HIGH-DIMENSIONAL DATA ANALYSIS

• US 20110307438A1
• Filed: 03/06/2011
• Published: 12/15/2011
• Est. Priority Date: 06/14/2010
• Status: Active Grant

• Current Assignee: Carmen Ng, Dexter Chin, Miscellany Creative SL
• Original Assignee: Blue Prism Technologies Pte., Ltd.
• Inventors: Fern+e,acu a+ee ndez Mart+e,acu i+ee nez, Juan Luis
• Granted Patent: US 8,688,616 B2
• Time in Patent Office: Days
• US Class Current: 706/52
• CPC Class Codes: G01V 20/00 Geomodelling in general
• CPC Class Codes: G01V 2210/62 Physical property of subsurface
• CPC Class Codes: G01V 3/38 Processing data, e.g. for analysis, for interpretation, for correction
• CPC Class Codes: G06N 5/048 Fuzzy inferencing
• CPC Class Codes: G06N 7/01 Probabilistic graphical models, e.g. probabilistic networks

Abstract

Described herein is a framework for analyzing data in high-dimensional space. In accordance with one implementation, observed data and at least one input model parameter set is received. The input model parameter set serves as a solution candidate of a predefined problem (e.g., inverse or optimization problem) and is related to the observed data via a model. To provide enhanced computational efficiency, a reduced base with lower dimensionality is determined based on the input model parameter set. The reduced base is associated with a set of coefficients, which represents the coordinates of any model parameter set in the reduced base. Sampling is performed within the reduced base to generate an output model parameter set in the reduced base. The output model parameter set is compatible with the input model parameter set and fits the observed data, via the model, within a predetermined threshold.

Claims

1. A method of analyzing data in high-dimensional space, comprising:

(i) receiving, by a processor, observed data from a data source and at least one input model parameter set serving as a solution candidate of a predefined problem, wherein the input model parameter set is related to the observed data via a model;

(ii) determining based on the input model parameter set, by the processor, a reduced base associated with a set of coefficients that represent coordinates of any model parameter set in the reduced base, wherein the coefficients in the reduced base are fewer than model parameters in the input model parameter set; and

(iii) sampling within the reduced base, by the processor, to generate an output model parameter set in the reduced base, wherein the output model parameter set is compatible with the input model parameter set and fits the observed data, via the model, within a predetermined threshold.

2. The method of claim 1 wherein the reduced base comprises a target oriented base.

3. The method of claim 2 wherein the step (ii) comprises determining the target oriented base by applying a learning, interpolation, or conditional simulation technique on one or more secondary attributes, hard model information or a combination thereof.

4. The method of claim 1 wherein the input model parameter set comprises a unique posterior model parameter set.

5. The method of claim 4 wherein the step (ii) comprises orthogonally transforming the posterior model parameter set to determine a posterior reduced base.

6. The method of claim 5 wherein the orthogonally transforming the posterior model parameter set comprises:

generating one or more orthogonal transformation matrices by performing a model reduction method;

projecting the posterior model parameter set onto at least one of the one or more orthogonal transformation matrices to generate one or more compressed terms; and

projecting the one or more compressed terms back onto an original canonical base associated with the posterior model parameter set to generate the posterior reduced base.

7. The method of claim 6 further comprises performing, on the one or more compressed terms, exact compression, group compression, or any combination thereof.

8. The method of claim 6 wherein the model reduction method comprises singular value decomposition, discrete cosine transform, discrete wavelet transform, discrete Chebyshev transform or independent component analysis.

9. The method of claim 5 wherein the posterior reduced base comprises a spatial indicator base.

10. The method of claim 1 wherein the step (iii) comprises hyperprism sampling, minimum norm geometric sampling, telescopic geometric sampling or logarithmic geometric sampling.

11. The method of claim 1 wherein the step (iii) comprises oriented sampling.

12. The method of claim 1 wherein the step (iii) comprises stochastic sampling.

13. The method of claim 12 wherein the step (ii) comprises:

receiving prior information;

determining a prior reduced base using the prior information;

performing optimization in the prior reduced base to locate a low misfit region; and

determining a posterior reduced base based on a good model of the low misfit region.

14. The method of claim 13 wherein the optimization comprises particle swarm optimization, differential evolution, Monte Carlo methods, or any combination thereof.

15. The method of claim 13 wherein the stochastic sampling comprises:

receiving a posterior reduced base; and

sampling in the posterior reduced base using a global optimization technique.

16. The method of claim 15 wherein the global optimization technique comprises particle swarm optimization, differential evolution, Monte Carlo methods, or a combination thereof.

17. The method of claim 1 wherein the step (iii) further comprises iteratively performing local optimization and hyperquadric sampling in the reduced base.

18. A system for determining uncertainty in high-dimensional data space, comprising:

a data source for storing digital observed data;

a computer system communicatively coupled to the data source to receive the digital observed data, the computer system including a memory device for storing computer readable program code and a processor in communication with the memory device, the processor being operative with the computer readable program code to;

(i) receive the digital observed data and at least one input model parameter set serving as a solution candidate of an inverse problem, wherein the input model parameter set is related to the digital observed data via a model;

(ii) determine, based on the input model parameter set, a reduced base associated with a set of coefficients that represents coordinates of any model parameter set in the reduced base, wherein the coefficients in the reduced base are fewer than model parameters in the input model parameter set;

(iii) sample within the reduced base to generate an output model parameter set in the reduced base, wherein the output model parameter set is compatible with the input model parameter set and fits the digital observed data, via the model, within a predetermined threshold; and

(iv) generate one or more uncertainty measures based on the output model parameter set.

19. The system of claim 18 wherein the data source comprises a data acquisition system operable to digitize observations of a physical system.

20. The system of claim 18 wherein the digital observed data comprises geophysical data, historical production data, pressure data, meteorological data, electrophysiological data, biomedical data or financial data.