1. The invention of hyperplane kinescopes is another technical innovation.

2. The separating hyperplane of traditional support vector machines is sensitive to noises and outliers.

3. Then the method to construct the optimal separating hyperplane and some basic concept are described simply.

4. Finally, a new separation hyperplane was generated through the optimization training.

5. Free arrangement is a very important kind of hyperplane arrangement.

6. The original optimal hyperplane algorithm proposed by Vladimir Vapnik in 1963 was a linear classifier.

7. A method based on fuzzy theory is applied to explain the classification of SVM and its optimal hyperplane. An expression of fuzzy membership on doubtful classification area is listed.

8. The idea of this algorithm is to find the optimal solution in the feasible region by an iterative step from one basic standard hyperplane to another.

9. Aiming at the different loss by error judge in fault diagnosis, the fuzzy membership based on the loss function is defined and optimal hyperplane is modified.

10. Then, an efficient implicit enumerative search is done on the nonbasic variables and new ones on the objective function hyperplane. The algorithm is of interests in theory.