Seriation and Multidimensional Scaling: A Data Analysis Approach to Scaling Asymmetric Proximity Matrices

A number of model-based scaling methods have been developed that apply to asymmetric proximity matrices. A flexible data analysis approach is pro posed that combines two psychometric procedures— seriation and multidimensional scaling (MDS). The method uses seriation to define an empirical order ing of the stimuli, and then uses MDS to scale the two separate triangles of the proximity matrix defined by this ordering. The MDS solution con tains directed distances, which define an "extra" dimension that would not otherwise be portrayed, because the dimension comes from relations between the two triangles rather than within triangles. The method is particularly appropriate for the analysis of proximities containing temporal information. A major difficulty is the computa tional intensity of existing seriation algorithms, which is handled by defining a nonmetric seriation algorithm that requires only one complete itera tion. The procedure is illustrated using a matrix of co-citations between recent presidents of the Psychometric Society.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Clarity from Confusion: Using Intended Interactions to Design Information Systems

Two tools are described that help designers visualize the structure of a system in the requirements phase of a project. First, a matrix is constructed that represents the tendency of components to interact. The matrix is derived from sequence diagrams, which in turn are based on textual scenarios. This interaction matrix is transformed into a structure plot of the system, showing a graph of the essential connections between actors. Second, this same matrix is used to generate a sequence plot: a sequence diagram optimized for problem-solving. We illustrate the effectiveness of this approach, first with a simulation study, and later with a participant-based study of inference from diagrams. The results suggest that a similarity-based approach to information systems design can generate new testable tools. Pragmatically, the tools help novices and experts alike by automatically generating candidate system configurations in the form of structural diagrams, and by generating better sequence diagrams

The Past, Present, and Future of Multidimensional Scaling

Multidimensional scaling (MDS) has established itself as a standard tool for statisticians and applied researchers. Its success is due to its simple and easily interpretable representation of potentially complex structural data. These data are typically embedded into a 2-dimensional map, where the objects of interest (items, attributes, stimuli, respondents, etc.) correspond to points such that those that are near to each other are empirically similar, and those that are far apart are different. In this paper, we pay tribute to several important developers of MDS and give a subjective overview of milestones in MDS developments. We also discuss the present situation of MDS and give a brief outlook on its future

A Geneaology of Correspondence Analysis: Part 2 - The Variants

In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Australian and New Zealand Journal of Statistics. That genealogy consisted of more than 270 key books and articles and focused on an historical development of the correspondence analysis,a statistical tool which provides the analyst with a visual inspection of the association between two or more categorical variables. In this new genealogy, we provide a brief overview of over 30 variants of correspondence analysis that now exist outside of the traditional approaches used to analysethe association between two or more categorical variables. It comprises of a bibliography of a more than 300 books and articles that were not included in the 2012 bibliography and highlights the growth in the development ofcorrespondence analysis across all areas of research

A New Measure for Analyzing and Fusing Sequences of Objects

This work is related to the combinatorial data analysis problem of seriation used for data visualization and exploratory analysis. Seriation re-sequences the data, so that more similar samples or objects appear closer together, whereas dissimilar ones are further apart. Despite the large number of current algorithms to realize such re-sequencing, there has not been a systematic way for analyzing the resulting sequences, comparing them, or fusing them to obtain a single unifying one. We propose a new positional proximity measure that evaluates the similarity of two arbitrary sequences based on their agreement on pairwise positional information of the sequenced objects. Furthermore, we present various statistical properties of this measure as well as its normalized version modeled as an instance of the generalized correlation coefficient. Based on this measure, we define a new procedure for consensus seriation that fuses multiple arbitrary sequences based on a quadratic assignment problem formulation and an efficient way of approximating its solution. We also derive theoretical links with other permutation distance functions and present their associated combinatorial optimization forms for consensus tasks. The utility of the proposed contributions is demonstrated through the comparison and fusion of multiple seriation algorithms we have implemented, using many real-world datasets from different application domains

A comparison between preference judgments of curvature and sharpness in architectural façades

Can curvature drive preference, perceived familiarity, complexity, stability and approachability for architectural façades? In this study, we generated four versions of the same reference building, varying only the amount of curvature introduced in the façade. Participants’ judgments were measured using three experimental methodologies. Multidimensional scaling on forced choices showed that the curved façade was the most preferred. Multidimensional unfolding on ranking task showed that the majority of participants expressed higher preferences for the curved façade compared to the sharp-angled and rectilinear ones. Ratings on different psychological variables provided supporting evidence for curvature significantly influencing liking and approachability judgments. Results from image analyses –using a dynamical model of the visual cortex and a model that characterizes discomfort in terms of adherence to the statistics of natural images – matched behavioural data. We discuss the implications of the findings on our understanding of human preferences, which are intrinsically dynamic and influenced by context and experience.PostprintPeer reviewe