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Sparse correspondence analysis for large contingency tables

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Abstract

We propose sparse variants of correspondence analysis (CA) for large contingency tables like documents-terms matrices used in text mining. By seeking to obtain many zero coefficients, sparse CA remedies to the difficulty of interpreting CA results when the size of the table is large. Since CA is a double weighted PCA (for rows and columns) or a weighted generalized SVD, we adapt known sparse versions of these methods with specific developments to obtain orthogonal solutions and to tune the sparseness parameters. We distinguish two cases depending on whether sparseness is asked for both rows and columns, or only for one set.

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Notes

  1. There are 45 presidents, but the speech data of presidents William Henry Harrison and James Garfield are missing.

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Authors and Affiliations

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, China

    Ruiping Liu

  2. CEDRIC Lab, Conservatoire national des arts et métiers, 292 rue Saint Martin, 75003, Paris, France

    Ndeye Niang & Gilbert Saporta

  3. School of Economics and Management and Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China

    Huiwen Wang

Authors
  1. Ruiping Liu
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  2. Ndeye Niang
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  3. Gilbert Saporta
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  4. Huiwen Wang
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Correspondence to Gilbert Saporta.

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Appendix: The 45 presidents of the United States

Appendix: The 45 presidents of the United States

1. George Washington

16. Abraham Lincoln

31. Herbert Hoover

2. John Adams

17. Andrew Johnson

32. Franklin D. Roosevelt

3. Thomas Jefferson

18. Ulysses S. Grant

33. Harry S. Truman

4. James Madison

19. Rutherford B. Hayes

34. Dwight D. Eisenhower

5. James Monroe

20. James A. Garfield

35. John F. Kennedy

6. John Quincy Adams

21. Chester A. Arthur

36. Lyndon B. Johnson

7. Andrew Jackson

22. Grover Cleveland

37. Richard Nixon

8. Martin Van Buren

23. Benjamin Harrison

38. Gerald R. Ford

9. William H. Harrison

24. Grover Cleveland

39. Jimmy Carter

10. John Tyler

25. William McKinley

40. Ronald Reagan

11. James Knox Polk

26. Theodore Roosevelt

41. George H.W. Bush

12. Zachary Taylor

27. William H. Taft

42. William J. Clinton

13. Millard Fillmore

28. Woodrow Wilson

43. George W. Bush

14. Franklin Pierce

29. Warren Harding

44. Barack Obama

15. James Buchanan

30. Calvin Coolidge

45. Donald Trump

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Liu, R., Niang, N., Saporta, G. et al. Sparse correspondence analysis for large contingency tables. Adv Data Anal Classif 17, 1037–1056 (2023). https://doi.org/10.1007/s11634-022-00531-5

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  • DOI: https://doi.org/10.1007/s11634-022-00531-5

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