Untitled Deck Flashcards
(30 cards)
What is the main goal of Support Vector Machines (SVMs)?
To find an optimal separator between two classes.
What method do SVMs use for separation?
Linear separation by means of hyperplanes and kernel functions.
What is a hyperplane in the context of SVMs?
A hyperplane divides a ( p )-dimensional space into regions.
How is a hyperplane formally defined?
(\beta_0 + \beta_1x_1 + \beta_2x_2 + \ldots + \beta_px_p = 0).
What is the maximal margin classifier?
It finds the hyperplane with the largest margin, which is the minimum perpendicular distance to the closest examples.
What are support vectors?
The examples that are equidistant from the hyperplane.
What is the role of the ‘margin’ in SVMs?
It defines the distance between the hyperplane and the nearest data points from both classes.
Why do we prefer to label examples with ( y = 1 ) or ( y = -1 )?
To increase the distance between classes.
What problem arises when a separating hyperplane does not exist?
A support vector classifier with a soft margin is used.
What does a soft margin allow in SVMs?
It allows some misclassification of examples by tolerating points within the margin.
What is the impact of a large ‘C’ hyperparameter in SVMs?
More examples can violate the margin, leading to higher bias and lower variance.
How do SVMs handle nonlinear boundaries?
By transforming the feature space using kernel functions.
What is the purpose of kernel functions in SVMs?
To transform the data into a higher-dimensional space where a linear separation is possible.
What are the most common types of kernel functions?
Polynomial, radial basis function (RBF), and sigmoid.
Write the equation of a polynomial kernel.
( K(x, y) = (x \cdot y + 1)^d ).
Write the equation of a radial basis function (RBF) kernel.
( K(x, y) = \exp\left(-\frac{||x \cdot y||^2}{2\sigma^2}\right) ).
What is the main idea behind multiclass classification in SVMs?
To use multiple SVMs to distinguish between more than two classes.
What are the two common strategies for multiclass SVM classification?
One-versus-all and one-versus-one approaches.
What is the one-versus-all strategy?
A single SVM is trained for each class against all other classes.
What is the one-versus-one strategy?
Multiple SVMs are trained for each pair of classes, and a voting scheme is used for classification.
What type of problem is solved by the support vector classification problem?
An optimization problem involving support vectors and similarity measures.
How do SVMs replace the inner product in the optimization problem?
By using kernel functions to compute more flexible decision boundaries.
Why are kernel functions essential for complex problems?
They enable SVMs to handle data that is not linearly separable in the original space.
What is the significance of the margin in SVMs?
A larger margin improves the generalization ability of the classifier.
