Inverse MDS: Inferring dissimilarity structure from multiple item arrangements
The pairwise dissimilarities of a set of items can be intuitively visualized by a 2D arrangement of the items, in which the distances reflect the dissimilarities. Such an arrangement can be obtained by multidimensional scaling (MDS). We propose a method for the inverse process: inferring the pairwis...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2012-07-01
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| Series: | Frontiers in Psychology |
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| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fpsyg.2012.00245/full |
| _version_ | 1818509439299223552 |
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| author | Nikolaus eKriegeskorte Marieke eMur Marieke eMur |
| author_facet | Nikolaus eKriegeskorte Marieke eMur Marieke eMur |
| author_sort | Nikolaus eKriegeskorte |
| collection | DOAJ |
| description | The pairwise dissimilarities of a set of items can be intuitively visualized by a 2D arrangement of the items, in which the distances reflect the dissimilarities. Such an arrangement can be obtained by multidimensional scaling (MDS). We propose a method for the inverse process: inferring the pairwise dissimilarities from multiple 2-dimensional arrangements of items. Perceptual dissimilarities are classically measured using pairwise dissimilarity judgments. However, alternative methods including free sorting and 2D arrangements have previously been proposed. The present proposal is novel (a) in that the dissimilarity matrix is estimated by inverse MDS based on multiple arrangements of item subsets, and (b) in that the subsets are designed by an adaptive algorithm that aims to provide optimal evidence for the dissimilarity estimates. The subject arranges the items (represented as icons on a computer screen) by means of mouse drag-and-drop operations. The multi-arrangement method can be construed as a generalization of simpler methods: It reduces to pairwise dissimilarity judgments if each arrangement contains only two items, and to free sorting if the items are categorically arranged into discrete piles. Multi-arrangement combines the advantages of these methods. It is efficient (because the subject communicates many dissimilarity judgments with each mouse drag), psychologically attractive (because dissimilarities are judged in context), and can characterize continuous high-dimensional dissimilarity structures. We present two procedures for estimating the dissimilarity matrix: a simple weighted-aligned-average of the partial dissimilarity matrices and a computationally intensive algorithm, which estimates the dissimilarity matrix by iteratively minimizing the error of MDS-predictions of the subject’s arrangements. The Matlab code for interactive arrangement and dissimilarity estimation is available from the authors upon request. |
| first_indexed | 2024-12-10T22:45:28Z |
| format | Article |
| id | doaj.art-db2a6b615eb94730b593f4872805a86a |
| institution | Directory Open Access Journal |
| issn | 1664-1078 |
| language | English |
| last_indexed | 2024-12-10T22:45:28Z |
| publishDate | 2012-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Psychology |
| spelling | doaj.art-db2a6b615eb94730b593f4872805a86a2022-12-22T01:30:36ZengFrontiers Media S.A.Frontiers in Psychology1664-10782012-07-01310.3389/fpsyg.2012.0024528167Inverse MDS: Inferring dissimilarity structure from multiple item arrangementsNikolaus eKriegeskorte0Marieke eMur1Marieke eMur2Medical Research Council Cognition and Brain Sciences UnitMedical Research Council Cognition and Brain Sciences UnitMaastricht UniversityThe pairwise dissimilarities of a set of items can be intuitively visualized by a 2D arrangement of the items, in which the distances reflect the dissimilarities. Such an arrangement can be obtained by multidimensional scaling (MDS). We propose a method for the inverse process: inferring the pairwise dissimilarities from multiple 2-dimensional arrangements of items. Perceptual dissimilarities are classically measured using pairwise dissimilarity judgments. However, alternative methods including free sorting and 2D arrangements have previously been proposed. The present proposal is novel (a) in that the dissimilarity matrix is estimated by inverse MDS based on multiple arrangements of item subsets, and (b) in that the subsets are designed by an adaptive algorithm that aims to provide optimal evidence for the dissimilarity estimates. The subject arranges the items (represented as icons on a computer screen) by means of mouse drag-and-drop operations. The multi-arrangement method can be construed as a generalization of simpler methods: It reduces to pairwise dissimilarity judgments if each arrangement contains only two items, and to free sorting if the items are categorically arranged into discrete piles. Multi-arrangement combines the advantages of these methods. It is efficient (because the subject communicates many dissimilarity judgments with each mouse drag), psychologically attractive (because dissimilarities are judged in context), and can characterize continuous high-dimensional dissimilarity structures. We present two procedures for estimating the dissimilarity matrix: a simple weighted-aligned-average of the partial dissimilarity matrices and a computationally intensive algorithm, which estimates the dissimilarity matrix by iteratively minimizing the error of MDS-predictions of the subject’s arrangements. The Matlab code for interactive arrangement and dissimilarity estimation is available from the authors upon request.http://journal.frontiersin.org/Journal/10.3389/fpsyg.2012.00245/fullrepresentationSimilaritymultidimensional scalingrepresentational similarity analysissimilarity judgment |
| spellingShingle | Nikolaus eKriegeskorte Marieke eMur Marieke eMur Inverse MDS: Inferring dissimilarity structure from multiple item arrangements Frontiers in Psychology representation Similarity multidimensional scaling representational similarity analysis similarity judgment |
| title | Inverse MDS: Inferring dissimilarity structure from multiple item arrangements |
| title_full | Inverse MDS: Inferring dissimilarity structure from multiple item arrangements |
| title_fullStr | Inverse MDS: Inferring dissimilarity structure from multiple item arrangements |
| title_full_unstemmed | Inverse MDS: Inferring dissimilarity structure from multiple item arrangements |
| title_short | Inverse MDS: Inferring dissimilarity structure from multiple item arrangements |
| title_sort | inverse mds inferring dissimilarity structure from multiple item arrangements |
| topic | representation Similarity multidimensional scaling representational similarity analysis similarity judgment |
| url | http://journal.frontiersin.org/Journal/10.3389/fpsyg.2012.00245/full |
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