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

Outlier detection using flexible categorisation and interrogative agendas

Categorization is one of the basic tasks in machine learning and data analysis. Building on formal concept analysis (FCA), the starting point of the present work is that different ways to categorize a given set of objects exist, which depend on the choice of the sets of features used to classify them, and different such sets of features may yield better or worse categorizations, relative to the task at hand. In their turn, the (a priori) choice of a particular set of features over another might be subjective and express a certain epistemic stance (e.g. interests, relevance, preferences) of an agent or a group of agents, namely, their interrogative agenda. In the present paper, we represent interrogative agendas as sets of features, and explore and compare different ways to categorize objects w.r.t. different sets of features (agendas). We first develop a simple unsupervised FCA-based algorithm for outlier detection which uses categorizations arising from different agendas. We then present a supervised meta-learning algorithm to learn suitable (fuzzy) agendas for categorization as sets of features with different weights or masses. We combine this meta-learning algorithm with the unsupervised outlier detection algorithm to obtain a supervised outlier detection algorithm. We show that these algorithms perform at par with commonly used algorithms for outlier detection on commonly used datasets in outlier detection. These algorithms provide both local and global explanations of their results