A support vector machine is a type of machine learning algorithm used for classification and regression analysis. It works by transforming the original data into a higher dimensional space and finding a hyperplane that maximally separates the data points of different classes. The hyperplane is chosen so that the distance to the nearest training data point of any class (so-called support vectors) is maximized.
A kernel function is a function that takes in two data points and outputs a similarity score between them. In the context of SVMs, kernel functions are used to transform the data into a higher dimensional space without explicitly computing the coordinates in that space. This is known as the kernel trick and allows SVMs to handle data that is not linearly separable in the original space.
A soft margin classifier is a type of SVM that allows for misclassifications of training data points. This is done by introducing slack variables that measure the extent to which a data point violates the margin constraints. The goal is to find a hyperplane that separates the classes as best as possible while minimizing the total amount of slack.
A maximal margin classifier is a type of SVM that finds the hyperplane with the maximum margin, i.e., the largest distance to the nearest data points of either class. A support vector classifier, on the other hand, is a type of SVM that finds the hyperplane that separates the classes with the maximum margin, while also allowing for misclassifications. The support vector classifier is a more flexible model that can handle non-linearly separable data.