Constructing Hierarchical Concepts via Analogical Generalization

Constructing Hierarchical Concepts via Analogical Generalization Chen Liang (chenliang2013@u.northwestern.edu) Kenneth D. Forbus (forbus@northwestern.edu) Qualitative Reasoning Group, Northwestern University, 2133 Sheridan Road Evanston, IL, 60208 USA hierarchical concepts. Next we describe three experiments, providing evidence that it can produce results that are compatible with human judgments, and with a prior Bayesian simulation on a data set for which no human data is available. We close with related and future work. Abstract Learning hierarchical concepts is a central problem in cognitive science. This paper explores the Nearest-Merge algorithm for creating hierarchical clusters that can handle both feature-based and relational information, building on the SAGE model of analogical generalization. We describe its results on three data sets, showing that it provides reasonable fits with human data and comparable results to Bayesian models. Keywords: Analogy, concept modeling, hierarchical clustering learning, Background computational Introduction How concepts are formed and organized is a central question in cognitive science. It has been argued that people group examples into categories to maximize within-category similarity and minimize between-category similarity (Mervis & Rosch, 1981). One important feature of categories is that they are not isolated from each other. Instead, people tend to organize the categories into a hierarchy or taxonomy (Collins & Quillian, 1969; Murphy & Lassaline, 1997). Most models of hierarchical category learning focus on feature-based representations (e.g. Medin & Schaffer, 1978; Fischer 1987). Feature-based representations cannot capture relational thinking, involved in explanation, causal reasoning, and planning, which is central to human cognition (Gentner & Kurtz, 2005). Bayesian models (Kemp et al. 2006; Kemp & Tenenbaum 2008) can create a variety of structures, including hierarchical structures, although to our knowledge they have not been tested on representations involving higher-order relations. Analogical generalization (Kuehne et al. 2000) can handle relational representations with higher-order relations as well as feature representations, but currently it does not create hierarchical conceptual structures. This paper explores how analogical generalization might be extended to model the formation of hierarchical conceptual structure. The basic insight is that the numerical similarity score computed via structure- mapping can serve the same roles as vector-based operations used in feature-based models of similarity, and hence many of the same ideas and insights of those models can be extended to handle relational (including higher-order relational) representations. We begin by summarizing relevant aspects of structure- mapping and the models that we are building upon. Then we describe the Nearest-Merge algorithms for constructing We assume Gentner’s (1983) structure-mapping theory. Our model is built upon the Sequential Analogical Generalization Engine (SAGE; McLure et al. 2010), which in turn uses the Structure-Mapping Engine (Falkenhainer et al 1989) for analogical comparison and MAC/FAC (Forbus et al 1995) for analogical retrieval. Thus we start with SME, since it is the most fundamental. SME takes as input two structured representations, a base and target, and produces one or more mappings. Each mapping provides a set of correspondences (i.e. what goes with what), a structural evaluation score which provides an overall estimate of match quality, and candidate inferences. We refer to the similarity score of a mapping as NSIM(base,target), which is normalized to [0,1] by dividing the raw score by the mean of the self-scores of the base and target 1 . Forward candidate inferences go from base to target, reverse candidate inferences go from target to base. MAC/FAC takes as input a case library, which is a set of structured descriptions, and a probe, which is a structured description. It returns one or more approximations to the most similar case in the case library, using a two-stage process that enables it to scale to large case libraries. The first stage uses a flattened version of the relational structure of cases, called content vectors, whose dimensions are proportional to the weighted number of occurrences of each predicate in a description. The dot product of two content vectors is an estimate of SME’s structural evaluation score for the structured representations, making it a useful coarse filter. Both SME and MAC/FAC have been used to model a variety of psychological phenomena. SAGE maintains, for each concept, a generalization context. A generalization context has a trigger, which is used to test whether or not an incoming example should be added to it. (An incoming example might satisfy multiple triggers, and hence be processed by several generalization contexts.) Each generalization context maintains a set of generalizations and a set of unassimilated examples. The mapped representations are subsets of both base and target, so its score is lower than either of their self-scores.