Serial pattern complexity: Irregularity and hierarchy

Peter A. van der Helm, Rob J. van Lier, Emanuel L. J. Leeuwenberg

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Abstract. In perception research, various models have been designed for the encoding of e.g. visual patterns, in order to predict the human interpretation of such patterns. Each of these encoding models provides a few coding rules to obtain codes of a pattern, each code expressing regularity and hierarchy in that pattern. Some of these models employ the minimum principle which states that the human interpretation of a pattern is reflected by the simplest code of that pattern. That is, the simplest code according to a given complexity metric. We propose a new complexity metric. This metric is based on a formal analysis of the concept of regularity. Some conclusions of this analysis are sketched. The formal analysis itself is presented elsewhere (van der Helm & Leeuwenberg, 1991). The new metric does not depend on artifacts of the coding rules (cf. Hatfield & Epstein, 1985). It accounts for the amounts of irregularity and hierarchy as represented in a code of a pattern, such that these two amounts can be added to determine the complexity of a code. We will discuss an experiment that shows that the new metric performs significantly better than metrics used before. In particular, the new metric predicts more local pattern organizations than the old metrics. This implies that various local pattern organizations do not falsify the minimum principle anymore.

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