Systems and Methods Employing Cooperative Optimization-Based Dimensionality Reduction

• US 20100040281A1
• Filed: 08/12/2008
• Published: 02/18/2010
• Est. Priority Date: 08/12/2008
• Status: Active Grant

• Current Assignee: Halliburton Energy Services Incorporated (Halliburton Company)
• Original Assignee: Halliburton Energy Services Incorporated (Halliburton Company)
• Inventors: CHEN, Dingding, DIX, Michael C., HAMID, Syed
• Granted Patent: US 9,514,388 B2
• Time in Patent Office: Days
• US Class Current: 382/156
• CPC Class Codes: E21B 47/12 Means for transmitting measuring-signals or control signals from the well to the surface, or from the surface to the well, e.g. for logging while drilling
• CPC Class Codes: E21B 49/08 Obtaining fluid samples or testing fluids, in boreholes or wells
• CPC Class Codes: E21B 49/0875 determining specific fluid parameters
• CPC Class Codes: G06F 18/2111 by using evolutionary computational techniques, e.g. genetic algorithms
• CPC Class Codes: G06F 18/21355 nonlinear criteria, e.g. embedding a manifold in a Euclidean space
• CPC Class Codes: G06F 2218/00 Aspects of pattern recognition specially adapted for signal processing
• CPC Class Codes: G06N 3/006 based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
• CPC Class Codes: G06N 3/045 Combinations of networks
• CPC Class Codes: G06N 3/08 Learning methods
• CPC Class Codes: G06N 3/086 using evolutionary algorithms, e.g. genetic algorithms or genetic programming

Abstract

Dimensionality reduction systems and methods facilitate visualization, understanding, and interpretation of high-dimensionality data sets, so long as the essential information of the data set is preserved during the dimensionality reduction process. In some of the disclosed embodiments, dimensionality reduction is accomplished using clustering, evolutionary computation of low-dimensionality coordinates for cluster kernels, particle swarm optimization of kernel positions, and training of neural networks based on the kernel mapping. The fitness function chosen for the evolutionary computation and particle swarm optimization is designed to preserve kernel distances and any other information deemed useful to the current application of the disclosed techniques, such as linear correlation with a variable that is to be predicted from future measurements. Various error measures are suitable and can be used.

Claims

1. A visualization method that comprises:

obtaining a data set having a dimensionality that is to be reduced;

identifying kernels that represent clusters within the data set;

representing low-dimensionality coordinates of each kernel as a corresponding gene on a chromosome in a population of such chromosomes;

subjecting said population to evolutionary computation to select a dimensionality reduction mapping; and

displaying the kernels at locations based on their low-dimensionality coordinates as determined from the selected dimensionality reduction mapping.

2. The visualization method of claim 1, further comprising:

refining the dimensionality reduction mapping using a particle swarm optimization search.

3. The visualization method of claim 1, further comprising:

training a neural network to map kernels to low-dimensionality coordinates derived from the selected dimensionality reduction mapping;

applying the neural network to members of the data set to determine corresponding low-dimensionality coordinates; and

displaying the members at locations based on their corresponding low-dimensionality coordinates.

4. The visualization method of claim 3, wherein the neural network is an ensemble of diverse neural networks that have been individually trained.

5. The visualization method of claim 1, wherein the evolutionary computation employs a multi-objective fitness function with a measure of kernel pair distance error and a measure of linear correlation with a prediction variable.

6. The visualization method of claim 5, wherein the evolutionary computation employs a fitness function that de-emphasizes effects of distance error for larger distances.

7. The visualization method of claim 1, wherein the evolutionary computation employs a fitness function that includes a measure of linear correlation between distances in the original data set and distances in a reduced-dimension data set.

8. The visualization method of claim 1, wherein the evolutionary computation employs conditional evolution to escape local minima in the fitness function.

9. The visualization method of claim 1, wherein the data set includes elemental compositions of rock samples.

10. The visualization method of claim 1, wherein the data set includes oxide measurements from sedimentary rock samples.

11. The visualization method of claim 1, wherein the data set includes one or more well logs obtained from different logging tools.

12. The visualization method of claim 1, wherein the data set includes collective flow properties of reservoir rock samples.

13. A visualization method that comprises:

obtaining a data set having a dimensionality that is to be reduced;

representing low-dimensionality coordinates of data set members as corresponding genes in a population of chromosomes;

subjecting said population to evolutionary computation to select a dimensionality reduction mapping; and

displaying the data set members at locations based on their low-dimensionality coordinates as determined from the selected dimensionality reduction mapping.

14. The visualization method of claim 13, further comprising:

refining the selected dimensionality reduction mapping using a particle swarm optimization search.

15. The visualization method of claim 14, further comprising:

training a neural network to map data set members to low-dimensionality coordinates given by the refined dimensionality reduction mapping;

applying the neural network to new data points to determine corresponding low-dimensionality coordinates; and

displaying the data points at locations based on their corresponding low-dimensionality coordinates.

16. The visualization method of claim 15, wherein the neural network is an ensemble of diverse neural networks that have been individually trained.

17. The visualization method of claim 13, wherein the evolutionary computation employs a multi-objective fitness function with a measure of kernel pair distance error and a measure of linear correlation with a prediction variable.

18. The visualization method of claim 13, wherein the evolutionary computation employs a fitness function that includes a measure of linear correlation between distances in the original data set and distances in a reduced-dimension data set.

19. A substance fingerprinting method that comprises:

performing a compositional analysis on a sample of a substance;

applying a dimensionality reduction transform to results of the compositional analysis to obtain a low-dimensionality representation;

using the low-dimensionality representation to match the sample with one or more closely-related substances in a data set; and

identifying one or more characteristics of the sample based on properties of the closely-related substances.

20. The method of claim 19, further comprising deriving the dimensionality reduction transform from the data set, wherein said deriving includes:

identifying kernels that represent clusters within the data set;

applying evolutionary computation to directly-encoded low-dimensionality coordinates for the kernels to select a bit-restricted initial encoding;

refining the initial encoding using a local search technique that is not bit-restricted; and

training at least one neural network to implement the dimensionality reduction transform based on the refined encoding.

21. The method of claim 20, wherein the local search technique employs particle swarm optimization.

22. The method of claim 20, wherein the substance is sedimentary rock, and wherein said one or more characteristics include one or more of the following:

lithology;

sedimentary facies in terms of original depositional environment;

reservoir quality; and

aquifer quality.

23. The method of claim 20, wherein the substance is igneous rock, and wherein said one or more characteristics include one or more of the following:

lithology;

source volcano(s) of a volcanic ash bed included in the igneous rock;

source location of volcanic lava from which the igneous rock originated;

tectonic setting in which magma making up the igneous rock was generated;

degree of fractional crystallization undergone by magma during its emplacement and cooling to form the igneous rock;

degree of contamination added by surrounding rock to magma making up the igneous rock.

24. The method of claim 20, wherein identifying one or more characteristics includes identifying a source and distribution of the substance.

25. The method of claim 24, wherein the substance is in the set consisting of hydrocarbons, kerogens, bitumens, water, water pollutants, and soil pollutants.

26. A well-telemetry method that comprises:

applying evolutionary computation to logging data to obtain a low-dimensionality encoding solution;

training a neural network ensemble with the solution;

configuring a downhole processor to apply the neural network ensemble to logging data to obtain reduced-dimension telemetry data for transmission uphole.

27. The method of claim 26, wherein the evolutionary computation employs a multi-objective fitness function with a measure of kernel pair distance error and a measure of linear correlation with a prediction variable.

28. The method of claim 26, wherein the low-dimensionality encoding solution is refined by particle swarm optimization.

29. The method of claim 26, further comprising:

generating predictions of one or more formation properties based on the telemetry data; and

displaying the telemetry data and predictions to a user.

30. A system employing dimensionality reduction, the system comprising:

a memory having software;

an output device; and

a processor coupled to the memory to execute the software, wherein the software configures the processor to;

obtain a high-dimensionality data set;

determine a low-dimensionality representation of the data set using evolutionary computation with particle swarm optimization; and

output results to a user based on the low-dimensionality representation.

31. The system of claim 30, wherein the software further configures the processor to train a neural network ensemble to implement a map from a data space of the high-dimensionality data set to a reduced-dimensionality data space.

32. The system of claim 30, wherein as part of determining the low-dimensionality representation, the software configures the processor to determine clusters in the data set, and wherein the evolutionary computation is applied only to representatives of the clusters.

33. The system of claim 30, wherein the software configures the processor to carry out the evolutionary computation with at least eight bits of resolution in each dimension of the low-dimensionality data space, and wherein positions within the low-dimensionality data space are expressed using Gray coding.

34. The system of claim 30, wherein the software enables the particle swarm optimization to expand the bounds of the low-dimensionality data space.