This page introduces the SVM formulation used in VLFeat. See Support Vector Machines (SVM) for more information on VLFeat SVM support.
Let $ ^d $ be a vector representing, for example, an image, an audio track, or a fragment of text. Our goal is to design a classifier*, i.e. a function that associates to each vector $$ a positive or negative label based on a desired criterion, for example the fact that the image contains or not a cat, that the audio track contains or not English speech, or that the text is or not a scientific paper.
The vector $$ is classified by looking at the sign of a *linear scoring function* $ , $. The goal of learning is to estimate the parameter $ ^d$ in such a way that the score is positive if the vector $$ belongs to the positive class and negative otherwise. In fact, in the standard SVM formulation the the goal is to have a score of *at least 1* in the first case, and of at most -1* in the second one, imposing a *margin*.
The parameter $$ is estimated or *learned* by fitting the scoring function to a training set of $n$ example pairs $(,y_i), i=1,,n$. Here $y_i -1,1