@incollection{212013,
author = "Dominik Endres and Martin A. Giese",
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]
",
doi = ":10.1068/v130302",
journal = "ECVP Abstract Supplement",
note = "not reviewed",
pages = "130",
title = "{T}esting the order-theoretic similariy model and making perceived similarity explicit with {F}ormal {C}oncept {A}nalysis",
volume = "42",
year = "2013",
}