Testing the order-theoretic similariy model and making perceived similarity explicit with Formal Concept Analysis D Endres, M A Giese |
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Computational Sensomotorics, HIH,CIN,BCCN, University Clinic Tuebingen, Germany
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| Similarity ratings are a widely used tool for the assessment of high-level perceptual similarity. Several approaches to conceptualizing similarity exist. We are concerned with the featural approach which was developed by [Tversky, 1977, Psychological Review 84:327-352] and mathematically formalized in [Lengnink, 1996, PhD Dissertation, TU Darmstadt]. This formalization posits a partial order between pairs of objects (stimuli) as the fundamental mathematical structure of similarity, traditional similarity measures (e.g. Russell-Rao, Jaccard etc.) are conceived as order-preserving mappings from the partial order between pairs into the (real) numbers. This approach preserves the main structural features of Tversky's model, and makes additional predictions about the (non-)comparability of similarity between pairs of objects. We tested these predictions experimentally: a) subjects rated the similarity between natural images on a 7-point Likert scale, and b) they ordered pairs of images by their perceived similarity. We find that the ordering predictions of ratings are well preserved (>85%). One drawback of similarity ratings is that they provide only an implicit measure of “relatedness”. We employ theoretical framework of Formal Concept Analysis [Ganter & Wille, 1996, Formal Concept Analysis, Springer, New York] to make the relationships explicit as concept lattices, which generalizes traditional approaches based on hierarchical clustering. |
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