Apparatus, system, and method for interpolating high-dimensional, non-linear data

1. A system to interpolate data, the system comprising:

a processor;

a source data set; and

a computation module comprising

a cluster module configured to locate a plurality of data clusters within the source data set using a center selection/clustering algorithm, each data cluster comprising a center and a radius wherein each data cluster maximizes the increment to the variance between the elements of the data cluster and the data cluster and avoids numerical ill-conditioning problems for the elements of the source data set encompassed by the data cluster and minimizes the number of data clusters;

a conversion selection module configured to select a conversion function for converting each data cluster;

a norm selection module configured to select a norm function for each data cluster;

an interpolation module configured to convert each data cluster to generate converted data clusters based on the selected conversion function and the selected norm function;

a cross validation module configured to cross validate among the converted data clusters and to optimize the converted data clusters in each of a plurality of iterations, wherein the cross validation module optimizes the converted data clusters by directing at least one of: the cluster module to relocate the plurality of data clusters, the conversion selection module to select another conversion function, and the norm selection module to select another norm function, wherein one or more of the modules of the computation module includes software instructions that are executed by the processor; and

a combination module configured to combine the converted data clusters.

2. The system of claim 1 , further comprising a weight module configured to determine a weight for each data cluster of each conversion function.

3. The system of claim 1 , further comprising a drift module configured to adjust a conversion parameter to compensate for device drift.

4. The system of claim 1 , wherein the data set comprises color space data and the interpolation module converts the color space data to color data for a specified printer.

5. A machine-readable storage medium that stores a program of machine-readable instructions executable by a digital processing apparatus to perform operations to interpolate data, the operations comprising:

locating a plurality of data clusters within a source data set using a center selection/clustering algorithm, each data cluster comprising a center and a radius wherein each data cluster maximizes the increment to the variance between the elements of the data cluster and the data cluster; and avoids numerical ill-conditioning problems for the elements of the source data set encompassed by the data cluster and minimizes the number of centers for the data set;

selecting a conversion function for converting each data cluster;

selecting a norm function for each data cluster;

converting each data cluster to generate converted data clusters based on the selected conversion function and the selected norm function;

cross validating among the converted data clusters and optimizing the converted data clusters in each of a plurality of iterations, wherein optimizing the converted data clusters comprises performing at least one of relocating the plurality of data clusters, selecting another conversion function, and selecting another norm function; and

combining the converted data clusters.

6. The machine-readable medium of claim 5 , wherein the instructions further comprise an operation to determine a weight for each data cluster of each conversion function.

7. The machine-readable medium of claim 5 , wherein the instructions further comprise an operation to adjust a conversion parameter to compensate for device drift.

8. The machine-readable medium of claim 5 , wherein the data set comprises color space data and the instructions further comprise an operation to convert the color space data to color data for a specified printer.

9. The machine-readable medium of claim 5 , wherein the center selection/clustering algorithm is selected from orthogonal least squares, K-mean, and non-linear optimization algorithms.

10. The machine-readable medium of claim 5 , wherein the conversion function selected from Gaussian, linear, cubic, thin plate spline, multiquadric, and inverse multiquadric functions and the norm function is an L-p norm function.

11. A method for deploying computer infrastructure, comprising integrating computer-readable code into a computing system, wherein the code in combination with the computing system is capable of performing the following:

locating a plurality of data clusters within a source data set using a center selection/clustering algorithm, each data cluster comprising a center and a radius wherein each data cluster maximizes the increment to the variance between the elements of the data cluster and the data cluster;

and avoids numerical ill-conditioning problems for the elements of the source data set encompassed by the data cluster and minimizes the number of centers for the data set;

selecting a conversion function for converting each data cluster;

selecting a norm function for each data cluster;

converting each data cluster to generate converted data clusters based on the selected conversion function and the selected norm function;

cross validating among the converted data clusters and optimizing the converted data clusters in each of a plurality of iterations, wherein optimizing the converted data clusters comprises performing at least one of relocating the plurality of data clusters, selecting another conversion function, and selecting another norm function; and

combining the converted data clusters.

12. The method of claim 11 , further comprising determining a weight for each data cluster of each conversion function.

13. The method of claim 11 , further comprising adjusting a conversion parameter to compensate for device drift.

14. The method of claim 11 , wherein the data set comprises color space data and method further comprises converting the color space data to color data for a specified printer.