Eigensolver Methods for Progressive Multidimensional Scaling of Large Data

2003 ◽

Vol 02 (01) ◽

pp. 135-159 ◽

Cited By ~ 12

Author(s):

SUNG-GI LEE ◽

DEOK-KYUN YUN

Keyword(s):

Multidimensional Scaling ◽

Clustering Algorithms ◽

Numerical Data ◽

Large Data ◽

Careful Analysis ◽

Mixed Data ◽

Coordinate Space ◽

Data Sets ◽

Categorical Attributes ◽

Categorical Attribute

In this paper, we present a concept based on the similarity of categorical attribute values considering implicit relationships and propose a new and effective clustering procedure for mixed data. Our procedure obtains similarities between categorical values from careful analysis and maps the values in each categorical attribute into points in two-dimensional coordinate space using multidimensional scaling. These mapped values make it possible to interpret the relationships between attribute values and to directly apply categorical attributes to clustering algorithms using a Euclidean distance. After trivial modifications, our procedure for clustering mixed data uses the k-means algorithm, well known for its efficiency in clustering large data sets. We use the familiar soybean disease and adult data sets to demonstrate the performance of our clustering procedure. The satisfactory results that we have obtained demonstrate the effectiveness of our algorithm in discovering structure in data.

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Goodness-of-fit filtering in classical metric multidimensional scaling with large datasets

10.1101/708339 ◽

2019 ◽

Author(s):

Jan Graffelman

Keyword(s):

Multidimensional Scaling ◽

Goodness Of Fit ◽

Large Data ◽

Distance Matrix ◽

Large Data Sets ◽

Data Sets ◽

Fit Statistics ◽

Metric Multidimensional Scaling ◽

Scientific Disciplines ◽

Almost All

AbstractMetric multidimensional scaling (MDS) is a widely used multivariate method with applications in almost all scientific disciplines. Eigenvalues obtained in the analysis are usually reported in order to calculate the over-all goodness-of-fit of the distance matrix. In this paper, we refine MDS goodness-of-fit calculations, proposing additional point and pairwise good-ness-of-fit statistics that can be used to filter poorly represented observations in MDS maps. The proposed statistics are especially relevant for large data sets that contain outliers, with typically many poorly fitted observations, and are helpful for improving MDS output and emphasising the most important features of the dataset. Several goodness-of-fit statistics are considered, and both Euclidean and non-Euclidean distance matrices are considered. Some examples with data from demographic, genetic and geographic studies are shown.

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An example of spectrum imaging used for comparison of EELS quantitative analysis techniques on Al-Li

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010008794x ◽

1991 ◽

Vol 49 ◽

pp. 726-727

Author(s):

John A. Hunt

Keyword(s):

Quantitative Analysis ◽

Large Data ◽

Difference Spectrum ◽

Large Data Sets ◽

Foil Thickness ◽

Data Sets ◽

Analysis Techniques ◽

Spectrum Imaging ◽

Normal Spectrum ◽

Electron Energy Loss

Spectrum-imaging is a useful technique for comparing different processing methods on very large data sets which are identical for each method. This paper is concerned with comparing methods of electron energy-loss spectroscopy (EELS) quantitative analysis on the Al-Li system. The spectrum-image analyzed here was obtained from an Al-10at%Li foil aged to produce δ' precipitates that can span the foil thickness. Two 1024 channel EELS spectra offset in energy by 1 eV were recorded and stored at each pixel in the 80x80 spectrum-image (25 Mbytes). An energy range of 39-89eV (20 channels/eV) are represented. During processing the spectra are either subtracted to create an artifact corrected difference spectrum, or the energy offset is numerically removed and the spectra are added to create a normal spectrum. The spectrum-images are processed into 2D floating-point images using methods and software described in [1].

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Cluster analysis for large data sets: applications to individual aerosol particles from the mid-pacific

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100132078 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1488-1489

Author(s):

Thomas W. Shattuck ◽

James R. Anderson ◽

Neil W. Tindale ◽

Peter R. Buseck

Keyword(s):

Cluster Analysis ◽

Chemical Reactivity ◽

Large Data ◽

Large Data Sets ◽

Particle Analysis ◽

Data Sets ◽

Halogen Chemistry ◽

Complete Study ◽

Components Analysis ◽

Automated Scanning

Individual particle analysis involves the study of tens of thousands of particles using automated scanning electron microscopy and elemental analysis by energy-dispersive, x-ray emission spectroscopy (EDS). EDS produces large data sets that must be analyzed using multi-variate statistical techniques. A complete study uses cluster analysis, discriminant analysis, and factor or principal components analysis (PCA). The three techniques are used in the study of particles sampled during the FeLine cruise to the mid-Pacific ocean in the summer of 1990. The mid-Pacific aerosol provides information on long range particle transport, iron deposition, sea salt ageing, and halogen chemistry.Aerosol particle data sets suffer from a number of difficulties for pattern recognition using cluster analysis. There is a great disparity in the number of observations per cluster and the range of the variables in each cluster. The variables are not normally distributed, they are subject to considerable experimental error, and many values are zero, because of finite detection limits. Many of the clusters show considerable overlap, because of natural variability, agglomeration, and chemical reactivity.

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Automated 3-D cell population analysis in thick tissue sections using laser-scanning confocal-microscopy data

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148642 ◽

1993 ◽

Vol 51 ◽

pp. 562-563

Author(s):

Hakan Ancin

Keyword(s):

Laser Scanning ◽

Population Analysis ◽

Three Dimensional ◽

Large Data ◽

Laser Scanning Confocal Microscopy ◽

Tissue Slices ◽

Scanning Confocal Microscopy ◽

Tissue Sections ◽

Spatially Adaptive ◽

Microscopy Data

This paper presents methods for performing detailed quantitative automated three dimensional (3-D) analysis of cell populations in thick tissue sections while preserving the relative 3-D locations of cells. Specifically, the method disambiguates overlapping clusters of cells, and accurately measures the volume, 3-D location, and shape parameters for each cell. Finally, the entire population of cells is analyzed to detect patterns and groupings with respect to various combinations of cell properties. All of the above is accomplished with zero subjective bias.In this method, a laser-scanning confocal light microscope (LSCM) is used to collect optical sections through the entire thickness (100 - 500μm) of fluorescently-labelled tissue slices. The acquired stack of optical slices is first subjected to axial deblurring using the expectation maximization (EM) algorithm. The resulting isotropic 3-D image is segmented using a spatially-adaptive Poisson based image segmentation algorithm with region-dependent smoothing parameters. Extracting the voxels that were labelled as "foreground" into an active voxel data structure results in a large data reduction.

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