Multidimensional scaling: I. Theory and method

Torgerson, Warren S.

doi:10.1007/bf02288916

Cited by 1,806 publications

(1,113 citation statements)

References 4 publications

Supporting

Mentioning

1,038

Contrasting

Unclassified

Order By: Relevance

“…combining those dimensions that are redundant in the restraints space. In the most simple implementation of the MDS algorithm, distance would be the minimum number of links between two nodes [26,27]. In contrast, here we give distances the meaning of a travelling time, so the MDS algorithm will lump together those distances that correspond to fast interconversions (i.e.…”

Section: The Conformation Space Network Of Watermentioning

confidence: 99%

Structural Inhomogeneity of Water by Complex Network Analysis

2010

View full text Add to dashboard Cite

There is still an open debate regarding the structure forming capabilities of water at ambient conditions. In order to probe the presence of such inhomogeneities, we apply complex networks analysis methods to a molecular dynamics simulation at room temperature. This study provides both a structural and quantitative characterization of kinetically homogeneous substates present in bulk water. We find that the conformation-space-network is highly modular, and that structural properties of water molecules are spatially correlated over at least two solvation shells. From a kinetic point of view, the free energy surface is characterized by multiple heterogeneous metastable regions with different populations and marginal barriers separating them. The typical timescale of hopping between them is 200-400 fs. A scanning in temperature reveals that those substates can be stabilized either entropically or enthalpically. The latter resembles an ice-like domain that extends for at least two solvation shells.

show abstract

Section: The Conformation Space Network Of Watermentioning

confidence: 99%

Structural Inhomogeneity of Water by Complex Network Analysis

2010

View full text Add to dashboard Cite

show abstract

“…Early research into visual exploration of data led to approaches such as multidimensional scaling [21,11] and projection pursuit [6,9]. Most recent research on this topic (also referred to as manifold learning) is still inspired by the aim of multi-dimensional scaling; find a low-dimensional embedding of points such that their distances in the high-dimensional space are 9 The R implementation used to produce Tab.…”

Section: Related Workmentioning

confidence: 99%

Interactive Visual Data Exploration with Subjective Feedback

Puolamäki

Kang

Lijffijt

et al. 2016

Machine Learning and Knowledge Discovery in Databases

View full text Add to dashboard Cite

Abstract. Data visualization and iterative/interactive data mining are growing rapidly in attention, both in research as well as in industry. However, integrated methods and tools that combine advanced visualization and data mining techniques are rare, and those that exist are often specialized to a single problem or domain. In this paper, we introduce a novel generic method for interactive visual exploration of highdimensional data. In contrast to most visualization tools, it is not based on the traditional dogma of manually zooming and rotating data. Instead, the tool initially presents the user with an 'interesting' projection of the data and then employs data randomization with constraints to allow users to flexibly and intuitively express their interests or beliefs using visual interactions that correspond to exactly defined constraints. These constraints expressed by the user are then taken into account by a projection-finding algorithm to compute a new 'interesting' projection, a process that can be iterated until the user runs out of time or finds that constraints explain everything she needs to find from the data. We present the tool by means of two case studies, one controlled study on synthetic data and another on real census data.

show abstract

“…The foundational ideas behind multidimensional scaling were first proposed by Young and Householder [25], then further developed by Torgerson [24] and given the name of MDS. Considerable research has gone into devising faster and more robust solutions.…”

Section: Previous Workmentioning

confidence: 99%

“…These spectral methods find embedding coordinates by computing the top eigenvectors of a "double-centered" transformation of the distance matrix sorted by decreasing eigenvalue. The original algorithm, Classic MDS [24], [25] computed a costly O(N 3 ) singular value decomposition of this matrix. Modern classical scaling methods quickly estimate the eigenvectors using the power method or other more sophisticated iterative methods that employ O(N 2 ) matrix-vector products.…”

Section: A Classical Scalingmentioning

confidence: 99%

Glimmer: Multilevel MDS on the GPU

Ingram

Munzner

Olano

2009

IEEE Trans. Visual. Comput. Graphics

162

View full text Add to dashboard Cite

Abstract-We present Glimmer, a new multilevel algorithm for multidimensional scaling designed to exploit modern graphics processing unit (GPU) hardware. We also present GPU-SF, a parallel, force-based subsystem used by Glimmer. Glimmer organizes input into a hierarchy of levels and recursively applies GPU-SF to combine and refine the levels. The multilevel nature of the algorithm makes local minima less likely while the GPU parallelism improves speed of computation. We propose a robust termination condition for GPU-SF based on a filtered approximation of the normalized stress function. We demonstrate the benefits of Glimmer in terms of speed, normalized stress, and visual quality against several previous algorithms for a range of synthetic and real benchmark datasets. We also show that the performance of Glimmer on GPUs is substantially faster than a CPU implementation of the same algorithm.

show abstract

Multidimensional scaling: I. Theory and method

Cited by 1,806 publications

References 4 publications

Structural Inhomogeneity of Water by Complex Network Analysis

Structural Inhomogeneity of Water by Complex Network Analysis

Interactive Visual Data Exploration with Subjective Feedback

Glimmer: Multilevel MDS on the GPU

Contact Info

Product

Resources

About