Techniques of generating input for a kernel-based machine learning system that uses a kernel to perform classification operations on data involve generating unbiased estimators for gaussian kernels according to a new framework called Structured Orthogonal Random Features (SORF). The unbiased estimator KSORF to the kernel involves a linear transformation matrix WSORF computed using products of a set of pairs of matrices, each pair including an orthogonal matrix and respective diagonal matrix whose elements are real numbers following a specified probability distribution. Typically, the orthogonal matrix is a Walsh-Hadamard matrix, the specified probability distribution is a Rademacher distribution, and there are at least two, usually three, pairs of matrices multiplied together to form the linear transformation matrix WSORF.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of generating input for a kernel-based machine learning system that uses a kernel to perform classification operations on data, comprising: generating, by processing circuitry of the kernel-based machine learning system, a set of diagonal matrices, each of the set of diagonal matrices having non-diagonal elements that are zero and diagonal elements that have values distributed according to a specified probability distribution function; producing, by the processing circuitry, a set of orthogonal matrices, each of the set of orthogonal matrices having mutually orthogonal rows; for each of the set of diagonal matrices, forming, by the processing circuitry, a set of matrix pairs, each of the set of matrix pairs including (i) that diagonal matrix, and (ii) a respective orthogonal matrix of the set of orthogonal matrices; and generating, by the processing circuitry, a product of each of the set of matrix pairs to produce a linear transformation matrix, the linear transformation matrix being an unbiased estimator of the kernel used by the kernel-based machine learning system. 2. The method as in claim 1, wherein generating the product of each of the set of matrix pairs includes, for each of the set of diagonal matrices, right-multiplying the respective orthogonal matrix by that diagonal matrix. 3. The method as in claim 1, wherein producing the set of orthogonal matrices includes generating, as the respective orthogonal matrix, a Walsh-Hadamard matrix having a size based on a specified dimension of the data. 4. The method as in claim 3, wherein generating the Walsh-Hadamard matrix includes forming the Walsh-Hadamard matrix having a dimension equal to the least power of two larger than the specified dimension of the data, and wherein the method further comprises multiplying the linear transformation matrix by a vector that represents a datum by (i) appending the vector with zeroes to produce a zero-padded vector having a length equal to the least power of two larger than the specified dimension of the data, (ii) performing an inner product calculation on each row of the linear transformation matrix and the zero-padded vector to produce an intermediate feature vector, and (iii) removing elements from an end of the intermediate feature vector to produce a final feature vector having a length equal to the specified dimension of the data. 5. The method as in claim 1, wherein each of the non-diagonal elements of each of the set of diagonal matrices is equal to one of 1 and −1. 6. The method as in claim 5, wherein the non-diagonal elements of each of the set of diagonal matrices are distributed according to a Rademacher distribution. 7. The method as in claim 1, wherein the set of diagonal matrices has at least two diagonal matrices. 8. A computer program product comprising a nontransitive storage medium, the computer program product including code that, when executed by processing circuitry of a sound rendering computer configured to generate input for a kernel-based machine learning system that uses a kernel to perform classification operations on data, causes the processing circuitry to perform a method, the method comprising: generating a set of diagonal matrices, each of the set of diagonal matrices having non-diagonal elements that are zero and diagonal elements that have values distributed according to a specified probability distribution function; producing a set of orthogonal matrices, each of the set of orthogonal matrices having mutually orthogonal rows; for each of the set of diagonal matrices, forming a set of matrix pairs, each of the set of matrix pairs including (i) that diagonal matrix, and (ii) a respective orthogonal matrix of the set of orthogonal matrices; and generating a product of each of the set of matrix pairs to produce a linear transformation matrix, the linear transformation matrix being an unbiased estimator of the kernel used by the kernel-based machine learning system. 9. The computer program product as in claim 8, wherein generating the product of each of the set of matrix pairs includes, for each of the set of diagonal matrices, right-multiplying the respective orthogonal matrix by that diagonal matrix. 10. The computer program product as in claim 8, wherein producing the set of orthogonal matrices includes generating, as the respective orthogonal matrix, a Walsh-Hadamard matrix having a size based on a specified dimension of the data. 11. The computer program product as in claim 10, wherein generating the Walsh-Hadamard matrix includes forming the Walsh-Hadamard matrix having a dimension equal to the least power of two larger than the specified dimension of the data, and wherein the method further comprises multiplying the linear transformation matrix by a vector that represents a datum by (i) appending the vector with zeroes to produce a zero-padded vector having a length equal to the least power of two larger than the specified dimension of the data, (ii) performing an inner product calculation on each row of the linear transformation matrix and the zero-padded vector to produce an intermediate feature vector, and (iii) removing elements from an end of the intermediate feature vector to produce a final feature vector having a length equal to the specified dimension of the data. 12. The computer program product as in claim 8, wherein each of the non-diagonal elements of each of the set of diagonal matrices is equal to one of 1 and −1. 13. The computer program product as in claim 12, wherein the non-diagonal elements of each of the set of diagonal matrices are distributed according to a Rademacher distribution. 14. The computer program product as in claim 8, wherein the set of diagonal matrices has at least two diagonal matrices. 15. An electronic apparatus configured to generate input for a kernel-based machine learning system that uses a kernel to perform classification operations on data, the electronic apparatus comprising: memory; and controlling circuitry coupled to the memory, the controlling circuitry being configured to: generate a set of diagonal matrices, each of the set of diagonal matrices having non-diagonal elements that are zero and diagonal elements that have values distributed according to a specified probability distribution function; produce a set of orthogonal matrices, each of the set of orthogonal matrices having mutually orthogonal rows; for each of the set of diagonal matrices, form a set of matrix pairs, each of the set of matrix pairs including (i) that diagonal matrix, and (ii) a respective orthogonal matrix of the set of orthogonal matrices; and generate a product of each of the set of matrix pairs to produce a linear transformation matrix, the linear transformation matrix being an unbiased estimator of the kernel used by the kernel-based machine learning system. 16. The electronic apparatus as in claim 15, wherein the controlling circuitry configured to generate the product of each of the set of matrix pairs is further configured to, for each of the set of diagonal matrices, right-multiply the respective orthogonal matrix by that diagonal matrix. 17. The electronic apparatus as in claim 15, wherein the controlling circuitry configured to produce the set of orthogonal matrices is further configured to generate, as the respective orthogonal matrix, a Walsh-Hadamard matrix having a size based on a specified dimension of the data. 18. The electronic apparatus as in claim 17, wherein the controlling circuitry configured to generate the Walsh-Hadamard matrix is further configured to form the Walsh-Hadamard matrix having a dimension equal to the least power of two larger than the specified dimension of the data, and wherein the controlling circuitry is further configured to multiply the linear transformation matrix by a vector that represents a datum by (i) appending the vector with zeroes to produce a zero-padded vector having a length equal to the least power of two larger than the specified dimension of the data, (ii) performing an inner product calculation on each row of the linear transformation matrix and the zero-padded vector to produce an intermediate feature vector, and (iii) removing elements from an end of the intermediate feature vector to produce a final feature vector having a length equal to the specified dimension of the data. 19. The electronic apparatus as in claim 15, wherein each of the non-diagonal elements of each of the set of diagonal matrices is equal to one of 1 and −1. 20. The electronic apparatus as in claim 19, wherein the non-diagonal elements of each of the set of diagonal matrices are distributed according to a Rademacher distribution.