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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 >.

 

Differential Ontology Diagram

 

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.