Jäkel, F. ; Schölkopf, B. ; Wichmann, F. A. (2008)
Similarity, Kernels and the Triangle Inequality.
In: Journal of Mathematical Psychology, 52 (5)
doi: 10.1016/j.jmp.2008.03.001
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
Similarity is used as an explanatory construct throughout psychology and multidimensional scaling (MDS) is the most popular way to assess similarity. In MDS, similarity is intimately connected to the idea of a geometric representation of stimuli in a perceptual space. Whilst connecting similarity and closeness of stimuli in a geometric representation may be intuitively plausible, Tversky and Gati Tversky, A., & Gati, I. (1982). Similarity, separability, and the triangle inequality. Psychological Review, 89(2), 123–154 have reported data which are inconsistent with the usual geometric representations that are based on segmental additivity. We show that similarity measures based on Shepard’s universal law of generalization Shepard, R. N. (1987). Toward a universal law of generalization for psychologica science. Science, 237(4820), 1317–1323 lead to an inner product representation in a reproducing kernel Hilbert space. In such a space stimuli are represented by their similarity to all other stimuli. This representation, based on Shepard’s law, has a natural metric that does not have additive segments whilst still retaining the intuitive notion of connecting similarity and distance between stimuli. Furthermore, this representation has the psychologically appealing property that the distance between stimuli is bounded.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2008 |
| Autor(en): | Jäkel, F. ; Schölkopf, B. ; Wichmann, F. A. |
| Art des Eintrags: | Bibliographie |
| Titel: | Similarity, Kernels and the Triangle Inequality |
| Sprache: | Englisch |
| Publikationsjahr: | 2008 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Journal of Mathematical Psychology |
| Jahrgang/Volume einer Zeitschrift: | 52 |
| (Heft-)Nummer: | 5 |
| DOI: | 10.1016/j.jmp.2008.03.001 |
| URL / URN: | https://doi.org/10.1016/j.jmp.2008.03.001 |
| Kurzbeschreibung (Abstract): | Similarity is used as an explanatory construct throughout psychology and multidimensional scaling (MDS) is the most popular way to assess similarity. In MDS, similarity is intimately connected to the idea of a geometric representation of stimuli in a perceptual space. Whilst connecting similarity and closeness of stimuli in a geometric representation may be intuitively plausible, Tversky and Gati Tversky, A., & Gati, I. (1982). Similarity, separability, and the triangle inequality. Psychological Review, 89(2), 123–154 have reported data which are inconsistent with the usual geometric representations that are based on segmental additivity. We show that similarity measures based on Shepard’s universal law of generalization Shepard, R. N. (1987). Toward a universal law of generalization for psychologica science. Science, 237(4820), 1317–1323 lead to an inner product representation in a reproducing kernel Hilbert space. In such a space stimuli are represented by their similarity to all other stimuli. This representation, based on Shepard’s law, has a natural metric that does not have additive segments whilst still retaining the intuitive notion of connecting similarity and distance between stimuli. Furthermore, this representation has the psychologically appealing property that the distance between stimuli is bounded. |
| Fachbereich(e)/-gebiet(e): | 03 Fachbereich Humanwissenschaften 03 Fachbereich Humanwissenschaften > Institut für Psychologie 03 Fachbereich Humanwissenschaften > Institut für Psychologie > Modelle höherer Kognition |
| Hinterlegungsdatum: | 09 Jul 2018 09:13 |
| Letzte Änderung: | 12 Okt 2020 11:25 |
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