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  1. Applied Multidimensional Scaling | Ingwer Borg | Springer
  2. Description
  3. INTRODUCTION
  4. Multidimensional scaling

Throughout this paper, if X upper case denotes a matrix, then we use lower case xij to denote its elements, xTi to denote its row vectors.

Applied Multidimensional Scaling | Ingwer Borg | Springer

Definition 2 Euclidean Distance Matrix. Generally, we neither know zi0 s nor the dimension q. We want to find a set of x1 , x2 , In a lower dimension, we will not be able to preserve the exact interpoint distances. In a higher dimension space, we will lose the uniqueness. So S is already double-centered. ZZ T is positive semi-definite, thus S is also positive semi-definite.

Following is the main theorem that finds a matrix X that takes D as its distance matrix: Theorem 1. Furthermore, this matrix X has columns summing up to zero. If X is a solution, then a rotation of X product of X with an orthogonal matrix is also a solution, since orthogonal transformations preserve dot product, thus preserve distances. So the sum of each column of X is zero. Then the process to find X that takes D as its interpoint distances is as followed: 1 1. The way to do it is fairly simple. Starting from matrix X that fully preserves interpoint distances above, we pick only the first k columns of X we make the same assumption that X is built by ranking the eigenvalues in decreasing order.

This set of row vectors of this new matrix would be the set of points that best preserves original interpoint distances. We state the following theorem about this result: Theorem 2. Theorem 3. If D is a distance matrix not necessary Euclidean , and k fixed.

Description

This will yield a set of n points in k-dimension space that best preserve original interpoint distances best in the sense of minimizing the loss function defined above. In , member of the House voted on roll calls. We ignore the first one, which is just Call of the House, and the second one, which vote for the House Speaker. Of the members, there are that members that vote from the beginning to the end. We will only consider these members. The plot is for the year , , , and We label the Democrats blue, and the Republican red, other parties green. User Tools. Sign In. Advanced Search.

Article Navigation. Research Article February 01, Visualizing the sedimentary response through the orogenic cycle: A multidimensional scaling approach Christopher J. Spencer Christopher J.

INTRODUCTION

Google Scholar. Christopher L. Kirkland Christopher L. Lithosphere 8 1 : Article history received:. To assess the relationship between detrital zircon populations and the tectonic settings of the Albany-Fraser orogeny in Western Australia Fig. Figure 1. View large Download slide. TABLE 1. Volume 8, Number 1. Previous Article Next Article. View Full GeoRef Record. Search ADS. Timing of sedimentation, metamorphism, and plutonism in the Helgeland nappe complex, north-central Norwegian Caledonides. Neoproterozoic recycling of the Sveconorwegian orogenic belt: Detrital-zircon data from the Sparagmite basins in the Scandinavian Caledonides.

Detrital zircon ages and Nd isotopic data from the Southern Appalachian crystalline core, Georgia, South Carolina, North Carolina, and Tennessee: New provenance constraints for part of the Laurentian margin. Ion microprobe age and geochemistry of Southern Appalachian basement, with implications for Proterozoic and Paleozoic reconstructions.

Paleogeographic development of the east Laurentian margin: Constraints from U-Pb dating of detrital zircons in the Newfoundland Appalachians. Source of the Dalradian Supergroup constrained by U-Pb dating of detrital zircon and implications for the East Laurentian margin. Laurentian provenance and an intracratonic tectonic setting for the Moine Supergroup, Scotland, constrained by detrital zircons from the Loch Eil and Glen Urquhart successions.

Provenance record of Laurentian passive-margin strata in the northern Caledonides: Implications for paleodrainage and paleogeography. Sedimentary basin and detrital zircon record along East Laurentia and Baltica during assembly and breakup of Rodinia.


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Neoproterozoic to early Paleozoic extensional and compressional history of East Laurentian margin sequences: The Moine Supergroup, Scottish Caledonides. Peri-Gondwana elements in the Caledonian nappes of Finnmark, northern Norway: Implications for the paleogeographic framework of the Scandinavian Caledonides.

U-Pb age constraints for the lithotectonic evolution of the Grenville Province along the Mauricie transect. Evidence for multiple recycling in Neoproterozoic through Pennsylvanian sedimentary rocks of the Central Appalachian Basin. Mesoproterozoic sedimentation, magmatism, and metamorphism in the southern part of the Grenville Province western Quebec : U-Pb geochronological constraints.

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Multidimensional scaling

Provenance of the Moine Supergroup of NW Scotland: Evidence from geochronology of detrital and inherited zircons from meta sedimentary rocks, granites and migmatites. Exhumed Himalayan-type syntaxis in the Grenville orogen, northeastern Laurentia. The Baltoscandian margin detrital zircon signatures of the central Scandes. Paleozoic and Triassic paleogeography and tectonics of western Nevada and Northern California. Cordilleran-margin quartzites in Baja California—Implications for tectonic transport.

The Putumayo orogen of Amazonia and its implications for Rodinia reconstructions: New U-Pb geochronological insights into the Proterozoic tectonic evolution of northwestern South America. Grenvillian and Caledonian evolution of eastern Svalbard—A tale of two orogenies. Granitic magmatism of Grenvillian and late Neoproterozoic age in Finnmark, Arctic Norway—Constraining pre-Scandian deformation in the Kalak nappe complex. Provenance and terrane evolution of the Kalak nappe complex, Norwegian Caledonides: Implications for Neoproterozoic paleogeography and tectonics.

Detrital zircon signature of the Moine Supergroup, Scotland: Contrasts and comparisons with other Neoproterozoic successions within the circum—North Atlantic region. Foreign contemporaries—Unravelling disparate isotopic signatures from Mesoproterozoic Central and Western Australia. The affinity of Archean crust on the Yilgarn—Albany-Fraser orogen boundary: Implications for gold mineralisation in the Tropicana zone. Understanding the roles of crustal growth and preservation in the detrital zircon record.

Evidence for Neoproterozoic orogenesis and early high temperature Scandian deformation events in the southern East Greenland Caledonides. Detrital zircon, detrital titanite and igneous clast U-Pb geochronology and basement-cover relationships of the Colonsay Group, SW Scotland: Laurentian provenance and correlation with the Neoproterozoic Dalradian Supergroup.

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Sampling Laurentia: Detrital zircon geochronology offers evidence for an extensive Neoproterozoic river system originating from the Grenville orogen. Detrital zircon geochronology and provenance of the Torridonian, NW Scotland. Continental growth and reworking on the edge of the Columbia and Rodinia supercontinents; 1. Geochronology of detrital zircons from the Elzevir and Frontenac terranes, Central metasedimentary belt, Grenville Province. Mixture modeling of multi-component data sets with application to ion-probe zircon ages.

Sensitive high resolution ion microprobe SHRIMP detrital zircon geochronology provides new evidence for a hidden Neoproterozoic foreland basin to the Grenville. Schneider Santos. Sensitive high resolution ion microprobe SHRIMP detrital zircon geochronology provides new evidence for a hidden Neoproterozoic foreland basin to the Grenville orogen in the eastern Midwest, U. Quantitative comparison of large sets of geochronological data using multivariate analysis: A provenance study example from Australia.

Comparison of detrital zircon age distributions by kernel functional estimation. Provenance of Neoproterozoic to Upper Cretaceous sedimentary rocks, eastern Greenland: Implications for recognizing the sources of sediments in the Norwegian Sea. Transformation of an Archean craton margin during Proterozoic basin formation and magmatism: The Albany—Fraser orogen, Western Australia.

Intermontane basins and bimodal volcanism at the onset of the Sveconorwegian Orogeny, southern Norway. Generation and preservation of continental crust in the Grenville orogeny. Genetic relationship of rift-stage crustal structure, terrane accretion, and foreland tectonics along the Southern Appalachian-Ouachita orogen.

Multidimensional Scaling

U-Pb age constraints on arenaceous and volcanic rocks of the Wakeham Group, eastern Grenville Province. Van Kranendonk. The Parry Sound domain: A far-travelled allochthon? New evidence from U-Pb zircon geochronology. Isotopic constraints on stratigraphy in the central and eastern Yilgarn craton, Western Australia. Citing articles via Web of Science Email alerts New issue alert. Early publications alert. Article activity alert. Related Articles. F — Goldschmidt Abstracts Mineralogical Magazine.

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