Binary Classifier with training data for one label only In some real-life problems such as authentication, we only have training data for one label (x is authenticated) while the other label doesn't have any data or only few entries (x is an imposter).
What kind of changes should we do in order to adjust a classifier to deal with a label targeted for other/unknown entries?
 A: This is actually a widespread situation, for example in industrial quality control, you want to decide whether a batch of product is fit for sale. Also medical diagnosis (if it isn't a differential diagnosis) often faces the same problem.
So-called one-class or unary classifiers address this. The idea is to model the "in" class independently of possible other classes. 
In chemometrics, SIMCA is a popular approach to this. Basically, you compress your class into a PCA models and then develop a boundary outside which you deem it sufficiently improbable that the case belongs to that class. (For multiple independent classes, you do this for each class separtely.)
D.M. Tax: One-class classification -- Concept-learning in the absence of counter-examples, Technische Universiteit Delft, 2001 develops a one-class SVM.
A: If I understood you correctly, you have many data for class A (auth.) and almost any for class B (imposter) in your (randomly chosen?) training set?
From Wikipedia (Pseudocount), 

In any observed data set or sample there is the possibility, especially with low-probability events and/or small data sets, of a possible event not occurring. Its observed frequency is therefore zero, apparently implying a probability of zero. This is an oversimplification, which is inaccurate and often unhelpful, particularly in probability-based machine learning techniques such as artificial neural networks and hidden Markov models. By artificially adjusting the probability of rare (but not impossible) events so those probabilities are not exactly zero, we avoid the zero-frequency problem. Also see Cromwell's rule.

So I would therefore artificially include some data for the other, very rare label/class. 
