Heuristic processor

Abstract

A heuristic processor incorporates a digital arithmetic unit arranged to compute the squared norm of each member of a training data set with respect to each member of a set of centers, and to transform the squared norms in accordance with a nonlinear function to produce training phi vectors. A systolic array arranged for QR decomposition and least mean squares processing forms combinations of the elements of each phi vector to provide a fit to corresponding training answers. The form of combination is then employed with like-transformed to provide estimates of unknown result. The processor is applicable to provide estimated results for problems which are nonlinear and for which explicit mathematical formalisms are unknown.

We claim:  
     
       1. An heuristic processor comprised of: 
       (1) non-linear transforming means for producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non-linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,  
       (2) processing means for combining training  φ  vector elements in a manner producing a training fit to a set of training answers, and  
       (3) means for generating result estimate values, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit  
       wherein the transforming means is a digital arithmetic unit computing differences between training data vector elements and corresponding center vector elements and for summing the squares of such differences associated with each data vector-center vector pair, and for converting each sum to a value in accordance with the non-linear transformation and for providing a respective training  φ  vector element, wherein the processing means is a systolic array of processing cells for implementing a rotation algorithm to provide QR decomposition of a Φ matrix  φ  vector rows and least squares fitting to the training answer set, the algorithm involving computation and application of rotation parameters and storage of updated decomposition matrix elements by the processing cells, and wherein the systolic array has a first row of processing cells arranged to receive  φ  vectors extended by training answers, each first row cell being arranged for input of a respective element of each extended vector.  
     
     
       2. A processor according to claim  1  wherein the processing cells are boundary and internal cells connected to form rows and columns of the systolic array and: 
       (1) each row begins with a boundary cell and continues with at least one internal cells which diminish in number down the array by one per row,  
       (2) the first array row contains a number of boundary and internal cells equal to the number of elements in an extended vector,  
       (3) the columns comprise a first column containing a boundary cell only, subsequent columns containing a respective boundary cell surmounted by numbers of internal cells increasing from one by one per column, and at least one outer column of internal cells arranged to receive training answer input,  
       (4) the boundary and internal cells are arranged to compute rotation parameters from input values and apply them to input values respectively, and to store respective updated decomposition matrix elements for use in such computation, and  
       (5) the cells have row and column nearest neighbour connections providing for rotation parameters to pass along rows and rotated values to pass down columns.  
     
     
       3. A processor according to claim  2  further including a multiplier cell (M) for multiplying cumulatively rotated values output from an outer column of internal cells by cumulatively multiplied and relatively delayed parameters generated by boundary cells in appropriate form for computing least squares residuals arising between combined elements of training data  φ  vectors and their respective training answers. 
     
     
       4. A processor according to claim  1 , wherein the means for generating result estimates values includes means for switching the systolic array to a test mode of operation in which decomposition matrix element update and training answer input are suppressed. 
     
     
       5. An heuristic processor comprised of: 
       (1) non-linear transforming means for producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non-linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,  
       (2) processing means for combining training  φ  vector elements in a manner producing a training fit to a set of training answers, and  
       (3) means for generating result estimate values, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit, wherein the heuristic processor consists at least partly of processing devices linked by connecting means incorporating clocked latches for data storage and propagation.  
     
     
       6. An heuristic processor comprised of: 
       (1) non-linear transforming means for producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non-linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,  
       (2) processing means for combining training  φ  vector elements in a manner producing a training fit to a set of training answers, said processing means consisting at least partly of programmed transputers interconnected together by single-bit data links and for performing calculation operations in parallel with one another, and  
       (3) means for generating result estimate values, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.  
     
     
       7. An heuristic processor comprised of: 
       (1) non-linear transforming means for producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non-linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,  
       (2) an electronically addressable memory incorporated in the transforming means, the memory “receiving” addresses in fixed point arithmetic format and “providing” output in floating point arithmetic format in the course of producing each said training  φ  vector in floating point format,  
       (3) processing means for combining training  φ  vector elements in a manner producing a training fit to a set of training answers, and  
       (4) means for generating result estimate values, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.  
     
     
       8. An heuristic processor comprised of: 
       (1) non-linear transforming means for producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non-linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,  
       (2) processing means for combining training  φ  vector elements in a manner producing a training fit to a set of training answers,  
       (3) means for generating result estimate values, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit, wherein the non-linear transforming means, the processing means and the means for generating result estimate values are interlinked by multibit buses and single-bit lines for data transmission purposes.  
     
     
       9. An heuristic processor comprised of: 
       (1) non-linear transforming means for producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non-linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,  
       (2) an electronically addressable memory incorporated in the transforming means, the memory being for “receiving” addresses in fixed point arithmetic format and “providing” output in floating point arithmetic format in the course of producing each said training  φ  vector in floating point format, said output in each case being a non-linear transformation of the respective address value,  
       (3) processing means for combining training  φ  vector elements in a manner producing a training fit to a set of training answers, and  
       (4) means for generating result estimate values, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.  
     
     
       10. An heuristic processor comprised of: 
       (   1   )  a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,    
       (   2   )  a combining processor combining training  φ  vector elements in a manner producing a training fit to a set of training answers, and    
       (   3   )  a result estimate value generator generating estimate values, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit, wherein the heuristic processor consists at least partly of processing devices linked by connectors incorporating clocked latches for data storage and propagation.   
     
     
       11. An heuristic processor comprised of: 
         a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,    
       
         electronically addressable memories incorporated in the transformation device, the memories “receiving” addresses in fixed point arithmetic format and “providing” output in floating point arithmetic format in the course of producing said elements of training  φ  vectors in floating point format, and  
       
       
         a combining processor combining training  φ  vector elements in a manner producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated,  
       
       
         each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       12. An heuristic processor comprised of: 
       (   1   )  a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,    
       (   2   )  a combining processor combining training  φ  vector elements in a manner producing a training fit to a set of training answers, and    
       (   3   )  a result estimate value generator generating estimate values, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit,    
         wherein the transformation device, the combining processor and the result estimate value generator are interlinked by multibit buses and single - bit lines for data transmission purposes.   
     
     
       13. An heuristic processor comprised of: 
         a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member form a respective center set member,    
         electronically addressable memories incorporated in the transformation device, the memories “receiving” addresses in fixed point arithmetic format and “providing” output in floating point arithmetic format in the course of producing said elements of training  φ  vectors in floating point format, said output in each case being a non - linear transformation of the respective address value,    
       
         a combining processor combining training  φ  vector elements in a manner producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated,  
       
       
         each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       14. An heuristic processor comprised of: 
         a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced,    
       
         a processor which weights and combines training  φ  vector elements and produces a training fit to a set of training answers, and  
       
         a result estimate value generator generating estimate values and producing a respective test  φ  vector from each ember of a set of test data, each test data set member having a displacement from each of said centers, where a norm of said test data set member displacement is calculable from each test data set member displacement and each element of a test  φ  vector consisting of said non - linear transformation of said norm of said test data set member displacement, each of said estimate values consisting of a combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.   
     
     
       15. A processor according to claim  14 , wherein the transformation device computes differences between training data vector elements and corresponding center elements, sums the squares of such differences associated with each center- data vector pair, converts each sum to a value in accordance with the non - linear transformation and provides a respective training  φ  vector element.   
     
     
       16. An heuristic processor comprised of: 
         a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced,    
       
         a processor which weights and combines training  φ  vector elements and produces a training fit to a set of training answers, and  
       
         a result estimate value generator generating estimate values and producing a respective test  φ  vector from each member of a set of test data, each test data set member having a displacement from each of said centers, where a norm of said test data set member displacement is calculable from each test data set member displacement and each element of a test  φ  vector consisting of said non - linear transformation of said norm of said test data set member displacement, each of said estimate values consisting of a combination of the elements of a respective test  φ  vector and each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit, wherein said processor comprises programmed processing devices for performing calculation operations in parallel with one another.   
     
     
       17. An heuristic processor comprised of: 
         a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced,    
       
         a processor which weights and combines training  φ  vector elements and produces a training fit to a set of training answers, wherein said processor comprises a digital electronic processor for performing calculations in floating point arithmetic, and  
       
         a result estimate value generator generating estimate values and producing a respective test  φ  vector from each member of a set of test data, each test data set member having a displacement from each of said centers, where a norm of said test data set member displacement is calculable from each test data set member displacement and each element of a test  φ  vector consisting of said non - linear transformation of said norm of said test data set member displacement, each of said estimate values consisting of a combination of the elements of a respective test  φ  vector and each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.   
     
     
       18. An heuristic processor comprised of: 
         a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced,    
       
         a processor which weights and combines training  φ  vector elements and produces a training fit to a set of training answers, and  
       
         a result estimate value generator generating estimate values and producing a respective test  φ  vector from each member of a set of test data, each test data set member having a displacement from each of said centers, where a norm of said test data set member displacement is calculable from each test data set member displacement and each element of a test  φ  vector consisting of said non - linear transformation of said norm of said test data set member displacement, each of said estimate values consisting of a combination of the elements of a respective test  φ  vector and each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.   
     
     
       19. An heuristic processor comprised of: 
         a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced,    
       
         a processor which weights and combines training  φ  vector elements and produces a training fit to a set of training answers, and  
       
         a result estimate value generator generating estimate values and producing a respective test  φ  vector from each member of a set of test data, each test data set member having a displacement from each of said centers, where a norm of said test data set member displacement is calculable from each test data set member displacement and each element of a test  φ  vector consisting of said non - linear transformation of said norm of said test data set member displacement, each of said estimate values consisting of a combination of the elements of a respective test  φ  vector and each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit, wherein the transformation device and the processor incorporate digital electronic signal processing devices controlled by clock signals.   
     
     
       20. An heuristic processor comprised of: 
         a non - linear transformation device producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced,    
       
         a processor which weights and combines training  φ  vector elements and produces a training fit to a set of training answers and comprises digital electronic signal processing devices for storing processing results for output after a delay, and  
       
         a result estimate value generator generating estimate values and producing a respective test  φ  vector from each member of a set of test data, each test data set member having a displacement from each of said centers, where a norm of said test data set member displacement is calculable from each test data set member displacement and each element of a test  φ  vector consisting of said non - linear transformation of said norm of said test data set member displacement, each of said estimate values consisting of a combination of the elements of a respective test  φ  vector and each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.   
     
     
       21. A method of training an heuristic processor, wherein the heuristic processor consists at least partly of processing devices linked by connectors incorporating clocked latches for data storage and propagation, said method comprising the steps of: 
       (   1   )  producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member, and    
       (   2   )  combining training  φ  vector elements in a manner producing a training fit to a set of training answers,    
       
         each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       22. A method of training an heuristic processor, said method comprising the steps of: 
       (   1   )  producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member said non - linear transformation being implemented with the aid of electronically addressable memories responsive to an input address in fixed point arithmetic format by providing output of a  φ  vector element as a transformation of that address in floating point format, and    
       (   2   )  combining training  φ  vector elements in a manner producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.   
     
     
       23. A method of training of heuristic processor, said processor including a non- linear transformation device, a combining processor and a result estimate value generator are interlinked by multibit buses and single - bit lines for data transmission purposes, said method comprising the steps of:    
       (   1   )  producing, in said non - linear transformation device, a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member, and    
       (   2   )  combining, in said combining processor, training  φ  vector elements in a manner producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit.   
     
     
       24. A method of training an heuristic processor, said method comprising the steps of: 
         producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member, said non - linear transformation being implemented with the aid of memory means which, when supplied with an input address in fixed point arithmetic format, provides output of an element of each said training  φ  vector as a transformation of that address in floating point format, and    
       
         combining training  φ  vector elements in a manner producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       25. A method of training an heuristic processor, said method comprising the steps of: 
         producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced, said non - linear transformation being implemented with the aid of memory means which, when supplied with an input address in fixed point arithmetic format, provides output of an element of each said training  φ  vector as a transformation of that address in floating point format, and    
       
         weighting and combining training  φ  vector elements and producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       26. A method of training an heuristic processor, according to claim  25 , wherein said first producing step includes the steps of: 
       
         computing differences between training vector elements and corresponding center elements;  
       
         summing the squares of such differences associated with each center - data vector pair;    
         converting each sum to a value in accordance with the non - linear transformation and    
       
         providing a respective training  φ  vector element. 
       
     
     
       27. A method of training an heuristic processor, wherein said processor comprises a programmed processing device for performing calculation operations in parallel with one another, said method comprising the steps of: 
         producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced, and    
       
         weighting and combining training  φ  vector elements and producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       28. A method of training an heuristic processor, wherein said processor comprises a digital electronic processor for performing calculations in floating point arithmetic, said method comprising the steps of: 
         producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced, and    
       
         weighting and combining training  φ  vector elements and producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, and each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       29. A method of training an heuristic processor, said method comprising the steps of: 
         producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced, and    
       
         weighting and combining training  φ  vector elements and producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, and each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       30. A method of training an heuristic processor, said processor including a non- linear transformation device and said processor and transformation device incorporate digital electronic signal processing devices controlled by clock signals, said method comprising the steps of:    
         producing, in said non - linear transformation device, a respective training  φ  vector form each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced, and    
       
         weighting and combining training  φ  vector elements and producing a training fit to a set of training answers in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, and each said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       31. A method of training an heuristic processor, said method comprising the steps of: 
         producing a respective training  φ  vector from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each displacement, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from which said training  φ  vector is produced, and    
       
         weighting and combining training  φ  vector elements and producing a training fit to a set of training answers in a digital electronic signal processing device for storing processing results for output after a delay in a form suitable for enabling result estimate values to be generated, each of said estimate values consisting of a combination of the elements of a respective  φ  vector produced from test data, and each of said combination being at least equivalent to a summation of vector elements weighted in accordance with the training fit. 
       
     
     
       32. A method of estimating results using an electronic processing device, the device including a means for the non- linear transformation of data, for combining elements of transformed data, and for weighting data, said method comprising arranging said electronic device to execute the steps of:    
       (   1   )  producing training  φ  vectors from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,    
       (   2   )  combining training  φ  vector elements in a manner producing a training fit to a set of training answers, and    
       (   3   )  generating result estimate values, each of said estimate values comprising a combination of weighted elements of a respective  φ  vector produced from test data, said weighting in accordance with the training fit.   
     
     
       33. A method of estimating results using first and second electronic processing devices, said first electronic processing device including a means for the non- linear transformation of data and for combining elements of transformed data, and said second electronic processing device including means for producing weighted combinations of vector elements, said method comprising arranging said first electronic processing device to execute the steps of:    
       (   1   )  producing training  φ  vectors from each member of a training data set on the basis of a set of centers, each training data set member having a displacement from each of said centers, where a norm of the displacement is calculable from each of said displacements, and each element of a  φ  vector consisting of a non - linear transformation of the norm of the displacement of the associated training data set member from a respective center set member,    
       (   2   )  combining training  φ  vector elements in a manner producing a training fit to a set of training answers, and    
       
         said second electronic processing device generating result estimate values, each of said estimate values comprising a combination of weighted elements of a respective  φ  vector produced from test data, said weighting in accordance with the training fit produced by said first electronic processing device.