Improving the efficiency and effectiveness of interactively selected MDS data designs

Green, Rex S.; Bentler, Peter M.

doi:10.1007/bf02293790

Cited by 6 publications

(7 citation statements)

References 6 publications

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“…The rms error remains below 9 mm for , even when nearly 40% of the measurements are unavailable, and also below 9 mm for , even when nearly 80% of the measurements are unavailable. These results confirm the statements of previous researchers that only about 25%-33% of the measurements are needed in practice [4], [5].…”

Section: B Handling Missing Datasupporting

confidence: 95%

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Microphone array position calibration by basis-point classical multidimensional scaling

Birchfield

Subramanya

2005

IEEE Trans. Speech Audio Process.

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Classical multidimensional scaling (MDS) is a global, noniterative technique for finding coordinates of points given their interpoint distances. We describe the algorithm and show how it yields a simple, inexpensive method for calibrating an array of microphones with a tape measure (or similar measuring device). We present an extension to the basic algorithm, called basis-point classical MDS (BCMDS), which handles the case when many of the distances are unavailable, thus yielding a technique that is practical for microphone arrays with a large number of microphones. We also show that BCMDS, when combined with a calibration target consisting of four synchronized sound sources, can be used for automatic calibration via time-delay estimation. We evaluate the accuracy of both classical MDS and BCMDS, investigating the sensitivity of the algorithms to noise and to the design parameters to yield insight as to the choice of those parameters. Our results validate the practical applicability of the algorithms, showing that errors on the order of 10-20 mm can be achieved in real scenarios.

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Section: B Handling Missing Datasupporting

confidence: 95%

“…The square of the residual distance from to the -axis can be computed from (2) and (3) (4) Rearranging terms yields a convenient formula that we will use again (5) Let us orient the axes so that a third point lies in the -plane (i.e.,…”

Section: B Deriving a 2-d Basismentioning

confidence: 99%

Microphone array position calibration by basis-point classical multidimensional scaling

Birchfield

Subramanya

2005

IEEE Trans. Speech Audio Process.

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“…However, the selection of the pairs before data collection results in little to no information on subsets of brands, respondents, and the relation between these two. The subset of brands can also be determined interactively during the judgment task [20]. However, such procedures are deterministic in nature, and the selection of which brands to be compared is based on technical details of the estimation procedure and not on brand or consumer factors that affect the quality of the judgments.…”

Section: The Scaling Of Large Brand Setsmentioning

confidence: 99%

Adaptive Multidimensional Scaling: Brand Positioning Based on Decision Sets and Dissimilarity Judgments

Bijmolt

Wedel

DeSarbo

2020

Cust. Need. and Solut.

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Assessing market structure by deriving a brand positioning map and segmenting customers is essential for supporting brand-related marketing decisions. We propose adaptive multidimensional scaling (ADMDS) for simultaneously deriving a brand positioning map and market segments using customer data on cognitive decision sets and brand dissimilarities. In ADMDS, the judgment task is adapted to the individual customer where dissimilarity judgments are collected only for those brands within a customers’ awareness set. Thus, respondent fatigue and unfamiliarity with the brands are circumvented thereby improving the validity of the dissimilarity data obtained, as well as the multidimensional spatial structure derived from them. Estimation of the ADMDS model results in a spatial map in which the brands and derived segments of customers are jointly represented as points. The closer a brand is positioned to a segment’s ideal brand, the higher the probability that the brand is considered and chosen. An assumption underlying this model representation is that brands within a customers’ consideration set are relatively similar. In an experiment with 200 respondents and 4 product categories, this assumption is validated. We illustrate adaptive multidimensional scaling model on commercial data for 20 midsize car brands evaluated by 212 members of an on-line consumer panel. Potential applications of the method and future research opportunities are discussed.

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“…Monte carlo evaluation (Baker & Young, 1978;Girard & Cliff, 1976;Hamer, 1978) has shown that when the Euclidean assumption is satisfied, ISIS performs well using only 25Te to 45% of the possible pairs and is generally superior to fixed designs with the same fraction of data. On the basis of monte carlo, and other work, an improved program called INTERS CAL has been developed (Cliff, Girard, Green, Kehoe, & I~®herty, 1977;Green & Bentler, 1979) and should probably be preferred to the earlier versions of ISIS. Of course, when the data do not satisfy the Euclidean assumption, it may be desirable to consider fixed designs or a procedure like ISO, which is discussed below.…”

Section: Incomplete Design Studiesmentioning

confidence: 99%

Monte Carlo Simulation Studies

Spence

1983

Applied Psychological Measurement

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This paper reviews the use of the monte carlo method to help illuminate various issues in the area of multidimensional scaling. Both two-way and three- way multidimensional scaling models and procedures are considered. Sampling distribution studies, studies comparing different procedures, and studies that have examined the basic capabilities of the methods under a variety of conditions are reviewed. Based upon the simulations, recommendations are given regarding several problems that face the user of multidimen sional scaling techniques, for example, choosing a computer program, deciding upon the appropriate di mensionality or whether useful structure exists in the data, and dealing with large stimulus sets. Practical advice is given regarding the use of several computer programs, including M-D-SCAL, TORSCA, SSA-I, KYST, MINISSA-I, INDSCAL, ALSCAL, and MULTISCALE, as well as traditional Young-House holder-Torgerson scaling.

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Improving the efficiency and effectiveness of interactively selected MDS data designs

Abstract: multidimensional scaling, INTERSCAL, incomplete data designs,

Cited by 6 publications

References 6 publications

Microphone array position calibration by basis-point classical multidimensional scaling

Microphone array position calibration by basis-point classical multidimensional scaling

Adaptive Multidimensional Scaling: Brand Positioning Based on Decision Sets and Dissimilarity Judgments

Monte Carlo Simulation Studies

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