Systems and methods employing cooperative optimization-based dimensionality reduction
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.
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;
generating a population of chromosomes having encoded low-dimensionality coordinates for each of the kernels;
subjecting said population of chromosomes to evolutionary computation to generate new chromosomes and corresponding low-dimensionality coordinates for the kernels based on a fitness function until a threshold fitness level or predetermined number of iterations is reached, wherein the new chromosomes are used 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 fitness function is 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 1 , wherein the fitness function de-emphasizes effects of distance error for larger distances.
7. The visualization method of claim 1 , wherein the fitness function 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. The visualization method of claim 1 , further comprising transmitting telemetry information from downhole to earth's surface, wherein the telemetry information is selected based on the dimensionality reduction mapping.
14. The visualization method of claim 13 , further comprising steering a drillstring based on the telemetry information.
15. A visualization method that comprises:
obtaining a data set having a dimensionality that is to be reduced;
generating a population of chromosomes having encoded low-dimensionality coordinates for data set members;
subjecting said population of chromosomes to evolutionary computation to generate new chromosomes and corresponding low-dimensionality coordinates for data set members based on a fitness function until a threshold fitness level or predetermined number of iterations is reached, wherein the new chromosomes are used 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.
16. The visualization method of claim 15 , further comprising:
refining the selected dimensionality reduction mapping using a particle swarm optimization search.
17. The visualization method of claim 16 , 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.
18. The visualization method of claim 17 , wherein the neural network is an ensemble of diverse neural networks that have been individually trained.
19. The visualization method of claim 15 , wherein the fitness function is a multi-objective fitness function with a measure of kernel pair distance error and a measure of linear correlation with a prediction variable.
20. The visualization method of claim 15 , wherein the fitness function includes a measure of linear correlation between distances in the original data set and distances in a reduced-dimension data set.
21. 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;
generate a population of chromosomes having encoded low-dimensionality coordinates for data set members;
subject said population of chromosomes to evolutionary computation to generate new chromosomes and corresponding low-dimensionality coordinates for data set members based on a fitness function until a threshold fitness level or predetermines number of iterations is reached;
apply a particle swarm optimization to the new chromosomes to select a dimensionality reduction mapping;
determine a low-dimensionality representation of the data set using the selected dimensionality reduction mapping; and
output results to a user based on the low-dimensionality representation.
22. The system of claim 21 , 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.
23. The system of claim 21 , 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.
24. The system of claim 21 , 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.
25. The system of claim 21 , wherein the software enables the particle swarm optimization to operate with relaxed limits and higher resolution than the evolutionary computation.