I. INTRODUCCIÓN
I.5. Aprendizaje on-line (e-learning) en radiología
I.5.2. E-learning en radiología
We noticed that variables have different magnitudes. Therefore, we proposed several scaling methods in order to seek the method that produces the best results. In this section, we use 5-year financial information starting from 2013 to 2017. 10 years is a relative long time period for a company. We focus on the 2017 credit rating so we think that the last 5 years of financial information is sufficient to compare different scaling methods and also save computational time.
Results for data without scaling with 10 grades is presented in Table4.5. The training error average per company is 1.752, which means that the average distance between the true and the predicted credit ratings is close to 2, i.e., it is a two-grade difference. The test error average per company is 2.28, which means that the distance between the true and the predicted credit ratings is
2, i.e., it is a two-grade difference. The average training error Total 0 (17.8) and training error Total 1 (7.2) indicate that for training data there are close to 18 companies for which the predicted result is the same as the true credit rating and there are 7 companies for which the predicted credit rating has a one-grade difference with the true credit rating. The average test error Total 0 (1.8) and test error Total 1 (3) indicate that for the test data there are close to 2 companies for which the predicted credit rating is the same as the true credit rating and there are 3 companies for which the predicted credit rating has a one-grade difference with the true credit rating.
TABLE4.5: Results without any transform with 10 Grades
Training Error Test Error
Total Total 0 Total 1 Total Total 0 Total 1
Test1 70 19 6 30 1 2 Test2 86 17 6 21 2 4 Test3 71 18 8 17 3 3 Test4 66 19 6 21 2 4 Test5 75 16 10 25 1 2 Average 73.6 17.8 7.2 22.8 1.8 3
Ave per Company 1.752 0.42 0.17 2.28 0. 18 0.3
Results of the use of scaling transformationstdx(X) with 10 categories are shown in Table4.6. The training error average per company is 1.514, which means that the average distance between the true and the predicted credit ratings is close to 2, i.e., it is a two-grade difference. The test error average per company is 2.72, which means that the distance between the true and the predicted credit ratings is close to 3, i.e., it is a three-grade difference. The average training error Total 0 (23.6) and training error Total 1 (6) indicate that for the training data there are close to 24 companies for which the predicted result is the same as the true credit rating and there are 6 companies for which the predicted credit rating has a one-grade difference with the true credit rat- ing. The average test error Total 0 (2.6) and test error Total 1 (2.4) indicate
4.2. Using Different Scaling Methods 47 that for the test data there are close to 3 companies for which the predicted credit rating is the same as the true credit rating and there are 2 companies for which the predicted credit rating has a one-grade difference with the true credit rating.
TABLE4.6: Results for the transformstd(X)x with 10 Grades
Training Error Test Error
Total Total 0 Total 1 Total Total 0 Total 1
Test 1 47 26 6 31 2 0 Test 2 78 19 7 14 4 4 Test 3 59 26 5 34 2 3 Test 4 60 24 7 37 2 2 Test 5 74 23 5 20 3 3 Average 63.6 23.6 6 27.2 2.6 2.4
Ave per Company 1.51 0.56 0.14 2.72 0.26 0.24
Results of the use of scaling method max(absx (X)) with 10 grades are in Table
4.7. The training error average per company is 1.581, which means that the average distance between the true and the predicted credit ratings is close to 2, i.e., it is a two-grade difference. The test error average per company is 3.22, which means that the distance between the true and the predicted credit ratings is 3, i.e., it is a three-grade difference. The average training error To- tal 0 (20.4) and training error Total 1 (7.4) indicate that for the training data there are 20 companies for which the predicted result is the same as the true credit rating and there are 7 companies for which the predicted credit rating has a one grade difference with the true credit rating. The average test error Total 0 (0) and test error Total 1 (2) indicate that for the test data there are no companies for which the predicted credit rating is the same as the true credit rating and there are 2 companies for which the predicted credit rating has a one-grade difference with the true credit rating.
TABLE4.7: Results for the transform max(abs(X))x with 10 Grades
Training Error Test Error
Total Total 0 Total 1 Total Total 0 Total 1
Test 1 74 22 4 32 0 2 Test 2 74 18 7 37 0 1 Test 3 73 24 1 35 0 3 Test 4 54 17 14 25 0 1 Test 5 57 21 11 32 0 3 Average 66.4 20.4 7.4 32.2 0 2
Ave per Company 1.58 0.48 0.17 3.22 0 0.2
shown in Table4.8. The training error average per company is 1.524, which means that the average distance between the true and the predicted credit ratings is close to 2, i.e., it is a two-grade difference. The test error average per company of of 2.92 for the test data means that the distance between the true credit rating and the predicted credit ratings is 3, which is a three-grade difference. The average training error Total 0 (20.8) and training error Total 1 (4.6) indicate that for the training data there are almost 21 companies for which the predicted result is the same as the true credit rating and there are close to 5 companies for which the predicted credit rating has a one grade dif- ference with the true credit rating. The average test error Total 0 (0.6) and test error Total 1 (2.2) indicate that for the test data there is almost one company for which the predicted credit rating is the same as the true credit rating and there are 2 companies for which the predicted credit rating has a one-grade difference with the true credit rating.
Results of the use of scaling transformation stdx−(XX¯) with 10 grades are shown in Table4.9. The training error average per company is 1.410, which means that the average distance between the true and the predicted credit ratings is 1,i.e., it is a one-grade difference. The test error average per company is 2.66, which means that the distance between the true and the predicted credit rat- ings is 3, i.e., it is a three-grade difference. The average training error Total 0
4.2. Using Different Scaling Methods 49
TABLE 4.8: Results for the transform maxx−min(X)(X)−min(X) with 10
Grades
Training Error Test Error
Total Total 0 Total 1 Total Total 0 Total 1
Test 1 70 21 1 33 0 3 Test 2 70 19 7 34 1 1 Test 3 56 23 6 35 0 2 Test 4 73 18 4 31 0 2 Test 5 51 23 5 13 2 3 Average 64 20.8 4.6 29.2 0.6 2.2
Ave per Company 1.52 0.45 0.11 2.92 0.06 0.22
(22.4) and training error Total 1 (4.4) indicate that for the training data there are 22 companies for which the predicted result is the same as the true credit rating and there are 4 companies for which the predicted credit rating has a one-grade difference with the true credit rating. The average test error Total 0 (1.2) and test error Total 1 (2.6) indicate that for the test data there is one company for which the predicted credit rating is the same as the true credit rating and there are close to 3 companies for which the predicted credit rat- ing has a one-grade difference with the true credit rating.
TABLE4.9: Results for the transformstd(X)x−X¯ with 10 Grades
Training Error Test Error
Total Total 0 Total 1 Total Total 0 Total 1
Test 1 58 20 2 26 0 5 Test 2 92 17 4 23 2 2 Test 3 46 27 4 30 1 3 Test 4 45 24 8 31 1 1 Test 5 55 24 4 23 2 2 Average 59.2 22.4 4.4 26.6 1.2 2.6
Ave per Company 1.41 0.53 0.10 2.66 0.12 0.26
We put a summary for all these methods in Table 4.10, where we can see that the scaling method with mean and standard deviation gives the smallest training error, where using no transformation gives the smallest test error.
However, the difference between the average test errors for the mean and standard deviation method and the case without transformation is not very large. If we only consider the training Total 0 and test Total 0 errors we con- clude that the scaling method with mean and standard deviation is the best for 10 grades.
TABLE4.10: Comparison of all the methods with 10 grades
Methods Average Training Error Average Test Error
Total Total 0 Total 1 Total Total 0 Total 1
Without Transform 1.752 17.8 7.2 2.28 1.8 3
Standard Deviation 1.514 23.6 6 2.72 2.6 2.4
Max and Absolute 1.581 20.4 7.4 3.22 0 2
Max and Min 1.524 20.8 4.6 2.92 0.6 2.2
Mean and
Standard Deviation 1.410 22.4 4.4 2.66 1.2 2.6