If you look through chapter 12 of the most recent (online) version of ESL by Hastie et al, you can get a good idea of how to think about what the soft-margin SV

If you look through chapter 12 of the most recent (online) version of ESL by Hastie et al, you can get a good idea of how to think about what the soft-margin SVM is doing. In particular, equation 12.25 on page 426 gives a formal mathematical equivalent to my previous verbal description. Personally, I find it helpful to think of most classification methods in terms of what loss function is being optimized and what sorts of regularization are being applied. Chapter 3 in ESL gives a nice introduction to the concepts required for such an approach, in addition to the info in chapter 12 that applies directly to SVMs. Building an SVM-based classifier from scratch is pretty straightforward but, as with many ML methods, making it efficient requires a bag of tricks. SVMLight and LibSVM both provide well-tested implementations of a variety of algorithms that are worth looking at (though the source may be hard to digest due to heavy optimization). You could also check out LibLinear, from the authors of LibSVM, which focuses on linear SVMs for use with large and high-dimensional datasets.