Multidimensional Scaling for Interval Data: INTERSCAL
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910294109847552 |
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| author | Winsberg, Susanne Rodriguez, Oldemar Diday, Edwin |
| author_facet | Winsberg, Susanne Rodriguez, Oldemar Diday, Edwin |
| contents | Standard multidimensional scaling takes as input a dissimilarity matrix of general term $δ_{ij}$ which is a numerical value. In this paper we input $δ_{ij}=[\underline{δ_{ij}},\overline{δ_{ij}}]$ where $\underline{δ_{ij}}$ and $\overline{δ_{ij}}$ are the lower bound and the upper bound of the ``dissimilarity'' between the stimulus/object $S_i$ and the stimulus/object $S_j$ respectively. As output instead of representing each stimulus/object on a factorial plane by a point, as in other multidimensional scaling methods, in the proposed method each stimulus/object is visualized by a rectangle, in order to represent dissimilarity variation. We generalize the classical scaling method looking for a method that produces results similar to those obtained by Tops Principal Components Analysis. Two examples are presented to illustrate the effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multidimensional Scaling for Interval Data: INTERSCAL Winsberg, Susanne Rodriguez, Oldemar Diday, Edwin Methodology Standard multidimensional scaling takes as input a dissimilarity matrix of general term $δ_{ij}$ which is a numerical value. In this paper we input $δ_{ij}=[\underline{δ_{ij}},\overline{δ_{ij}}]$ where $\underline{δ_{ij}}$ and $\overline{δ_{ij}}$ are the lower bound and the upper bound of the ``dissimilarity'' between the stimulus/object $S_i$ and the stimulus/object $S_j$ respectively. As output instead of representing each stimulus/object on a factorial plane by a point, as in other multidimensional scaling methods, in the proposed method each stimulus/object is visualized by a rectangle, in order to represent dissimilarity variation. We generalize the classical scaling method looking for a method that produces results similar to those obtained by Tops Principal Components Analysis. Two examples are presented to illustrate the effectiveness of the proposed method. |
| title | Multidimensional Scaling for Interval Data: INTERSCAL |
| topic | Methodology |
| url | https://arxiv.org/abs/2401.05466 |