Multidimensional Scaling

Abstract

Multidimensional scaling is a statistical technique to visualize dissimilarity data. In multidimensional scaling, objects are represented as points in a usually two dimensional space, such that the distances between the points match the observed dissimilarities as closely as possible. Here, we discuss what kind of data can be used for multidimensional scaling, what the essence of the technique is, how to choose the dimensionality, transformations of the dissimilarities, and some pitfalls to watch out for when using multidimensional scaling.

Assessing and Quantifying Clusteredness: The OPTICS Cordillera

“…Projections were made based on the IPCC high emission scenario (A2) and the moderate emission scenario (B1) (Nakicenovic and We subject the dataset to six dimension-reduction techniques for visualization and representation in two dimensions: PCA (e.g., Jolliffe 2002), locally linear embedding (LLE; Roweis and Saul 2000), Sammon mapping (Sammon 1969), Isomap (Tenenbaum, De Silva, and Langford 2000), Power-Stress MDS (POST-MDS; Buja et al 2008;Groenen and De Leeuw 2010) and t-SNE (van der Maaten and Hinton 2008) and explore the clusteredness structure in these results.…”

Identification of new food alternatives: How do consumers categorize meat and meat substitutes?

“…The co-occurrence matrix was submitted to a multi-dimensional scaling (MDS) procedure (ALSCAL procedure in SPSS). This analysis gives a visual presentation of the perceptual distance between products by a reduction of the co-occurrence data into a 2-dimensional space (see Faye et al (2006) and Groenen & Van de Velden (2005) for more background on MDS). The goodness of fit was only moderate (stress value of 0.18), so in order to have a more fine-grained picture of the relation between products, a hierarchical cluster analysis was performed with the co-occurrence matrix (method: between-group linkage and chi-square measure) to generate a clusterdendogram.…”

Dimensional mapping: Applying DQR and MDS to explore the perceptions of seniors' role in advertising

“…Several formal criteria are commonly found in literature (e.g., MSPACE, screeplot), mainly based on stress values indicating goodness of fit (Kruskal & Wish, 1977;Spence & Graef, 1974;Young & Hamer, 1994). Many authors, however, are skeptical about using goodness-of-fit criteria as primary indicators for choosing dimensionality (Groenen & Van de Velden, 2005;Jaworska & ChupetlovskaAnastasova, 2009;Steyvers, 2002;Wu, 2006). As pointed out by Chen (2003, p. 79), the ultimate goal of MDS is not merely to minimize the stress value but to generate a meaningful and informative map of the assessed stimuli.…”