Implementing two dimensional segment inversions with inversion-conforming data sets processing being rendered to include generalized composite weight factors in the processing of error-affected multivariate data samples

• US 20060111844A1
• Filed: 11/04/2005
• Published: 05/25/2006
• Est. Priority Date: 11/12/2004
• Status: Active Grant

• Current Assignee: Larry S. Chandler
• Original Assignee: Larry S. Chandler
• Inventors: Chandler, Larry S.
• Granted Patent: US 7,383,128 B2
• Time in Patent Office: Days
• US Class Current: 702/1
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

Representations of data inversions are generated by alternate forms of maximum likelihood estimating and associated least-squares and regression analysis which are rendered in correspondence with either single component residual deviations or projections between data samples and inversion-conforming data sets. Deficiencies in representing likelihood as related to errors-in-variables data and heterogeneous precision are compensated by composite weighting of likelihood elements. Composite weight factors employ both normalization to establish non-skewed homogeneous likelihood elements and fundamental weighting to compensate for associated non-linearly and establish common units for combining orthogonal coordinate-oriented data-point projections. Respective weight factors are related to alternately considered fundamental variables. Variance or alternate representation, as related to statistically independent sampling, is utilized as assumed applicable or replaced by composite variability representing single coordinate variations as affected by orthogonal coordinate sampling dispersions. Statistical rendition is generated as a replacement for unquantifiable dependent variable representation.

Claims

1. A method for accessing processing and representing information whereby a data representation is generated in correspondence with at least one two dimensional segment,

said two dimensional segment comprising single-coordinate data samples and respective dependent variable correspondence,

said single-coordinate data samples being included in a set of coordinate designations,

said coordinate designations being represented by respective coordinate related measurements in orthogonal correspondence with said single-coordinate data samples,

said set of coordinate designations comprising coordinate related measurements from an ensemble of variable related observations,

said set of coordinate designations comprising pertinent said variable related observation measurements corresponding to more independent variable coordinates than dependent variable coordinates,

said data representation being rendered in correspondence with data from said ensemble of variable related observations, and

said data representation comprising representation of evaluated adjustment parameters;

said method comprising;

activating means for said accessing processing and representing information,

accessing provided data,

representing information whereby at least one form of data processing is effectuated in correspondence with a parametric approximative form, and

effectuating said at least one form of data processing;

said effectuating including;

abstracting said single-coordinate data samples from said ensemble of variable related observations,

establishing said parametric approximative form in correspondence with said single-coordinate data samples and said dependent variable correspondence, and

effecting at least one form of data manipulating whereby said adjustment parameters are evaluated;

said abstracting including;

abstracting said set of coordinate designations in correspondence with criteria related to a subset of said set, and

said two dimensional segment being established in correspondence with said criteria;

said criteria including;

said subset only comprising coordinate designations corresponding to substantially constant measurements,

said substantially constant measurements being associated with respective variable coordinates and represented by respective said coordinate related measurements,

said coordinate related measurements being established to be substantially constant as considered within prescribed limits,

said subset excluding said single-coordinate data samples, and

said subset excluding said dependent variable correspondence;

said means for accessing processing and representing information comprising;

a control system, and

said control system being configured for providing said activating, said accessing, said effectuating, and said representing information.

2. A method as in claim 1 wherein said abstracting includes sequencing multivariate representations to establish a plurality of two dimensional segments,

3. A method as in claim 1 wherein said dependent variable correspondence is represented by sample measurements,

said sample measurements being included in said set of coordinate designations,

said sample measurements being excluded from said subset.

4. A method as in claim 1 wherein said data processing includes processing said two dimensional segment in the absence of dependent variable sample measurements,

said dependent variable correspondence being generated in correspondence with said set of coordinate designations.

5. A method as in claim 4 wherein said ensemble of variable related observations represents data samples corresponding to only one dimension, and wherein said subset is a null subset,

said data representation being rendered in correspondence with said single-coordinate data samples and said dependent variable correspondence.

6. A method as in claim 1 wherein said effectuating includes implementing proportionate composite weighting,

said data representation being generated in correspondence with said implementing,

said implementing including:

establishing said composite weighting in proportion to the respective products of fundamental weight factors being multiplied times the square of corresponding deviation normalization coefficients,

said deviation normalization coefficients rendering the products of un-normalized deviations multiplied by said deviation normalization coefficients so as to be substantially characterized by non-skewed homogeneous uncertainty distributions,

said fundamental weight factors being established in correspondence with the products of said un-normalized deviations multiplied by said deviation normalization coefficients, and

said deviation normalization coefficients being considered as constant during the rendition of representation for respective said fundamental weight factors;

said data manipulating including optimizing said approximative form in correspondence with a sum of addends,

said addends being established as represented by the square of said un-normalized deviations being rendered to include said proportionate composite weighting.

7. A method as in claim 6 wherein said un-normalized deviations are data-point projections and wherein said data processing includes inversion conforming data sets processing,

said data representation being generated in correspondence with a plurality of data-point projections,

said data-point projections extending along orthogonal paths to intersect an approximating relationship,

said data-point projections extending from coordinates comprising said single-coordinate data samples and said dependent variable correspondence,

intersections of said data-point projections with said approximating relationship substantially establishing respective inversion-conforming data sets,

said inversion-conforming data sets comprising projected coordinates for points that conform to a corresponding data inversion at respective said intersections.

8. A method for accessing processing and representing information whereby a data representation is generated in correspondence with proportionate composite weighting,

said processing including implementing said proportionate composite weighting,

said implementing including:

establishing said composite weighting in proportion to the respective products of fundamental weight factors being multiplied times the square of corresponding deviation normalization coefficients,

said deviation normalization coefficients rendering the products of un-normalized deviations multiplied by said deviation normalization coefficients so as to be substantially characterized by non-skewed homogeneous uncertainty distributions,

said fundamental weight factors being established in correspondence with products of said deviation normalization coefficients and respective said un-normalized function deviations,

said deviation normalization coefficients being considered as constant during the rendering of representation for respective said fundamental weight factors, and

said fundamental weight factors being related to products of change in normalized function deviations considered with respect to change in pertinent fundamental variables;

said method comprising;

activating means for said accessing processing and representing information,

accessing provided data,

representing information whereby at least one form of data processing is effectuated in correspondence with a parametric approximative form, and

effectuating said at least one form of data processing,

said effectuating including;

implementing at least one form of calculus of variation to optimize representation for said adjustment parameters in correspondence with a sum of addends,

said data representation comprising representation of established said adjustment parameters,

said addends being established as represented by the square of said un-normalized deviations being rendered to include said proportionate composite weighting;

said means for accessing processing and representing information comprising;

a control system, and

said control system being configured for providing said activating, said effectuating, and said representing information;

said implementing excluding the generating and implementing of the square of inverse deviation variation weighting to establish the weighting of squared single component residual deviations,

said implementing excluding the generating and implementing of inverse deviation variation weighting to establish the weighting of single component residual deviations,

said implementing excluding the generating and implementing of cross term minimizing weight factors to establish the weighting of squared single component residual deviations,

said implementing excluding the generating and implementing of transformation weight factors to establish the weighting of squared single component residual deviations,

said implementing excluding the representing and implementing of precision weighting as rendered in correspondence with forms of discriminate reduction data processing for the weighting of the square of single component residual deviations.

9. A method as in claim 8 wherein said un-normalized deviations are data-point projections and wherein said data processing includes inversion conforming data sets processing,

said data representation being generated in correspondence with a plurality of data-point projections,

each of said data-point projections extending from respective data-related coordinates to intersect an approximating relationship,

intersections of said data-point projections with said approximating relationship substantially establishing respective inversion-conforming data sets which comprise projected coordinates for points that conform to a corresponding data inversion at respective said intersections,

intersections of said data-point projections with said approximating relationship substantially establishing respective inversion-conforming data sets,

said inversion-conforming data sets comprising projected coordinates for points that conform to a corresponding data inversion at respective said intersection.

10. A method as in claim 8 whereby said data representation is generated in correspondence with at least one two dimensional segment,

said two dimensional segment comprising two dimensional data-related coordinates,

said data-related coordinates being represented by single-coordinate data samples and respective dependent variable correspondence,

said un-normalized deviations being rendered in correspondence with said single-coordinate data samples and said dependent variable correspondence;

said single-coordinate data samples being included in a set of coordinate designations,

said coordinate designations being represented by respective coordinate related measurements in orthogonal correspondence with said single-coordinate data samples,

said set of coordinate designations comprising coordinate related measurements from an ensemble of variable related observations,

said data representation being rendered in correspondence with data from said ensemble of variable related observations, and

said set of coordinate designations comprising pertinent said variable related observation measurements corresponding to more independent variable coordinates than dependent variable coordinates;

said effectuating including;

abstracting said single-coordinate data samples from said ensemble of variable related observations, and

establishing said parametric approximative form in correspondence with said single-coordinate data samples and said dependent variable correspondence;

said abstracting including;

abstracting said set of coordinate designations in correspondence with criteria related to a subset of said set, and

said two dimensional segment being established in correspondence with said criteria;

said criteria including;

said subset only comprising coordinate designations corresponding to substantially constant measurements,

said substantially constant measurements being associated with respective variable coordinates and represented by respective said coordinate related measurements,

said coordinate related measurements being established to be substantially constant as considered within prescribed limits,

said subset excluding said single-coordinate data samples, and

said subset excluding said dependent variable correspondence.

11. A data processing system comprising:

a control system,

means for accessing, processing, and representing information,

said control system being configured for providing said accessing, processing, and representing information, and

said control system being configured for generating at least one data representation in correspondence with at least one two dimensional segment,

said two dimensional segment comprising single-coordinate data samples and respective dependent variable correspondence,

said single-coordinate data samples being included in a set of coordinate designations,

said coordinate designations being represented by respective coordinate related measurements in orthogonal correspondence with said single-coordinate data samples,

said set of coordinate designations comprising coordinate related measurements from an ensemble of variable related observations,

said set of coordinate designations comprising pertinent said variable related observation measurements corresponding to more independent variable coordinates than dependent variable coordinates,

said data representation being rendered in correspondence with data from said ensemble of variable related observations, and

said data representation comprising representation of evaluated adjustment parameters;

coordinates;

said generating including;

activating means for said accessing processing and representing information,

accessing provided data,

representing information whereby at least one form of data processing is effectuated in correspondence with a parametric approximative form, and

effectuating said at least one form of data processing whereby said data representation is generated;

said effectuating including;

abstracting said single-coordinate data samples from said ensemble of variable related observations,

establishing said parametric approximative form in correspondence with said single-coordinate data samples and said dependent variable correspondence, and

effecting at least one form of data manipulating whereby said adjustment parameters are evaluated;

said abstracting including;

abstracting said set of coordinate designations in correspondence with criteria related to a subset of said set, and

said two dimensional segment being established in correspondence with said criteria;

said criteria including;

said subset only comprising coordinate designations corresponding to substantially constant measurements,

said substantially constant measurements being associated with respective variable coordinates and represented by respective said coordinate related measurements,

said coordinate related measurements being established to be substantially constant as considered within prescribed limits,

said subset excluding said single-coordinate data samples, and

said subset excluding said dependent variable correspondence.

12. A data processing system as in claim 11 wherein said abstracting includes sequencing multivariate representations over regions of non constant valued measurements to establish a plurality of two dimensional segments,

said sequencing including:

assigning a sequence digit column to each considered variable that is represented in said ensemble,

assigning a numerical value to said digit column which respectively corresponds to non constant regions of each considered variable sample,

creating a digital code for each set of observation coordinates,

said code comprising digital representation of non constant regions corresponding to respective segments for each said set of observation coordinates,

numerically sequencing the respective digital codes, and establish said two dimensional segments over sections whose non constant regions do not overlap.

13. A data processing system as in claim 11 wherein said dependent variable correspondence is represented by sample measurements,

said sample measurements being included in said set of coordinate designations,

said sample measurements being excluded from said subset.

14. A data processing system as in claim 11 wherein said effectuating includes processing said two dimensional segment in the absence of dependent variable sample measurements,

said dependent variable correspondence being generated in correspondence with said set of coordinate designations.

15. A data processing system as in claim 14 wherein said ensemble of variable related observations represents data samples corresponding to only one dimension, and wherein said subset is a null subset,

said data representation being rendered in correspondence with said single-coordinate data samples and said dependent variable correspondence.

16. A data processing system as in claim 11 wherein said effectuating includes implementing proportionate composite weighting,

said data representation being generated in correspondence with said implementing,

said implementing including:

establishing said composite weighting in proportion to the respective products of fundamental weight factors being multiplied times the square of corresponding deviation normalization coefficients,

said deviation normalization coefficients rendering the products of un-normalized deviations multiplied by said deviation normalization coefficients so as to be substantially characterized by non-skewed homogeneous uncertainty distributions,

said fundamental weight factors being established in correspondence with the products of said un-normalized deviations multiplied by said deviation normalization coefficients, and

said deviation normalization coefficients being considered as constant during the rendition of representation for respective said fundamental weight factors;

said data manipulating including optimizing said approximative form in correspondence with a sum of addends,

said addends being established as represented by the square of said un-normalized deviations being rendered to include said proportionate composite weighting.

17. An output product comprising a data representation

generated by a data processing system,

said data representation comprising representation of dependent variable response being associated with variable related observations,

said data representation being rendered in correspondence with at least one two dimensional segment,

said two dimensional segment comprising single-coordinate data samples and respective dependent variable correspondence,

said single-coordinate data samples being included in a set of coordinate designations,

said coordinate designations being represented by respective coordinate related measurements in orthogonal correspondence with said single-coordinate data samples,

said set of coordinate designations comprising coordinate related measurements from an ensemble of variable related observations,

said set of coordinate designations comprising pertinent said variable related observation measurements corresponding to more independent variable coordinates than dependent variable coordinates,

said data representation being rendered in correspondence with data from said ensemble of variable related observations, and

said data representation comprising representation of evaluated adjustment parameters;

said evaluated adjustment parameters being generated by;

activating means for said accessing processing and representing information,

accessing provided data,

representing information whereby at least one form of data processing is effectuated in correspondence with a parametric approximative form, and

effectuating said at least one form of data processing;

said effectuating including;

abstracting said single-coordinate data samples from said ensemble of variable related observations,

establishing said parametric approximative form in correspondence with said single-coordinate data samples and said dependent variable correspondence, and

effecting at least one form of data manipulating whereby said adjustment parameters are evaluated;

said abstracting including;

abstracting said set of coordinate designations in correspondence with criteria related to a subset of said set, and

said two dimensional segment being established in correspondence with said criteria;

said criteria including;

said subset only comprising coordinate designations corresponding to substantially constant measurements,

said substantially constant measurements being associated with respective variable coordinates and represented by respective said coordinate related measurements,

said coordinate related measurements being established to be substantially constant as considered within prescribed limits,

said subset excluding said single-coordinate data samples, and

said subset excluding said dependent variable correspondence;

said means for accessing processing and representing information comprising;

a control system, and

said control system being configured for providing said activating, said accessing, said effectuating, and said representing information.

18. An output product as in claim 17 wherein said abstracting includes sequencing multivariate representations to establish a plurality of two dimensional segments.

19. An output product as in claim 17 wherein said dependent variable correspondence is represented by sample measurements,

said sample measurements being included in said set of coordinate designations,

said sample measurements being excluded from said subset.

20. An output product as in claim 17 wherein said effectuating includes processing said two dimensional segment in the absence of dependent variable sample measurements,

said dependent variable correspondence being generated in correspondence with said set of coordinate designations.

21. An output product as in claim 17 wherein said effectuating includes implementing proportionate composite weighting,

said data representation being generated in correspondence with said implementing,

said implementing including:

establishing said composite weighting in proportion to the respective products of fundamental weight factors being multiplied times the square of corresponding deviation normalization coefficients,

said deviation normalization coefficients rendering the products of un-normalized deviations multiplied by said deviation normalization coefficients so as to be substantially characterized by non-skewed homogeneous uncertainty distributions,

said fundamental weight factors being established in correspondence with the products of

said un-normalized deviations multiplied by said deviation normalization coefficients, and

said deviation normalization coefficients being considered as constant during the rendition of representation for respective said fundamental weight factors;

said data manipulating including optimizing said approximative form in correspondence with a sum of addends,

said addends being established as represented by the square of said un-normalized deviations being rendered to include said proportionate composite weighting.

22. An output product as in claim 17 comprising a memory for storing data for access by an application program being executed on a processing system, said data representation being stored in said memory.