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
First Claim
1. A method of using a data processing system for generating a data inversion in correspondence with at least one two dimensional segment comprising two dimensional data-related coordinates represented by a plurality of single-coordinate data samples and respective dependent variable correspondence;
- said plurality of single-coordinate data samples being included in a set of coordinate designators comprising characteristic observation measurements selected from an ensemble of variable related observations;
said characteristic observation measurements corresponding to more independent variable coordinates than dependent variable coordinates,said set of coordinate designators comprising at least one subset defined by the criteria that said subset excludes said plurality of single-coordinate data samples and said dependent variable correspondence, and comprises only respective coordinate related observation measurements that correspond to substantially constant variable measurements along respective variable coordinates and are presumed to be orthogonal to respective measurements corresponding to said plurality of single-coordinate data samples;
said substantially constant measurements being associated with said respective variable coordinates and represented by respective coordinate related observation measurements,said respective coordinate related observation measurements being substantially constant as considered within prescribed limits, andsaid data inversion comprising a representation of evaluated adjustment parameters;
said method comprising;
activating means for accessing processing and representing information, accessing provided data,designating said at least one two dimensional segment, said designating including identifying said set of coordinate designators in correspondence with the criteria which define said subset;
abstracting said plurality of single-coordinate data samples from said ensemble of variable related observations in correspondence with said at least one two dimensional segment,establishing a parametric approximative form in correspondence with said plurality of single-coordinate data samples and said dependent variable correspondence, andeffecting at least one form of data manipulation whereby said adjustment parameters are evaluated.
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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.
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Citations
21 Claims
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1. A method of using a data processing system for generating a data inversion in correspondence with at least one two dimensional segment comprising two dimensional data-related coordinates represented by a plurality of single-coordinate data samples and respective dependent variable correspondence;
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said plurality of single-coordinate data samples being included in a set of coordinate designators comprising characteristic observation measurements selected from an ensemble of variable related observations; said characteristic observation measurements corresponding to more independent variable coordinates than dependent variable coordinates, said set of coordinate designators comprising at least one subset defined by the criteria that said subset excludes said plurality of single-coordinate data samples and said dependent variable correspondence, and comprises only respective coordinate related observation measurements that correspond to substantially constant variable measurements along respective variable coordinates and are presumed to be orthogonal to respective measurements corresponding to said plurality of single-coordinate data samples; said substantially constant measurements being associated with said respective variable coordinates and represented by respective coordinate related observation measurements, said respective coordinate related observation measurements being substantially constant as considered within prescribed limits, and said data inversion comprising a representation of evaluated adjustment parameters; said method comprising; activating means for accessing processing and representing information, accessing provided data, designating said at least one two dimensional segment, said designating including identifying said set of coordinate designators in correspondence with the criteria which define said subset; abstracting said plurality of single-coordinate data samples from said ensemble of variable related observations in correspondence with said at least one two dimensional segment, establishing a parametric approximative form in correspondence with said plurality of single-coordinate data samples and said dependent variable correspondence, and effecting at least one form of data manipulation whereby said adjustment parameters are evaluated. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A method of using a data processing system for generating a data inversion in correspondence with at least one set of coordinate related measurements and a plurality of composite weight factors,
said at least one set of coordinate related measurements comprising a plurality of single-coordinate data samples, said composite weight factors comprising products of fundamental weight factors multiplied times the squares of respective 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 normalized function deviations, said normalized function deviations comprising products of said deviation normalization coefficients and the respective un-normalized deviations, said deviation normalization coefficients being evaluated in correspondence with currently considered estimates for adjustment parameters, said fundamental weight factors being related to products of change in said normalized function deviations, said change in normalized function deviations being considered with respect to change in pertinent fundamental variables, and said deviation normalization coefficients being considered as constant during the rendition of said change; -
said method comprising; establishing a parametric approximative form in correspondence with said plurality of single-coordinate data samples and respective dependent variable correspondence; arranging a digitized representation of the normalized function deviations in a form for computer processing; arranging a digitized representation of the fundamental weight factors in correspondence with said normalized function deviations in a form for computer processing; determining said composite weight factors in proportion to the respective products of multiplying the fundamental weight factors times the squares of the corresponding deviation normalization coefficients; establishing initial estimates for said adjustment parameters; activating means for accessing processing and representing information;
accessing provided data;evaluating initial estimates for the respective composite weight factors in correspondence with said plurality of single-coordinate data samples, said initial estimates for adjustment parameters, and said parametric approximative form, and effecting at least one form of data manipulation whereby said adjustment parameters are evaluated in correspondence with a plurality of said un-normalized deviations and successive approximations for said composite weight factors, said effecting including representing information whereby at least one form of automated data processing is effectuated in correspondence with said parametric approximative form, and said automated data processing 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 composite weight factors being considered as constant during the optimizing steps related to application of said at least one form of calculus of variation; said addends being established as represented by the squares of said un-normalized deviations being rendered to include proportionate successive estimates for said composite weight factors, and said data inversion comprising optimized representation for said adjustment parameters; said at least one form of data manipulation excluding; the generating and implementing of the square of inverse deviation variation weighting to establish the weighting of squared single component residual deviations, the generating and implementing of inverse deviation variation weighting to establish the weighting of single component residual deviations, the generating and implementing of cross term minimizing weight factors to establish the weighting of squared single component residual deviations, the generating and implementing of transformation weight factors to establish the weighting of squared single component residual deviations, and the representing and implementing of precision weighting as rendered in correspondence with forms of discriminate reduction data processing for the weighting of the squares of single component residual deviations. - View Dependent Claims (9, 10)
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11. A product comprising a memory device having stored thereon an electronic or electromagnetic representation of a data inversion generated by a data processing system,
said data inversion comprising a proportionate representation of an un-quantified dependent variable response associated with a plurality of single-coordinate data samples abstracted from an ensemble of variable related observations, said data inversion being rendered in correspondence with at least one two dimensional segment, said two dimensional segment comprising two dimensional data-related coordinates represented by said plurality of single-coordinate data samples and respective dependent variable correspondence, said plurality of single-coordinate data samples being included in a set of coordinate designators, said set of coordinate designators comprising characteristic observation measurements selected from said ensemble of variable related observations, said set of coordinate designators comprising at least one subset defined by the criteria that said subset excludes said plurality of single-coordinate data samples and said dependent variable correspondence and comprises only coordinate related observation measurements which are presumed to be orthogonal to respective measurements corresponding to said plurality of single-coordinate data samples and coordinate designators which correspond to substantially constant measurements along respective variable coordinates; -
said substantially constant measurements being associated with said respective variable coordinates and represented by corresponding coordinate related observation measurements which are substantially constant within prescribed limits, and said data inversion comprising a representation of evaluated adjustment parameters wherein said evaluated adjustment parameters are generated by; activating means for 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; designating said at least one two dimensional segment, said designating including identifying said set of coordinate designators in correspondence with the criteria defining said subset, abstracting said plurality of single-coordinate data samples from said ensemble of variable related observations in correspondence with said at least one two dimensional segment, establishing said parametric approximative form in correspondence with said plurality of single-coordinate data samples and said dependent variable correspondence, and effecting at least one form of data manipulation whereby said adjustment parameters are evaluated, said effecting including processing said at least one two dimensional segment in the absence of dependent variable sample measurements; wherein said dependent variable correspondence is generated in correspondence with a sequenced digital representation of said plurality of single-coordinate data samples. - View Dependent Claims (12, 13, 14)
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14. A product as claimed in claim 11, wherein said effectuating includes implementing proportionate composite weighting,
said data inversion being generated in correspondence with said implementing, and said implementing including establishing said composite weighting in proportion to the respective products of fundamental weight factors being multiplied times the squares 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 normalized function deviations comprising the products of said un-normalized deviations multiplied by said deviation normalization coefficients; said deviation normalization coefficients being considered as constant during the rendition of representation for the respective fundamental weight factors;
said data manipulation including optimizing said parametric approximative form in correspondence with a sum of addends;said addends being established as represented by the squares of said un-normalized deviations being rendered to include said proportionate composite weighting, wherein successive approximations for said proportionate composite weighting are held constant during said optimizing.
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15. A data processing system comprising means for accessing, processing, and representing information whereby a data representation is generated in correspondence with at least one two dimensional segment comprising two dimensional data-related coordinates represented by a plurality of single-coordinate data samples and respective dependent variable correspondence;
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said plurality of single-coordinate data samples being included in a set of coordinate designators comprising characteristic observation measurements selected from an ensemble of variable related observations; said characteristic observation measurements corresponding to more independent variable coordinates than dependent variable coordinates, said set of coordinate designators comprising at least one subset defined by the criteria that said subset excludes said plurality of single-coordinate data samples and said dependent variable correspondence, and comprises only respective coordinate related observation measurements that correspond to substantially constant variable measurements along respective variable coordinates and are presumed to be orthogonal to respective measurements corresponding to said plurality of single-coordinate data samples, and said substantially constant measurements being associated with said respective variable coordinates and represented by the respective coordinate related observation measurements, the respective coordinate related observation measurements being established to be substantially constant as considered within prescribed limits, and said data representation comprising representation of evaluated adjustment parameters; wherein said data representation is generated by; activating the means for said accessing processing and representing information, accessing provided data, designating said at least one two dimensional segment, said designating including identifying said set of coordinate designators in correspondence with criteria related to said subset; abstracting said plurality of single-coordinate data samples from said ensemble of variable related observations in correspondence with said at least one two dimensional segment, establishing parametric approximative form in correspondence with said plurality of single-coordinate data samples and said dependent variable correspondence, and effecting at least one form of data manipulation whereby said adjustment parameters are evaluated. - View Dependent Claims (16, 17, 18, 19, 20, 21)
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Specification