Multidimensional Scaling of Varietal Data in Sedimentary Provenance Analysis

Vermeesch P, Lipp AG, Hatzenbühler D, Caracciolo L, Chew D (2023)

Publication Type: Journal article

Publication year: 2023


Book Volume: 128

Article Number: e2022JF006992

Journal Issue: 3

DOI: 10.1029/2022JF006992


Varietal studies of sedimentary provenance use the properties of individual minerals or mineral groups. These are recorded as lists of numerical tables that can be difficult to interpret. Multidimensional Scaling (MDS) is a popular multivariate ordination technique for analyzing other types of provenance data based on, for example, detrital geochronology or petrography. Applying MDS to varietal data would allow them to be treated on an equal footing with those other provenance proxies. MDS requires a method to quantify the dissimilarity between two samples. This paper introduces three ways to do so. The first method (“treatment-by-row”) turns lists of (compositional) data tables into lists of vectors, using principal component analysis. These lists of vectors can then be treated as “distributional” data and subjected to MDS analysis using dissimilarity measures such as the Kolmogorov-Smirnov statistic. The second method (“treatment-by-column”) turns lists of compositional data tables into multiple lists of vectors, each representing a single component of the varietal data. These multiple distributional data sets are subsequently subjected to Procrustes analysis or 3-way MDS. The third method uses the Wasserstein-2 distance to jointly compare the rows and columns of varietal data. This arguably makes the best use of the data but acts more like a “black box” than the other two methods. Applying the three methods to a detrital titanite data set from Colombia yields similar results. After converting varietal data to dissimilarity matrices, they can be combined with other types of provenance data, again using Procrustes analysis or 3-way MDS.

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Vermeesch, P., Lipp, A.G., Hatzenbühler, D., Caracciolo, L., & Chew, D. (2023). Multidimensional Scaling of Varietal Data in Sedimentary Provenance Analysis. Journal of Geophysical Research F: Earth Surface, 128(3).


Vermeesch, P., et al. "Multidimensional Scaling of Varietal Data in Sedimentary Provenance Analysis." Journal of Geophysical Research F: Earth Surface 128.3 (2023).

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