Method for generating analyses of categorical data

• US 6,714,897 B2
• Filed: 01/02/2001
• Issued: 03/30/2004
• Est. Priority Date: 01/02/2001
• Status: Active Grant

• Current Assignee: Battelle Memorial Institute
• Original Assignee: Battelle Memorial Institute
• Inventors: Whitney, Paul D., Daly, Don S., Ferryman, Thomas A.
• Primary Examiner(s): Nghiem, Michael
• Assistant Examiner(s): LAU, TUNG S
• Application Number:
  US09/753,401
• Publication Number:
  US 20020123865A1
• Time in Patent Office: 1,183 Days
• Field of Search: 702/189, 345/440, 706/12, 706/60, 704/256, 367/73
• US Class Current: 702/189
• CPC Class Codes: G06F 17/17 Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method G06F17/18 takes precedence ; interpolation for numerical control G05B19/18

Abstract

According to the present invention, a conversion or representation of categorical data was created that allows a significant number of exploratory multivariate analysis methods to be brought to bear on categorical data. Whereas previously, each response to a question might have been modeled as an outcome from a multinomial probability distribution; according to the present invention each response is represented as an actual discrete probability distribution with all its mass in one cell. With this interpretation or conversion, the vector of measurements for each individual can be viewed as a member of the linear space that includes vectors of probability distributions.

Claims

1. A method of generating analyses of categorical data that will allow the application of exploratory multivariate analysis procedures constructed from inner products, distances, vector additions, and scalar multiplications to said categorical data having a plurality of responses, the method comprising the steps of:

a. encoding said categorical data to provide plurality of probability distribution representations,

b. transforming said exploratory multivariate analysis procedures based on inner products, distances, vector additions and scalar multiplications to work with said probability distribution representations, and

c. applying said transformed exploratory multivariate analysis procedures constructed from inner products, distances, vector additions, and scalar multiplications to said probability distribution representation of said categorical data to allow browsing, retrieving and viewing of said converted categorical data.

2. The method as recited in claim 1, further comprising labeling said categorical data as ordinal or nominal measurement.

3. The method as recited in claim 2, further comprising constructing a distribution representation for said ordinal measurements, so that the probability mass is smeared across adjacent categories.

4. The method as recited in claim 3, wherein the amount of said smear is a parameter.

5. The method as recited in claim 2, further comprising constructing a point mass distribution on the response category for said nominal measurements.

6. The method as recited in claim 1, further comprising providing said probability distribution with its mass in one cell.

7. The method as recited in claim 1, further comprising providing said probability distribution as discrete distributed probability distribution.

8. The method as recited in claim 1, further comprising providing said probability distribution representations as continuously distributed probability distribution.

9. The method as recited in claim 1, wherein the probability distribution representation of said categorical data is a vector of discrete probability distribution.

10. The method as recited in claim 1, wherein said multivariate analysis procedures are selected from the group consisting of least squares, spectral decomposition, self-organizing maps, classification, discriminant analysis, pattern recognition, chemometric techniques, display of continuous multivariate data, dimension reduction and ordination, multivariate linear modes, and transforms.

11. The method as recited in claim 1, wherein said categorical data is selected from the group comprising of clinical data, survey data, data mining, patents, warranty cards and combinations thereof.

12. The method as recited in claim 11, further comprising labeling said categorical data as ordinal or nominal measurement.

13. The method as recited in claim 12, wherein the amount of said smear is a parameter.

14. The method as recited in claim 11, further comprising providing said probability distribution with its mass in one cell.

15. The method as recited in claim 11, further comprising providing said probability distribution as discrete distributed probability distribution.

16. The method as recited in claim 11, further comprising providing said probability distribution representations as continuously distributed probability distribution.

17. The method as recited in claim 11, wherein the probability distribution representation of said categorical data is a vector of discrete probability distribution.

18. The method as recited in claim 11, wherein said multivariate analysis procedures are selected from the group consisting of least squares, spectral decomposition, self-organizing maps, classification, discriminant analysis, pattern recognition, chemometric techniques, display of continuous multivariate data, dimension reduction and ordination, multivariate linear modes, and transforms.

19. The method as recited in claim 11, wherein said categorical data is selected from the group comprising of clinical data, survey data, data mining, patents, warranty cards and combinations thereof.

20. A method of generating analyses of categorical data that will allow the application of exploratory multivariate analysis procedures constructed from inner products, distances, vector additions, and scalar multiplications to said categorical data having a plurality of responses, the method comprising the steps of:

a. encoding said categorical data into members of a linear space,

b. transforming said exploratory multivariate analysis procedures based on inner products, distances, vector additions and scalar multiplications to work with said members of linear space, and

c. applying said transformed exploratory multivariate analysis procedures constructed from inner products, distances, vector additions, and scalar multiplications to said members of linear space to allow browsing, retrieving and viewing of said converted categorical data.

21. The method as recited in claim 20, further comprising constructing a distribution representation for said ordinal measurements, so that the probability mass is smeared across adjacent categories.

22. The method as recited in claim 20, further comprising constructing a point mass distribution on the response category for said nominal measurements.

23. A method for analyzing categorical data having a plurality of responses comprising:

encoding said categorical data into probability distribution representations, wherein each response of said categorical data is converted to a corresponding probability distribution representation,

transforming exploratory multivariate analysis procedures to work with said probability distribution representations, and

applying said transformed exploratory multivariate analysis procedures to said probability distribution representations to allow browsing, retrieving and viewing of said categorical data.

24. The method of claim 23 further comprising labeling said categorical data as ordinal or nominal measurement.

25. The method of claim 24 further comprising constructing a distribution representation for said ordinal measurements, so that the probability mass is smeared across adjacent categories.

26. The method of claim 25 wherein the amount of said smear is a parameter.

27. The method of claim 24 further comprising constructing a point mass distribution on the response category for said nominal measurements.

28. The method of claim 23 further comprising providing said probability distribution with its mass in one cell.

29. The method of claim 23 further comprising providing said probability distribution as discrete distributed probability distribution.

30. The method of claim 23 further comprising providing said probability distribution representations as continuously distributed probability distribution.

31. The method of claim 23 wherein the probability distribution representation of said categorical data is a vector of discrete probability distribution.

32. The method of claim 23 wherein said multivariate analysis procedures are selected from least squares, spectral decomposition, self-organizing maps, classification, discriminant analysis, pattern recognition, chemometric techniques, display of continuous multivariate data, dimension reduction and ordination, multivariate linear modes, and transforms.

33. The method of claim 23 wherein said categorical data is selected from clinical data, survey data, data mining, patents, warranty cards and combinations thereof.