System and method for partitioning chemometric analysis

1. A computer-implemented method for identifying an unknown material, the method comprising, by a processor:

providing a vector space comprising a plurality of known vectors representing a plurality of spectra of known materials;

partitioning the vector space into a plurality of subspaces according to a degree of partitioning determined based on a density of the plurality of known vectors, the plurality of subspaces comprising at least one of the plurality of known vectors, wherein partitioning the vector space comprises:

determining a ratio of known vectors occupying each of a first plurality of partitioned subspaces as a percentage of a total number of known vectors, and

further subdividing the vector space into a second plurality of partitioned subspaces if the ratio exceeds a threshold;

accessing a spectrum of the unknown material;

reducing the spectrum to generate a target vector;

mapping the target vector into one of the first or second plurality of subspaces;

searching the subspace into which the target vector is mapped to determine a correlation between the target vector and each of the plurality of known vectors in the subspace; and

identifying the unknown material based on the correlation.

2. The method of claim 1 , further comprising: repeating the searching and the identifying at least once.

3. A computer-implemented method for conducting a spectral library search to identify an unknown compound comprising, by a processor:

accessing at least one spectrum of the unknown compound;

representing the at least one spectrum as a target vector;

providing an n-dimensional space having a plurality of partitioned subspaces representing a plurality of known vectors of known materials, each of the plurality of partitioned subspaces comprising at least one of the plurality of known vectors, the n-dimensional space being partitioned according to a degree of partitioning determined based on a density of the plurality of known vectors, wherein providing the n-dimensional space comprises:

determining a ratio of known vectors occupying each of the first plurality of partitioned subspaces as a percentage of a total number of known vectors, and

further subdividing the n-dimensional space into a second plurality of partitioned subspaces if the ratio exceeds a threshold;

mapping each target vector to one of the first or second plurality of the partitioned subspaces to form a mapped partitioned subspace;

identifying one or more known vectors which approximate the target vector; and

identifying the unknown compound by searching within the mapped partitioned subspace to identify a known vector which is a closest approximation to the target vector.

4. The method of claim 3 , wherein the target vector is generated through principal component analysis.

5. The method of claim 3 , wherein providing the n-dimensional space further comprises:

configuring the n-dimensional space to have the plurality of known vectors in n-dimensions;

finding a minimum point and a maximum point for each coordinate axes of the n-dimensional space; and

dividing each of the coordinate axes of the n-dimensional space by a positive integer M to provide the first plurality of partitioned subspaces, wherein at least one of the first plurality of partitioned subspaces comprises a known vector.

6. The method of claim 5 , further comprising finding a minimum point and a maximum point for each of the plurality of known vectors.

7. The method of claim 3 , wherein the threshold is selected algorithmically.

8. The method of claim 3 , wherein the threshold is in the range of 5-90%.

9. The method of claim 3 , wherein mapping the target vector further comprises:

representing each target data point as a data point target vector; and

identifying each of the plurality of partitioned subspaces where the data point target vector resides.

10. The method of claim 3 , wherein the at least one spectrum is a function of at least one of intensity, wavelength, wave number, frequency, and combinations thereof.

11. A system for identifying the composition of an unknown material comprising:

a processor in operable communication with a spectroscopic device configured to acquire at least one spectrum of the unknown material; and

a non-transitory, computer-readable storage medium in operable communication with the processor, wherein the computer-readable storage medium contains one or more programming instructions that, when executed, cause the processor to:

receive the at least one spectrum,

represent the at least one spectrum as a target vector,

provide a plurality of partitioned subspaces representing a plurality of known vectors of known materials, each of the plurality of partitioned subspaces comprising at least one of the plurality of known vectors, the plurality of partitioned subspaces being partitioned according to a degree of partitioning determined based on a density of the plurality of known vectors, wherein providing the plurality of partitioned subspaces comprises:

determining a ratio of known vectors occupying each of a first plurality of partitioned subspaces as a percentage of a total number of known vectors, and

further subdividing the n-dimensional space into a second plurality of partitioned subspaces if the ratio exceeds a threshold,

map the target vector to one of the first or second plurality of partitioned subspaces to form a mapped partitioned subspace, search within the mapped partitioned subspace to identify one or more known vectors which approximate the target vector, and

identify the unknown material by selecting a known vector which provides a closest approximation to the target vector.

12. The system of claim 11 , wherein the target vector defines a set of points in the at least one spectrum.

13. The system of claim 11 , wherein the target vector is generated through principal component analysis.

14. The system of claim 11 , wherein providing a plurality of partitioned subspaces further comprises:

providing an n-dimensional space having the plurality of known vectors in n-dimensions;

finding a minimum point and a maximum point for each coordinate axes of the n-dimensions; and

dividing each of the coordinate axes by a positive integer M to provide the first plurality of partitioned subspaces, wherein at least one of the first plurality of partitioned subspaces comprises at least one of the plurality of known vectors.

15. The system of claim 11 , wherein the threshold is selected algorithmically.

16. The system of claim 11 , wherein the threshold is in the range of 5-90%.

17. The system of claim 11 , wherein mapping the target vector further comprises representing each target data point as a data point target vector and identifying each of the plurality of partitioned subspaces where the data point target vector resides.

18. The system of claim 11 , wherein the at least one spectrum is a function of at least one of intensity, wavelength, wave number, frequency, and combinations thereof.

19. An apparatus for conducting a spectral library search to identify an unknown material comprising:

a spectroscopic device configured to acquire at least one spectrum of the unknown material;

a processor in operable communication with the spectroscopic device; and

a non-transitory, computer-readable storage medium in operable communication with the processor, wherein the computer-readable storage medium contains one or more programming instructions that, when executed, cause the processor to:

receive the at least one spectrum,

represent the at least one spectrum as at least one target vector,

provide an n-dimensional space with a plurality of partitioned subspaces representing a plurality of known vectors of known materials, each of the plurality of partitioned subspaces comprising at least one of the plurality of known vectors, the n-dimensional space being partitioned according to a degree of partitioning determined based on a density of the plurality of known vectors, wherein providing an n-dimensional space comprises:

determining a ratio of known vectors occupying each of a first plurality of partitioned subspaces as a percentage of a total number of known vectors, and

further subdividing the n-dimensional space into a second plurality of partitioned subspaces if the ratio exceeds a threshold,

mapping the at least one target vector to one of the first or second plurality of the partitioned subspaces to form a mapped partitioned subspace,

identify one or more known vectors within the mapped partitioned subspace which approximate the target vector, and

identify the unknown material by searching the mapped partitioned subspace to identify a known vector that provides a closest approximation to the target vector.

20. The apparatus of claim 19 , wherein the target vector is generated through principal component analysis.

21. The apparatus of claim 19 , wherein providing the n-dimensional space comprises:

configuring the n-dimensional space to have the plurality of known vectors in n-dimensions;

finding a minimum point and a maximum point for each coordinate axes of the n-dimensional space; and

dividing each of the coordinate axes of the n-dimensional space by a positive integer M to provide the first plurality of partitioned subspaces, wherein at least one of the first plurality of partitioned subspaces comprises at least one of the known vectors.

22. The apparatus of claim 21 , further comprising finding the minimum point and the maximum point for each of the plurality of known vectors.

23. The apparatus of claim 19 , wherein the threshold is selected algorithmically.

24. The apparatus of claim 19 , wherein the threshold is in the range of 5-90%.

25. The apparatus of claim 19 , wherein mapping the at least one target vector to one of the plurality of partitioned subspaces further comprises representing each target data point as a data point target vector and identifying a partitioned subspace where the data point target vector resides.

26. The apparatus of claim 19 , wherein the at least one spectrum is a function of at least one of intensity, wavelength, wave number, frequency, and combinations thereof.

27. A computer-implemented method for identifying an unknown material, the method comprising, by a processor:

accessing at least one spectrum of the unknown material;

representing the at least one spectrum as a target vector;

providing a plurality of partitioned subspaces representing a plurality of known vectors of known materials, wherein at least one of said plurality of partitioned subspaces comprises at least one known vector representing a known material, wherein providing the plurality of partitioned subspaces comprises:

determining a ratio of known vectors occupying each of a first plurality of partitioned subspaces as a percentage of a total number of known vectors, and

further subdividing the n-dimensional space into a second plurality of partitioned subspaces if the ratio exceeds a threshold;

map the target vector to one of the first or second plurality of partitioned subspaces to form a mapped partitioned subspace;

identify at least one of the plurality of known vectors within the mapped partitioned subspace which approximates the target vector;

identify adjacent mapped partitioned subspaces having at least one vector approximating the target vector; and

calculate a correlation between the target vector and each of the plurality of known vectors in the plurality of partitioned subspaces and the adjacent mapped partitioned subspaces;

identify the unknown material based on the correlation.

28. The method of claim 27 , wherein the target vector defines a set of points in the at least one spectrum.

29. The method of claim 27 , wherein the target vector is generated through principal component analysis.

30. The method of claim 27 , wherein providing a plurality of partitioned subspaces further comprises:

providing an n-dimensional space having a plurality of known vectors in n-dimensions;

finding a minimum point and a maximum point of each coordinate axes of the n-dimensional space; and

dividing each of the coordinate axes of the n-dimensional data space by a positive integer M to provide the first plurality of partitioned subspaces, wherein at least one of the subspaces comprises at least one of the plurality of known vectors.

31. The method of claim 27 , wherein the threshold is selected algorithmically.

32. The method of claim 27 , wherein the threshold is in the range of 5-90%.

33. The method of claim 27 , wherein mapping the target vector further comprises representing each target data point as a data point target vector and identifying each of the plurality of partitioned subspaces where the data point target vector resides.

34. The method of claim 27 , wherein the at least one spectrum is a function of at least one of intensity, wavelength, wave number, frequency, and combinations thereof.

35. A system for identifying of an unknown material comprising;

a processor in operable communication with a spectroscopic device configured to acquire at least one spectrum of the unknown material;

a non-transitory, computer-readable storage medium in operable communication with the processor, wherein the computer-readable storage medium contains one or more programming instructions that, when executed, cause the processor to:

receive the at least one spectrum,

represent the at least one spectrum as a target vector,

provide a plurality of partitioned subspaces representing a plurality of known vectors of known materials, each of the plurality of partitioned subspaces comprising at least one of the plurality of known vectors, the plurality of partitioned subspaces being partitioned according to a degree of partitioning determined based on a density of the plurality of known vectors, wherein providing the plurality of partitioned subspaces comprises:

determining a ratio of known vectors occupying each of the first plurality of partitioned subspaces as a percentage of a total number of known vectors, and

further subdividing the n-dimensional space into a second plurality of subspaces if the ratio exceeds a threshold,

map the target vector to one of the first or second plurality of partitioned subspaces to form a mapped partitioned subspace,

search within the mapped partitioned subspace to identify one or more known vectors which approximate the target vector,

identify adjacent mapped partitioned subspaces having at least one vector approximating the target vector,

calculate a correlation between the target vector and each of the plurality of known vectors in the plurality of partitioned subspaces and the adjacent mapped partitioned subspaces, and

identifying the unknown material based on the correlation.

36. The system of claim 35 , wherein the target vector defines a set of points in the at least one spectrum.

37. The system of claim 35 , wherein the target vector is generated through principal components analysis.

38. The system of claim 35 , wherein providing a plurality of partitioned spaces further comprises:

providing an n-dimensional space having the plurality of known vectors in n-dimensions

finding a minimum point and a maximum point of each coordinate axes of the n-dimensional space; and

dividing each of the coordinate axes of the n-dimensional data space by a positive integer M to provide the first plurality of partitioned subspaces, wherein at least one of the subspaces comprises at least one of the plurality of known vectors.

39. The system of claim 35 , wherein the threshold is selected algorithmically.

40. The system of claim 35 , wherein the threshold is in the range of 5-90%.

41. The system of claim 35 , wherein mapping the target vector further comprises representing each target data point as a data pint target vector and identifying each of the plurality of partitioned subspaces where the data point target vector resides.

42. The system of claim 35 , wherein the at least one spectrum is a function of at least one of intensity, wavelength, wave number, frequency, and combinations thereof.