interprete the vector positions as spatial
coordinates, then every aritifact encoded in such a
a scheme will have a specific location in a multi-
dimensional space, of dimensionality equal to the
the number of attributes.
Artifacts close to each other in that space would,
presumably, be classed together.
If you choose a set of attributes, you might first
validate their implied clusterings to see if they
match results derived by other methods.
b. The technique is prominent in some cognitive linguistic
work on semantic classification of words.
The most recent and active work of this kind
uses the term 'high dimensional space', and uses
an approximation to n-th order Markov chains
to compute scalar size of distance between pairs
of words; the values are not binary, but they
approach does imply a 'cognitive space' of a
dimensionality equal to the number of features.
[The data bases are multi-million word texts
found on the internet-- the values are linear
functions of distance of co-occurence of words
from each other in sentences--usually reflecting
a distance of 1 to 10 word positions, with the
furthest distance being given the lowest weight.]
c. Alternative interpretations of the boolean vectors:
if the ordering of attributes is important,
each vector may be viewed as a path down a
binary decision tree, and may be interpreted
as a heirarchical classification scheme.
one may view each binary vector as defining
a multi-dimensional cube: 2 attributes would
define a square, 3, a cube, 4, a 4-dimensional
cube, n, an n-dimensional cube (or hypercube).
one may choose not to treat the vectors as
defining higher order spaces, and, instead,
process them in other ways.
Sheldon
Sheldon Klein
University of Wisconsin-Madison
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