White paper on Quasi Artifactual Intelligence
About ∞ White paper ∞ QuasiMatrix Code ∞ QAT Code ∞ Data Examples ∞ Scatter-Gather Explained ∞ The Plow Share ∞
A development of 911 era category theory applied as a front-end category engine for machine learning and control —a plowpoint project, presenting:
Developing a perceptive envelope of reckoning for an artifactual intelligence —quasiAI: the perceptor
Editors note: Wow! The QAT is fascinating to revisit after a couple of decades! When re-examined and documented, the example concept-soup below will redact in an attempt to reveal the fascinating things from the mind of Dr. Prueitt.
Introduction
The Quasi Axiomatic Theory (QAT) was developed as a big-data tool to discover significant events in the live-edge of the expanding world-corpus —Cyberspace: 2000
As a category theory, a sampling of the world corpus, would contain a sampling of most of the categories of interest.
As a formal mathematics, self-categorization of the data-stream values were the categories of analysis. Conveniently, a binary-tree technology, needed for massive data scales, is exactly a value-categorizer.
As an investigatory tool, The QAT could isolate category trends and waves of change in large data samples, planet sized, by taking a sparse sample of the expanding world corpus.
The QAT paradigm was implemented as an in-memory data engine of all records of the data sampling (the sparse set), such that when categories of significance were discovered by visual examination. With interest category-frequency-trends, the cause of the change-wave may be reverse-searched from category, to data-event, by a category-link explorer, made to step through smaller sets of significant categories.
These algorithmic approaches are termed, 'categorical abstraction' (a scatter-gather visual map), and 'eventChemistry' as the category explorer.
Here we explore the QAT algorithms to expose how machine learning can be afforded a place in the analysis loop —a keen plowpoint
Visual Abstraction —mapping cross-category coincidence-frequency dynamics
The visual abstraction of the random-scatter mapping appears as points (representing value categories) that move on a mapping, which map the category-points were randomly scattered upon.
The 'magic' ingredient of the QAT algorithms that afford visual abstraction (vA) of relational events is the Cartesian product of the value categories found in the data stream sample for analysis. The magic is conjured by a tight iteration (programmatic loop) that moves two points slightly closer together upon the map.
Moving random point-pairs in the vA by micro-movements toward each the other, produces a clustering of categories upon the vA mapping. The coincedent-proportionality subset of a,b permutations of the Cartesian product is established by the occurrence-frequency of members in a category as sampled from the data stream.
With an animated spectrum of motion-activated groups of map-points moving, an operator of this technology, typically an NSA analyst, could partition the categorical-dynamics with a sub-selection of the time-windows sampled for analysis.
This describes the Category Abstraction (cA) portion of the Quasi Axiomatic Theory and Paradigm (QAT).
Event Chemistry
A further affordance of the QAT is inference technique availed by the displayed cross-channel relationships, termed Event Chemistry (eC).
Once interesting groups of categories within the data-stream are isolated by category abstraction mapping, groupings of interest are selected from the clusters on the cA mapping.
Isolation of small groups ... event chemistry abstraction as a interactive classical graph of circles connected with lines, allowed inference techniques to sleuth the chemistry of categorical interactions.
With contributions nationally, during the 911 response era, aiding in the global cause were the data structures of the QAT visual abstraction, navigable with event chemistry, providing access back to the source-moment of any categorical trend. A basic butterfly hunter.
Implementation of QAT Data Structures
Term: QAT.SLIP affords cross-column category-frequency stratification.
In this paradigm of measurement and category-frequency stratification, the data is a recording 'mapped' into memory in ordered sequence addressable by numeric index.
This is a simple array data structure.
The minimum pointer-set to implement a binary-tree combined with a linked list of tree-node members is stored as an array of integers, explained by their monikers:
A delete function for a tree node isn't needed. In the category theory implementation, the data may be sparsely sampled with the same results.
By structuring the data-sample stream, or some sparse selection of samples over time, into a structure including all members in an accessible structure, the tree-list composite becomes a rudimentary ontology of the data-stream structured by value-comparisons against a data-relationship, and time-reversible (or re-build-able to any certain event on the time line).
Additionally, as a time-series log, there is implicitly a time-line addressable ontology.
Two measurement channels provide one QAT dimension of analysisQAT.I-RIB providing visual abstraction of relationships in the cross-comparison. This occurs by randomly scattering onto a visual map the set of points representing all existing pairs within dual channels of measurement in the data ontology widget. The gather process accesses the proportionality map to animate the category-mapping- wherein this is a visual abstraction of dynamic relationships translated to a stratification of motions within the category-scatter-map.
I-RIB: In-memory Referential Information Base. A term coined by P. S. Prueitt. Foundational Paper on Referential Bases, Paul S Prueitt Ph.D, October 31, 2006
http://www.bcngroup.org/beadgames/TaosDiscussion/referentialBases.htm
"URLs for Orbs and Ribs are scattered in the OntologyStream Inc and BCNGroup Inc web sites, in particular:
http://www.bcngroup.org/area1/2005beads/GIF/RoadMap.htm and
http://www.ontologystream.com/OS/clientTechnology.htm
A question on nomenclature
Is a data structure of a tree-of-categories sharing indices with a linked-list headed with each category node, with the list comprising as pointers to all members of a value category —then may the pointer matrix be properly termed an ontology? An ontological primitive?
Rigorous loose thoughts
In this notational paradigm of measurement and category frequency trending, the data is a recording and remains immutable.
A binary tree implementation for data access has no need to balance an immutable log.
A delete function for a tree node isn't needed, moreover, the data element tree/list nodes are each a demarcation of their category membership, in order on the time-line.
In the category theory implementation, the data may be sparsely sampled with the same results, within limits.
Should a data-access excursion on the tree-list structure get lengthy (as an unbalanced binary-tree) in any certain data sample, it is simply rejected as part of the un-sampled, dis-obviating any need for binary tree balancing.
The outcome of the paradigm rendered to notation is a binary-tree/linked-list data widget where all members of a category value are linked as a chain, as category-member-chains attached to each binary tree node.
The binary-tree nodes each have a chain of equivalent values indexed in natural order as a linked list. The fully structured data widget affords any data by relational-path-access, including lower_category, higher_category, next_member, previous_member, with all index values anywhere within the structure also indicating relative age by natural order, i.e., the magntitude of the access-index is a relative age value in a time-line sampling.
With structured historical data access of a measured channel, a second structure is referenced holding a second channel of measurements. These two structures provide the prismatic affordance of the proportionality map of their implicit relational dynamics across a sampling of events within a time line.
Future Development
- Hyper-accelerating quasiAI category-perception with the Cartesian product sub-set on high-speed data-streams as a running-recent-average analysis window (or any previous history of the data-stream)
- Implement a video-frame-rate capability of gather processes on a random-scatter map, providing a gather-process that stratifies category-frequency-dynamics of a data-stream sample AS compared to an unknown data-stream. I.e., dual-channel-expansion of how category-frequency dynamics of unknown data.
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- Known </> Unknown ==> meaningful results to a domain expert, where '</>' represents a cluster-process based on a determinant.
- Known </> Known ==> machine intelligence training scenario
- Unknown </> Unknown ==> interesting patterns which can be traced back to the causal instances of a value-category-occurrence in the sampled data stream/log.
- Trace-back to root causality of existing unknown category dynamics is available to adjust sampling resolution.
- This affords in principles of an applicable domain a domestication of Maxwell's demon over events of chaotic environment, capable of isolating causal-determinants in ongoing apparent chaos.
- Massive parallel circuits on FPGA configurations customized for UI customized/calibrated to units and measures of the data stream for analysis.
- Implement N-Dimensional QAT analysis, with an N-quasiAI