Communications on a National Project
On the nature of
scatter-gather and Orbs
3/7/2004 8:58 AM
As a side note,
Latent Semantic Indexing (both the linear algebra form and
the stochastic forms) is a means for measuring holonomic constraints directly
using the gather of local fields of "relationship". The algebraic inversion of a high
dimensional matrix is a slow iterative process just like the scatter gather text analysis,
and neural network categorization methods.
Sigh, it is a conjecture that comes from my work on scatter
gather on a compactification of the embedding space that lead me to realize
that the projection from this high dimensional space is in fact fully
conserving of all local measures of related-ness IF one knows what the
dimension and the topological “shape” of the embedding manifold. Sorry to be technical, this line of
reasoning is fully documented in the research notes I published at:
SLIP Technology Browser - Index
This is the insight that lead me to the hypothesis that a form of "differential ontology" would allow a mapping to occur between
1.
the continuum mathematics in stochastic LSI and in algebraic
LSI
2.
sets of ordered triples in the form < a, r, b >.
I discuss
this extensively and feel that this is the foundation for mapping between
Sowa's CLCE (Common Logic Controlled
English) and natural language.
The Ontology
referential base (Orbs) does several
things.
First the
underlying I-RIB data encoding
solves the set theoretical question about when does an element belong in a set,
where the set if very large.
The
computational task is reduced to less than n machine cycles given the set is of
size less than 2^n. The Orb also
finds where the element is if it is in the set.
Anyway,
this can be easily shown, and is discussed in the SLIP Index materials.