1. For a linearly separable binary classification task sample set, there are many hyperplanes that separate the training samples. What conditions does the support vector machine try to find to satisfy the hyperplane? (A)
A. In the "middle" of positive and negative samples
B. Close to positive samples
C. Close to negative samples
D. None of the above statements are correct
Analysis : From an intuitive point of view, when the found hyperplane is exactly in the "middle" of the positive and negative sample points, the modified hyperplane is the most robust to the classification result, and has the strongest generalization ability to unknown examples.
2. Which of the following statements about support vector machines is wrong? (D)
A. The basic type of support vector machine is a convex quadratic programming problem
B. The hyperplane separating the training samples is only determined by the support vector
C. The core idea of the support vector machine is to maximize the interval
D. The above options are all wrong
Analysis : The essence of support vector machine is a convex quadratic programming problem, so option A is correct; the support vector machine model itself only depends on a few support vectors, so option B is correct; the core idea of support vector machine is to maximize the interval to Get the strongest generalization ability and robustness, so C is correct. To sum up, only option D is wrong.
3. The sum of the distances of two heterogeneous support vectors to the hyperplane is called (interval).
Analysis : The interval refers to the sum of the distances from two heterogeneous support vectors to the hyperplane, and the interval maximization is the goal of the support vector machine.
4. The dual problem of support vector machine can be obtained by (Lagrangian multiplier method).
Analysis : The dual problem of the support vector machine can be obtained through the Lagrange multiplier method, which is a conceptual problem.
5. The wrong statement is (C) when solving the intercept item of the support vector machine.
A. The intercept term can be solved by any support vector
B. In order to improve robustness, the average value of all support vector solutions is usually used
C. The intercept term can be solved by any sample
D. The solution of the intercept term can Indicates that the hyperplane learned by the support vector machine is only related to a small number of support vectors
Analysis : All support vectors can be solved for an intercept item, option A is correct; the average value of all support vector solutions is often used to solve the intercept item to improve robustness, option B is correct; only the samples corresponding to the support vectors can be The intercept item is solved, and option C is wrong; since the intercept item can only be solved by support vectors, it can be seen that the hyperplane obtained by the support vector machine is only related to a few support vectors.
6. What should I do if there is no hyperplane that can correctly divide the two types of samples? (A)
A. Map the sample from the original space to a higher-dimensional feature space, so that the sample is linearly separable in this feature space B.
Map the sample from the original space to a higher-dimensional feature space, so that the sample is in this feature space Inner linear inseparability
C. Map the sample from the original space to a lower-dimensional feature space, so that the sample is linearly separable in this feature space D.
Map the sample from the original space to a lower-dimensional feature space, so that the sample is in Linearly inseparable in this feature space
Analysis : In the support vector machine, if there is no hyperplane that can completely and correctly divide the two types of samples in the current dimension, then the samples can be mapped from the original space to a higher-dimensional feature space, so that the samples are in this higher dimension. The feature space of dimension is linearly separable. At the same time, it can be proved that such a feature space must exist.
7. Regarding the statement about the kernel function, the correct one is (D).
A. Can bypass explicit consideration of feature maps
B. Can ease the difficulty of calculating high-dimensional inner products
C. Can be directly calculated in the original feature space
D. The above statements are correct
Analysis : The kernel function can transform the calculation process of the inner product of two vectors in the high-dimensional feature space into solving the kernel function value of the two vectors in the original feature space, thereby greatly reducing the difficulty of calculating the high-dimensional inner product, and the mapping method is determined by The kernel function itself is uniquely and explicitly determined. To sum up, option D is wrong.
8. Which of the following usages about support vector machines is correct? (D)
A. When the data is linearly separable, you can consider the basic type of support vector machine.
B. When the data is linearly inseparable, you can consider the support vector machine with kernel function.
C. If you use the support vector machine with kernel function, you can pass Model selection and other techniques to select a more appropriate kernel function
D. The above statements are correct
Analysis : For linearly separable problems, you can directly use the basic support vector machine for classification and solution; for linearly inseparable data problems, you can consider introducing a kernel function to make the data in a higher-dimensional regenerating kernel Hilbert space Linearly separable to solve, and the most suitable kernel function can be selected through model selection technology. To sum up, option D should be selected for this question.
9. What are the properties of the solution of the support vector machine? (sparseness)
Analysis : The solution of the support vector machine is sparse, which means that the model parameters of the support vector machine are only related to a small number of support vectors in the sample feature vector, and have nothing to do with most sample points.