https://isiarticles.com/bundles/Article/pre/pdf/24298.pdf

Constrained linear regression models for symbolic interval-valued variables

Frequency Analysis and Periodicity Detection in Hearing.

The fuzzy approach to statistical analysis

Holt’s exponential smoothing and neural network models for forecasting interval-valued time series

An experimenter who performs a multidimensional analysis of speech perception data must deal with two problems: (1) differences among subjects in the data and (2) rotation of axes in the solution. The rotational problem is crucial when one seeks to determine whether the “true” perceptual dimensions correspond to a particular set of acoustic measures or articulatory features of the stimuli. A new multidimensional scaling technique devised by Carroll and Chang [Psychometrika, (1970) (to be published)] offers a solution to the rotational problem arrived at by capitalizing on individual differences: the axes derived are those that best account for variations among individuals in terms of a differential weighting model. This paper illustrates the promise this method holds for speech perception studies by an example: data on dissimilarities among nine Swedish vowels published by Hanson [Ericsson Technics 23, 3–175 (1967)] are re‐analyzed. Whereas the stimulus set represented three distinctive features, the published solution recovered only two. The Carroll‐Chang solution is interpretable in terms of all three features and formant frequencies as well. Additional procedures show that the two solutions differ chiefly in rotation and illustrate how other (superficially rational) rotational criteria can lead to less informative solutions.

Individual Differences and Multidimensional Scaling of Speech Perception Data

I-Scal: Multidimensional scaling of interval dissimilarities

Multidimensional scaling aims at reconstructing dissimilarities between pairs of objects by distances in a low dimensional space. However, in some cases the dissimilarity itself is unknown, but the range of the dissimilarity is given. Such fuzzy data fall in the wider class of symbolic data (Bock & Diday, 2000). Denœux and Masson (2002) have proposed to model an interval dissimilarity by a range of the distance defined as the minimum and maximum distance between two rectangles representing the objects. In this paper, we provide a new algorithm called SymScal that is based on iterative majorization. The advantage is that each iteration is guaranteed to improve the solution until no improvement is possible. In a simulation study, we investigate the quality of this algorithm. We discuss the use of SymScal on empirical dissimilarity intervals of sounds.

https://repub.eur.nl/pub/1924/ei2005-15.pdf

SymScal: symbolic multidimensional scaling of interval dissimilarities

Multidimensional scaling aims at reconstructing dissimilarities between pairs of objects by distances in a low dimensional space. However, in some cases the dissimilarity itself is unknown, but the range, or a histogram of the dissimilarities is given. This type of data fall in the wider class of symbolic data (see Bock and Diday (2000)). We model a histogram of dissimilarities by a histogram of the distances defined as the minimum and maximum distance between two sets of embedded rectangles representing the objects. In this paper, we provide a new algorithm called Hist-Scal using iterative majorization, that is based on an algorithm, I-Scal developed for the case where the dissimilarities are given by a range of values ie an interval (see Groenen et al. (in press)). The advantage of iterative majorization is that each iteration is guaranteed to improve the solution until no improvement is possible. We present the results on an empirical data set on synthetic musical tones.

Multidimensional Scaling of Histogram Dissimilarities

Multidimensional scaling aims at reconstructing dissimilarities between pairs of objects by distances in a low dimensional space. However, in some cases the dissimilarity itself is not known, but the range, or a histogram of the dissimilarities is given. This type of data fall in the wider class of symbolic data (see Bock and Diday (2000)). We model three-way two-mode data consisting of an interval of dissimilarities for each object pair from each of K sources by a set of intervals of the distances defined as the minimum and maximum distance between two sets of embedded rectangles representing the objects. In this paper, we provide a new algorithm called 3WaySym-Scal using iterative majorization, that is based on an algorithm, I-Scal developed for the two-way case where the dissimilarities are given by a range of values ie an interval (see Groenen et al. (2006)). The advantage of iterative majorization is that each iteration is guaranteed to improve the solution until no improvement is possible. We present the results on an empirical data set on synthetic musical tones.

/pdf/3waysym-scal-three-way-symbolic-multidimensional-scaling-wvuf06eztq.pdf

S. Winsberg

Papers

I-Scal: Multidimensional scaling of interval dissimilarities

SymScal: symbolic multidimensional scaling of interval dissimilarities

Multidimensional Scaling of Histogram Dissimilarities

3WaySym-Scal: three-way symbolic multidimensional scaling

3WaySym-Scal: three-way symbolic multidimensional scaling