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Dyadic multi-dimensionality informs the variation that exists within and between network ties and suggests that ties are not all the same and not all equally strategic. This chapter presents a model of dyadic evolution grounded in dyadic multi-dimensionality and framed within actor-level, dyadic-level, endogenous, and exogenous contexts. These contexts generate both strategic catalysts that motivate network action and bounded agency that may constrain such network action. Assuming the need to navigate within bounded agency, the model highlights three strategic processes that demonstrate how dyadic multi-dimensionality underlies the evolution of strategic network ties.

Identifying the dimensionality of a construct and selecting appropriate items for measuring the dimensions are important elements of marketing scale development. Scales for measuring marketing constructs such as service quality, brand equity, and marketing orientation have typically been developed using the influential classical test theory paradigm (Churchill, 1979), or some variant thereof. Users of the paradigm typically assume, albeit implicitly, that items and respondents are the only sources of variance and respondents are the objects of measurement. Yet, marketers need scales for other important managerial purposes, such as benchmarking, tracking, and perceptual mapping, each of which requires a scaling of objects other than respondents such as products, brands, retail stores, websites, firms, advertisements, or social media content. Scales that are developed without such objects in mind might not perform as expected. Finn and Kayande (2005) proposed a multivariate multiple objective random effects methodology (referred to here as M-MORE) could be used to identify construct dimensionality and select appropriate items for multiple objects of measurement. This chapter applies M-MORE to multivariate generalizability theory data collected to assess online retailer websites in the early 2000s to identify the dimensionality of and to select appropriate items for scaling website quality. The results are compared with those produced by traditional methods.

The purpose of this paper is to introduce a new hybrid method for reducing dimensionality of high dimensional data.

Literature on dimensionality reduction (DR) witnesses the research efforts that combine random projections (RP) and singular value decomposition (SVD) so as to derive the benefit of both of these methods. However, SVD is well known for its computational complexity. Clustering under the notion of concept decomposition is proved to be less computationally complex than SVD and useful for DR. The method proposed in this paper combines RP and fuzzy k‐means clustering (FKM) for reducing dimensionality of the data.

The proposed RP‐FKM is computationally less complex than SVD, RP‐SVD. On the image data, the proposed RP‐FKM has produced less amount of distortion when compared with RP. The proposed RP‐FKM provides better text retrieval results when compared with conventional RP and performs similar to RP‐SVD. For the text retrieval task, superiority of SVD over other DR methods noted here is in good agreement with the analysis reported by Moravec.

The hybrid method proposed in this paper, combining RP and FKM, is new. Experimental results indicate that the proposed method is useful for reducing dimensionality of high‐dimensional data such as images, text, etc.

This chapter addresses one aspect of the broad issue of the psychological foundations of the dimensions of multidimensional scaling (MDS) solutions. Using empirical data from three independent studies, it is shown that the dimensionality of MDS solutions is negatively related to individual differences in the level of cognitive differentiation and integrative complexity of individuals and positively related to the individual's ability to discriminate within dimensions. MDS dimensionality is also shown to be affected by a variety of task-related variables such as perceived task difficulty, consistency in providing similarity judgments, confidence, familiarity, and importance attached to the stimuli. The chapter concludes by raising the issue of whether MDS can be validly used to describe complex cognitive processes.

Aerodynamic shape optimisation is complex because of the high dimensionality of the problem, the associated non-linearity and its large computational cost. These three aspects have an impact on the overall time of the design process. To overcome these challenges, this paper aims to develop a method for transonic aerodynamic design with dimensionality reduction and multifidelity techniques.

The developed methodology is used for the optimisation of an installed civil ultra-high bypass ratio aero-engine nacelle. As such, the effects of airframe-engine integration are considered during the optimisation routine. The active subspace method is applied to reduce the dimensionality of the problem from 32 to 2 design variables with a database compiled with Euler computational fluid dynamics (CFD) calculations. In the reduced dimensional space, a co-Kriging model is built to combine Euler lower-fidelity and Reynolds-averaged Navier stokes higher-fidelity CFD evaluations.

Relative to a baseline aero-engine nacelle derived from an isolated optimisation process, the proposed method yielded a non-axisymmetric nacelle configuration with an increment in net vehicle force of 0.65% of the nominal standard net thrust.

This work investigates the viability of CFD optimisation through a combination of dimensionality reduction and multifidelity method and demonstrates that the developed methodology enables the optimisation of complex aerodynamic problems.

The purpose of this paper is to study the problem of fashion flat sketches classification and proposed an integrated approach. It aims to propose a fast, reliable method to handle multi-class fashion flat sketches classification problems and lay the foundation for the garment style query in the next step.

The proposed integrated approach adopts wavelet Fourier descriptor (WFD), linear discriminant analysis (LDA) and extreme learning machine (ELM). First, the discrete wavelet and Fourier transform are adopted to extract the shape features of fashion flat sketches. Then, LDA is employed for multi-class classification to reduce dimensionality. Finally, ELM is used as the classifier.

The experimental results show that the classification accuracy of the integrated approach is obtained at about 100 percent. Contrary to the traditional approaches, efficiency and accuracy are the advantages of the present approach.

Fashion concept is conveyed often in the form of the fashion illustration or sketch. This type of sketch is useful to imply the style and overall feel of the design. However, this sketch gives no clue about the parts or sections that make up each garment. For this reason, this paper only studies the classification of flat sketches.

A new shape descriptor named WFD is proposed. The WFD acquires high classification accuracy comparing with Fourier descriptor (FD) and multiscale Fourier descriptor (MFD) without dimensionality reduction and nearly the same classification accuracy comparing with FD while MFD easily causes small sample size problem with dimensionality reduction using LDA. In addition, ELM is first used as the classifier in the textiles field related to the classification problem.

Joint space multidimensional scaling (MDS) maps are often utilized for positioning analyses and are estimated with survey data of consumer preferences, choices, considerations, intentions, etc. so as to provide a parsimonious spatial depiction of the competitive landscape. However, little attention has been given to the possibility that consumers may display heterogeneity in their information usage (Bettman et al., 1998) and the possible impact this may have on the corresponding estimated joint space maps. This paper aims to address this important issue and proposes a new Bayesian multidimensional unfolding model for the analysis of two or three-way dominance (e.g. preference) data. The authors’ new MDS model explicitly accommodates dimension selection and preference heterogeneity simultaneously in a unified framework.

This manuscript introduces a new Bayesian hierarchical spatial MDS model with accompanying Markov chain Monte Carlo algorithm for estimation that explicitly places constraints on a set of scale parameters in such a way as to model a consumer using or not using each latent dimension in forming his/her preferences while at the same time permitting consumers to differentially weigh each utilized latent dimension. In this manner, both preference heterogeneity and dimensionality selection heterogeneity are modeled simultaneously.

The superiority of this model over existing spatial models is demonstrated in both the case of simulated data, where the structure of the data is known in advance, as well as in an empirical application/illustration relating to the positioning of digital cameras. In the empirical application/illustration, the policy implications of accounting for the presence of dimensionality selection heterogeneity is shown to be derived from the Bayesian spatial analyses conducted. The results demonstrate that a model that incorporates dimensionality selection heterogeneity outperforms models that cannot recognize that consumers may be selective in the product information that they choose to process. Such results also show that a marketing manager may encounter biased parameter estimates and distorted market structures if he/she ignores such dimensionality selection heterogeneity.

The proposed Bayesian spatial model provides information regarding how individual consumers utilize each dimension and how the relationship with behavioral variables can help marketers understand the underlying reasons for selective dimensional usage. Further, the proposed approach helps a marketing manager to identify major dimension(s) that could maximize the effect of a change of brand positioning, and thus identify potential opportunities/threats that existing MDS methods cannot provides.

To date, no existent spatial model utilized for brand positioning can accommodate the various forms of heterogeneity exhibited by real consumers mentioned above. The end result can be very inaccurate and biased portrayals of competitive market structure whose strategy implications may be wrong and non-optimal. Given the role of such spatial models in the classical segmentation-targeting-positioning paradigm which forms the basis of all marketing strategy, the value of such research can be dramatic in many marketing applications, as illustrated in the manuscript via analyses of both synthetic and actual data.

The purpose of this paper is to consider extension of the Kőnig‐Egerváry theorem to apply to matrices of dimensionality greater the two. It is shown that the theorem holds for matrices of any dimensionality, in the standard case where “cover” of selected elements is by lines, and the criterion for independence is also with reference to lines. Attention is also given to the case where cover and (hyper‐independence) are with reference to planes, or submatrices of higher dimensionality, rather than lines, and counter‐examples are given that show the theorem does not then hold universally. A preliminary survey is made of the diverse proofs that have been devised for the basic theorem, and in an Appendix an approach to the multidimensional Transportation Problem is reviewed.

Interest in generalisation of the theorem arose from the attempt to extend the Hungarian Method for the Assignment Problem to higher dimensionality. The results are also interesting as purely mathematical theory.

The theorem has been shown to extend to the multidimensional case when cover and independence are defined with reference to lines, but not universally otherwise.

Extension of the theorem to higher dimensionality has not produced a rigorous corresponding extension of the Hungarian Method, but may stimulate further studies. An approximate extension of the method (approximate insofar as it gives no guarantee of convergence on an optimum) will be described in a later publication. The study of the multidimensional Transportation Problem, reviewed in the Appendix, confirms the general difficulty of extending a class of methods from elegant solutions in the two‐dimensional case to versions for higher dimensionality.

The paper's results are believed to be original. Their main value is likely to be in stimulating interest that may lead to further developments as suggested.

Firm performance remains at the heart of strategic management. In the quest to refine the field’s contribution, Venkatraman and Ramanujam (1986) argued that reliance upon single measures of firm performance is risky and firm performance should be treated as a multidimensional construct. Subsequently, researchers have examined trends in firm performance measurement ever since. Over a decade since the last examination of this issue, this study aims to add to the ongoing conversation.

The authors investigated 1,972 research papers published in five premier management journals for the years 2015–2019 to determine if multidimensional measurement of firm performance has improved.

The findings suggest that approximately two-thirds of papers that measure firm performance are published using only a single measure of firm performance, and approximately three-fourths do not measure firm performance across multiple dimensions.

This study contributes to the literature by emphasizing the necessity to consider the dimensionality of firm performance, use multiple measures and consistently ground firm performance variables with theory – especially control variables – to keep firm performance as the focus of the strategy field. Evidence and implications are discussed and recommendations for researchers and reviewers are provided.

To overcome the shortcomings of traditional industry classification systems such as the Standard Industrial Classification Standard Industrial Classification, North American Industry Classification System North American Industry Classification System, and Global Industry Classification Standard Global Industry Classification Standard, the authors explore industry classifications using machine learning methods as an application of interpretable artificial intelligence (AI).

The authors propose a text-based industry classification combined with a machine learning technique by extracting distinguishable features from business descriptions in financial reports. The proposed method can reduce the dimensions of word vectors to avoid the curse of dimensionality when measuring the similarities of firms.

Using the proposed method, the sample firms form clusters of distinctive industries, thus overcoming the limitations of existing classifications. The method also clarifies industry boundaries based on lower-dimensional information. The graphical closeness between industries can reflect the industry-level relationship as well as the closeness between individual firms.

The authors’ work contributes to the industry classification literature by empirically investigating the effectiveness of machine learning methods. The text mining method resolves issues concerning the timeliness of traditional industry classifications by capturing new information in annual reports. In addition, the authors’ approach can solve the computing concerns of high dimensionality.