Three–Way Classification: Ambiguity and Abstention in Machine Learning

The three-way-in and three-way-out framework to treat and exploit ambiguity in data

“…Then, if we set = 0.1, we have that A(x) * 1 = 0.3 (thus, in particular the most probable alternative is 2), thus A(x) tw amb = {1, 2, 5}. As regards the second strategy, which is a generalization of previous work on three-way classification [28], it is based on a decision-theoretic framework and consists in balancing the costs of errors and abstentions. Let…”

“…Decision-Theoretic Approach. In this section, we will present two strategies for converting probabilistic classifiers into three-way classifiers, generalizing the work in [28].…”

“…Interestingly, if ∀i, j ij = with constant, we can greatly reduce the computational cost. Indeed, as shown in [28], in this case the optimization problem in Equation 3.5 can be reformulated as: . The two just outlined strategies can be applied independently from the learning algorithm.…”

“…In [28] the authors also defined an ensemble learning procedure, inspired by Random Forests. Basically, the learning process, as in standard Random Forest learning, first induces a set of n TWDT estimators, which we denote as T 1 , ..., T n .…”

“…The loss function determined by the decision procedure described in Section 3 is not convex and not smooth. In [28], a convex upper bound of the loss function is defined as a piece-wise linear approximation also providing a one-vs-one scheme, based on evidence theory, for extending the above introduced loss function to multiclass problems.…”