Matrices, Compression, Learning Curves: Formulation, and the GROUPNTEACH Algorithms

Suppose you are a teacher, and have to convey a set of object-property pairs ('lions eat meat'). A good teacher will convey a lot of information, with little effort on the student side. What is the best and most intuitive way to convey this information to the student, without the student being overwhelmed? A related, harder problem is: how can we assign a numerical score to each lesson plan (i.e., way of conveying information)? Here, we give a formal definition of this problem of forming learning units and we provide a metric for comparing different approaches based on information theory. We also design an algorithm, GROUPNTEACH, for this problem. Our proposed GROUPNTEACH is scalable (near-linear in the dataset size); it is effective, achieving excellent results on real data, both with respect to our proposed metric, but also with respect to encoding length; and it is intuitive, conforming to wellknown educational principles. Experiments on real and synthetic datasets demonstrate the effectiveness of GROUPNTEACH.