Asymmetric multidimensional scaling of two-mode three-way proximities

Okada, Akinori; Imaizumi, Tadashi

doi:10.1007/s003579900010

Cited by 60 publications

(11 citation statements)

References 30 publications

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“…Chino, 1990); while models of most of the other asymmetric multidimensional scaling represent two components separately (Borg & Groenen, 2005, ch. 23;Chino, 1990;Okada & Imaizumi, 1987, 1997Zielman & Heiser, 1993, 1996. This suggests that the interpretation of the result of the present asymmetric multidimensional scaling is not difficult.…”

Section: The Methodsmentioning

confidence: 58%

“…The present brand switching matrix was not normalized before the analysis (cf. Harshman, Green, Wind, & Lundy, 1982;Okada, 1988;Okada & Imaizumi, 1987, 1997. In the present study the matrix of raw frequencies among 12 margarine brands was analyzed by asymmetric multidimensional scaling (Okada, 2009(Okada, , 2011 which also was used to analyze the car switching data (Okada, in press).…”

Section: The Datamentioning

confidence: 99%

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Asymmetric Multidimensional Scaling of Brand Switching Among Margarine Brands

Okada

Tsurumi

2012

Behaviormetrika

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Brand switching data among 12 margarine brands were analyzed by the asymmetric multidimensional scaling based on the singular value decomposition. A two-dimensional result was adopted as the solution. A configuration based on the left and right singular vectors is given along each dimension. The left singular vector represents an outward tendency of switching from the corresponding brand to the other brands, and the right singular vector represents an inward tendency of being switched to the corresponding brand from the other brands. The configuration along Dimension 1 shows that the three brands with the larger market share compete vigorously with each other. The configuration along Dimension 2 classifies 12 brands into two groups; the brand switching between two groups is small, while that within each group is large.

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Section: The Methodsmentioning

confidence: 58%

Section: The Datamentioning

confidence: 99%

Asymmetric Multidimensional Scaling of Brand Switching Among Margarine Brands

Okada

Tsurumi

2012

Behaviormetrika

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“…The research of Okada and Imaizumi [12][13][14] is focused on using the dominance point governing asymmetry in the proximity relationships among objects, represented as points in the multidimensional Euclidean space. They claim that ignoring or neglecting the asymmetry in proximity analysis discards potentially valuable information.…”

Section: Asymmetry In Datamentioning

confidence: 99%

Asymmetric k-means Clustering of the Asymmetric Self-Organizing Map

Olszewski

Kacprzyk

Zadrożny

2014

Artificial Intelligence and Soft Computing

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Abstract. In this paper, an asymmetric approach to clustering of the asymmetric Self-Organizing Map (SOM) is proposed. The clustering is performed using an improved asymmetric version of the well-known kmeans algorithm. The improved asymmetric k-means algorithm is the second proposal of this paper. As a result, we obtain the two-stage fullyasymmetric data analysis technique. In this way, we maintain the structural consistency of the both utilized methods, because they are both formulated in asymmetric version, and consequently, they both properly adjust to asymmetric relationships in analyzed data. The results of our experiments confirm the effectiveness of the proposed approach.

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“…Some of them deal with twomode three-way proximities (see e.g. : Zielman, Heiser 1993, DeSarbo et al 1992, Okada, Imaizumi 1997, and some deal with one-mode two-way proximities (see e.g. : Borg, Groenen 2005: 495-516, Okada, Imaizumi 2007.…”

Section: Introductionmentioning

confidence: 99%

The Presentation of Changes in Preferences by Dynamic Scaling

Zaborski

2016

Folia Oeconomica

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Dynamic scaling is a set of methods in which the geometrical representation of the similarity data for T different time periods is made. This article presents the use of two-dynamic scaling methods for studying changes in the preferences. In the first method the location of points on the perceptual map is made on the basis of the super-dissimilarity matrix. In the second method multidimensional scaling for the respective periods is carried out and the obtained configurations are matched by transformations preserving the proportions of distances between points. The presentation of the methods is illustrated by an empirical example in which calculations were performed with use of SPSS and New MDSX packages.

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Asymmetric multidimensional scaling of two-mode three-way proximities

Abstract: Asymmetric proximity, Multidimensional scaling, Two-mode three-way data,

Cited by 60 publications

References 30 publications

Asymmetric Multidimensional Scaling of Brand Switching Among Margarine Brands

Asymmetric Multidimensional Scaling of Brand Switching Among Margarine Brands

Asymmetric k-means Clustering of the Asymmetric Self-Organizing Map

The Presentation of Changes in Preferences by Dynamic Scaling

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