[Case Study]Quadratic Discriminant Analysis using Julia

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Quadratic Discriminant Analysis using Julia

---

Quadratic discriminant analysis, qda, has all the same parameters as lda with the exception ofrrlda since there is no opportunity to reduce the dimensions.

1. julia> qda_mod = qda(fm, iris[train,:], gamma=0.1, tol=0.0001)
   
2. Formula: Species ~ :(+(Sepal_Length,Sepal_Width,Petal_Length,Petal_Width))
   
3. 
   
4. Response:
   
5. 
   
6. 3x3 DataFrame:
   
7.                Group    Prior Count
   
8. [1,]        "setosa" 0.333333    37
   
9. [2,]    "versicolor" 0.333333    37
   
10. [3,]     "virginica" 0.333333    38
    
11. 
    
12. 
    
13. Gamma: 0.1
    
14. 
    
15. Class means:
    
16. 3x5 DataFrame:
    
17.                Group Sepal_Length Sepal_Width Petal_Length Petal_Width
    
18. [1,]        "setosa"      5.01622     3.48649      1.46757    0.243243
    
19. [2,]    "versicolor"      5.87297     2.77568      4.23514     1.32973
    
20. [3,]     "virginica"      6.68158     2.98158      5.59474     2.03421
    
21. 
    
22. 
    
23. 
    
24. julia> qda_pred = predict(qda_mod,iris[test,:])
    
25. 38x1 PooledDataArray{UTF8String,Uint32,2}:  
    
26. "setosa"   
    
27. ⋮         
    
28. "virginica"
    
29. 
    
30. julia> 100*sum(qda_pred .== y[test])/length(y[test])
    
31. 100.0
    
32. 
    
33. julia> scaling(qda_mod)
    
34. 4x4x3 Array{Float64,3}:
    
35. [:, :, 1] =
    
36. -0.718864   0.225921  -2.21662    1.08868
    
37. -1.87503   -0.911666   1.57226   -0.984448
    
38. -0.10516    1.58782   -0.841958  -2.53646
    
39. -0.554306   4.69676    2.47484    2.86637
    
40. 
    
41. [:, :, 2] =
    
42. -0.540377   0.689292  -1.69643   -0.712444
    
43. -0.648636  -2.67637   -0.628192   0.760625
    
44. -0.741854   0.837311   0.729449   1.83986
    
45. -1.25651   -0.245052   2.69873   -3.94103
    
46. 
    
47. [:, :, 3] =
    
48. 0.633468  -0.535131   0.304746   1.55392
    
49. 0.438729   0.726428   2.40918   -0.750259
    
50. 0.716968  -0.576765  -0.461987  -1.65265
    
51. 1.13231    2.37764   -1.89922    0.656749

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关键词：discriminant Discriminan Case study Quadratic Analysis reduce