An evaluation of the use of multidimensional scaling for understanding brain connectivity

Abstract

A large amount of data is now available about the pattern of connections between brain regions. Computational methods are increasingly relevant for uncovering structure in such datasets. There has been recent interest in the use of non-metric multidimensional scaling (NMDS) for such analysis. NMDS produces a spatial representation of the 'dissimilarities' between a number of entities. Normally, it is applied to data matrices containing a large number of levels of dissimilarity, whereas for brain connectivity data there is a very small number. We address the suitability of NMDS for this case. Systematic numerical studies are presented to evaluate the ability of this method to reconstruct known geometrical configurations from dissimilarity data processing few levels. In this case there is a strong bias for NMDS to produce annular configurations, whether or not such structure exists in the original data. For the case of a connectivity dataset derived from the primate cortical visual system, we demonstrate that great caution is needed in interpreting the resulting configuration. Application of an independent method that we developed also strongly suggests that the visual system NMDS configuration is affected by an annular bias. We question the strength of support that an NMDS analysis of the visual system data provides for the two streams view of visual processing.

Complex networks: Structure and dynamics

“…The organization into clusters has been evaluated by means of a non-parametric clustering [724,737] or a hierarchical clustering approach [735]. Although a careful statistical analysis is required in interpreting results from the NMDS of small data sets [738], the topology obtained suggested a clustering organization of cortical brain areas which is consistent with neurophysiological studies [724,727,729,[733][734][735].…”

Comparison of Methods for Collecting and Modeling Dissimilarity Data: Applications to Complex Sound Stimuli

“…The • transform decreases the strength of horseshoe and annular biases in nonmetric MDS (Goodhill et al, 1995), and does not alter the accuracy of MDS models of noisy data such as the behavioral dissimilarities from this study (Dragsgow & Jones, 1979). For consistency, binary dissimilarities were •-transformed prior to fitting any model.…”

“…The primary approach to ties, which attempts to assign the same model distance to tied input data, was not considered, because it is prone to annular and horseshoe biases (Goodhill et al, 1995). With the exception of CENM and CENMSQ, which have an exact least-squares solution, all models involve iterative criterion-minimization routines and are thus potentially prone to local minima problems (i.e., the fitting routines are not always guaranteed to converge on a globally optimal solution).…”

“…However, the price of the increased efficiency is seldom considered: for example, free sorts are known to be less accurate than dissimilarity ratings (Subkoviak & Roecks, 1976). Further, other differences between free sorting and dissimilarity ratings are simply unknown: no study has compared their reliability, and redundancy studies (Bertino & Lawless, 1993;Bonebright, 1996;Cartier et al, 2006;Ward, 1977) are often carried out by focusing on MDS models, rather than on raw data (for an exception, see Harbke, 2003), despite the known inaccuracies of the MDS analysis of the binary freesorting dissimilarities (Goodhill, Simmen, & Willshaw, 1995;Kendall, 1975;Simmen, 1996) and the vulnerability of the fit of these models to variations in the distributional properties of the input data (Pruzansky, Tversky, & Carroll, 1982).…”

Feed-forward neural networks and topographic mappings for exploratory data analysis

“…More recently, MDS has been applied to analysis of the connectivity of regions within the primate visual cortex [33]. However, in response to this, some controversy has arisen surrounding the interpretation of MDS feature spaces as to whether such maps imply genuine structure in the original data, or alternatively, whether such apparent structure is an artefact of the method [6]. Recall our previous comments that care should be taken in interpreting any method of dimension-reducing topographic mapping.…”