Laplacian unit-hyperplane learning from positive and unlabeled examples

• We propose a Laplacian unit-hyperplane classifier (LUHC) for PU learning.
• LUHC employs both geometrical and discriminant properties of PU information.
• The QPP in LUHC is rather small, resulting in its faster training speed.
• A parameter ν is introduced to control the upper bounds on the fractions of positive examples with margin errors.
• Experimental results show its efficiency and superiority.

In machine learning and data mining, learning from positive and unlabeled examples (PU learning) has attracted a great deal of attention, and the corresponding classifiers are required because of its applications in many practical areas. For PU learning, we propose a novel classifier called Laplacian unit-hyperplane classifier (LUHC), which determines a decision unit-hyperplane by solving a quadratic programming problem (QPP). The advantages of our LUHC are as follows: (1) Both geometrical and discriminant properties of the examples are exploited, resulting in better classification performance. (2) The size of QPP to be solved is small since it depends only on the number of the positive examples, resulting in faster training speed. (3) A meaningful parameter ν is introduced to control the upper bounds on the fractions of positive examples with margin errors. Preliminary experiments on both synthetic and real data sets show high level of agreement with aforementioned hypothesis, suggesting that our LUHC is superior to biased support vector machine, spy-expectation maximization, and naive Bayes in both classification ability and computation efficiency.