Testing the order-theoretic similariy model and making perceived similarity explicit with Formal Concept Analysis

Year:
2013
Type of Publication:
In Collection
Authors:
Endres, Dominik
Giese, Martin A.
Pages:
130
BibTex:
Note:
not reviewed
Abstract:

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. [Support from EU Commission, EC FP7-ICT-248311 AMARSi, ABC PITN-GA-011-290011: DFG GI 305/4-1, DFG GZ: KA 1258/15-1, BMBF, FKZ: 01GQ1002A]