Logistic regression is widely used to predict a binary response. This is a linear method that can be written mathematically as follows:

In the preceding equation, L(w; x, y) is the loss function is called logistic loss.

For binary classification problems, the algorithm will output a binary logistic regression model. Given a new data point, denoted by x, the model makes predictions by applying the logistic function:

Where z = w^Tx, and by default, if f(w^Tx)>0.5, the outcome is positive, or negative otherwise, though unlike linear SVMs, the raw output of the logistic regression model, f(z), has a probabilistic interpretation (that is, the probability that x is positive).

Linear SVM is the newest extremely fast machine learning (data mining) algorithm for solving multiclass classification problems from ultralarge datasets that implements an original proprietary version of a cutting plane algorithm for designing a linear support vector machine (source: www.linearsvm.com/ ).