Semi-supervised learning on closed set lattices

We propose a new approach for semi-supervised learning using closed set lattices, which have been recently used for frequent pattern mining within the framework of the data analysis technique of Formal Concept Analysis (FCA). We present a learning algorithm, called SELF (SEmi-supervised Learning via FCA), which performs as a multiclass classifier and a label ranker for mixed-type data containing both discrete and continuous variables, while only few learning algorithms such as the decision tree-based classifier can directly handle mixed-type data. From both labeled and unlabeled data, SELF constructs a closed set lattice, which is a partially ordered set of data clusters with respect to subset inclusion, via FCA together with discretizing continuous variables, followed by learning classification rules through finding maximal clusters on the lattice. Moreover, it can weight each classification rule using the lattice, which gives a partial order of preference over class labels. We illustrate experimentally the competitive performance of SELF in classification and ranking compared to other learning algorithms using UCI datasets.