Multi-class classification by training a machine learning system based on training inputs each of which includes features and at least one class label. Each training input is assigned a membership value that can indicate if an entity having the features of the training input is a member of the class corresponding to the class label that is also included in the training input. To determine if an entity having test features is a member of several test classes, test inputs can be constructed where each input includes the test features and a class label corresponding to one of the test classes. The test inputs are processed by the trained machine learning system, which produces as outputs test membership values that represent the likelihood that the entity having the features in the test input belong to the test class corresponding to the test class label also included in the test input.