Classification with Positive and Negative Equivalence Constraints: Theory, Computation and Human Experiments

We tested the efficiency of category learning when participants are provided only with pairs of objects, known to belong either to the same class (Positive Equivalence Constraints or PECs) or to different classes (Negative Equivalence Constraints or NECs). Our results in a series of cognitive experiments show dramatic differences in the usability of these two information building blocks, even when they are chosen to contain the same amount of information. Specifically, PECs seem to be used intuitively and quite efficiently, while people are rarely able to gain much information from NECs (unless they are specifically directed for the best way of using them). Tests with a constrained EM clustering algorithm under similar conditions also show superior performance with PECs. We conclude with a theoretical analysis, showing (by analogy to graph cut problems) that the satisfaction of NECs is computationally intractable, whereas the satisfaction of PECs is straightforward. Furthermore, we show that PECs convey more information than NECs by relating their information content to the number of different graph colorings. These inherent differences between PECs and NECs may explain why people readily use PECs, while many of them need specific directions to be able to use NECs effectively.