Package restlos. June 18, 2013
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1 Package restlos June 18, 2013 Type Package Title Robust estimation of location and scatter Version Date Author Steffen Liebscher and Thomas Kirschstein Maintainer Steffen Liebscher The package implements some recently introduced methodology for robust estimation of location and scatter as well as outlier identification. Depends som, rgl, ade4, geometry, nnclust License GPL (>= 2) LazyLoad yes NeedsCompilation no Repository CRAN Date/Publication :16:56 R topics documented: restlos-package flood halle plot.flood plot.pmst plot.rdela pmst rdela Index 10 1
2 2 flood restlos-package Robust estimation of location and scatter The package implements some recently introduced methodology for robust estimation of location and scatter as well as outlier identification. Package: restlos Type: Package Version: Date: License: GPL (>= 2) LazyLoad: yes Steffen Liebscher and Thomas Kirschstein Maintainer: Steffen Liebscher Kirschstein, T., Liebscher, S., and Becker, C. (2013): Robust estimation of location and scatter by pruning the minimum spanning tree, Journal of Multivariate Analysis, 120, , DOI: /j.jmva Liebscher, S., Kirschstein, T., and Becker, C. (2012): The Flood Algorithm - A Multivariate, Self-Organizing-Map-Based, Robust Location and Covariance Estimator, Statistics and Computing, 22(1), , DOI: /s Liebscher, S., Kirschstein, T., and Becker, C. (2013): RDELA - A Delaunay-Triangulation-based, Location and Covariance Estimator with High Breakdown Point, Statistics and Computing, DOI: /s flood The Flood Algorithm The function determines a robust subsample utilizing self-organizing maps (SOM).
3 flood 3 flood(data, Nx=10, Ny=10, rlen=2000) data Value At least a two-dimensional data matrix is required. Number of observations needs to be greater than number of dimensions. Nx Size of the SOM-net in x direction. Default is 10. Ny Size of the SOM-net in y direction. Default is 10. rlen Number of iterations during SOM learn process. Default is The function first calls the som function within the som-package. The results are subsequently used to determine a robust subsample. Nx, Ny and rlen are passed to som. These arguments should be selected depending on the size of the data set (number of observations/dimensions). The larger the data set the larger the net size and the number of iterations should be. Note: At the moment only rectangular and quadratic SOM nets are supported. som.results som.neigh umatrix winneuron lib lin geb l fafh fafh.lib fafh.drin drin SOM results as delivered by som. A matrix showing for every neuron (first column) the index off the neighboring neurons (columns 2-5). The U-matrix shows the U-value for every neuron. Vector of length n giving the index of the nearest neuron (Euclidean distance). List of all basins found. Index of neurons. Smallest subsample of size (n+d+1)/2. List of all neighboring neurons per basin. Index of neurons. Smallest subsample of size (n+d+1)/2. Number of associated data points per basin. Smallest subsample of size (n+d+1)/2. Internal value necessary for plotting. Data for plotting the flood area flood height curve. Internal data necessary for plotting extented flooding. Internal data necessary for plotting extented flooding. Robust subsample of minimal size. Steffen Liebscher <steffen.liebscher@wiwi.uni-halle.de> Liebscher, S., Kirschstein, T., and Becker, C. (2012): The Flood Algorithm - A Multivariate, Self-Organizing-Map-Based, Robust Location and Covariance Estimator, Statistics and Computing, 22(1), , DOI: /s
4 4 plot.flood #flood(halle) halle halle data set Artificial data set containing a total of 1600 observations in two dimensions (in three groups with 100, 1000, 500 obs. from top to bottom). Central cluster is quadratically transformed leading to a U-shaped main part of the data. halle #plot(halle) plot.flood Plot function for objects of class flood Function to plot the results obtained by function flood ## S3 method for class flood plot(x,..., level = 0) x level Object of class flood. Flood level. Numeric value between 0 and 1. Default is 0 (i.e. all plots are based on the smallest robust subsample).... Further graphical parameters. The resulting plots depend on the dimensionality of the data set. For d=2 and d=3 the data set and the superimposed SOM net are plotted. For d>3 a Mahalanobis distance plot is generated instead. The U-landscape and the Flood-Area-Flood-Height-curve are always plotted.
5 plot.pmst 5 Note At the moment no additional graphical parameters can be passed. Steffen Liebscher <steffen.liebscher@wiwi.uni-halle.de> Liebscher, S., Kirschstein, T., and Becker, C. (2012): The Flood Algorithm - A Multivariate, Self-Organizing-Map-Based, Robust Location and Covariance Estimator, Statistics and Computing, 22(1), , DOI: /s #plot(flood(halle)) plot.pmst Plot function for objects of class pmst Function to plot the results obtained by the functions pmst. ## S3 method for class pmst plot(x,...) x Object of class pmst.... Further graphical parameters. The resulting plots display the LC- and the AL-plot to support the decision on the size of the robust subsample, see references. Moreover, if data set has dimension 2 or 3 the data set is plotted where the chosen robust subset is superimposed as red points. Thomas Kirschstein <thomas.kirschstein@wiwi.uni-halle.de> Kirschstein, T., Liebscher, S., and Becker, C. (2013): Robust estimation of location and scatter by pruning the minimum spanning tree, Journal of Multivariate Analysis, 120, , DOI: /j.jmva
6 6 plot.rdela #plot(pmst(halle)) plot.rdela Plot function for objects of class rdela Function to plot the results obtained by function rdela ## S3 method for class rdela plot(x,...) x Object of class rdela.... Further graphical parameters. The resulting plots depend on the dimensionality of the data set. For d=2 and d=3 the data set and the selected robust subsample are plotted. For d>3 a Mahalanobis distance plot is generated instead. Note At the moment no additional graphical parameters can be passed. Steffen Liebscher <steffen.liebscher@wiwi.uni-halle.de> Liebscher, S., Kirschstein, T., and Becker, C. (2013): RDELA - A Delaunay-Triangulation-based, Location and Covariance Estimator with High Breakdown Point, Statistics and Computing, DOI: /s #plot(rdela(halle))
7 pmst 7 pmst pmst (minimum spanning tree pruning) The function determines a robust subsample and computes estimates of location and scatter on the subset. pmst(data, N = floor((dim(data)[1] + dim(data)[2] + 1)/2), lmax = dim(data)[1] * 100) data N lmax data set to be analyzed, at least a 2-dimensional matrix whose number of rows (i.e. observations n) is greater then the number of columns (i.e. dimension d) Size of the (robust) subsample to be determined. Default is (n+d+1)/2 Numerical option: determines the maximal number pruning steps, see deteils. The function uses the mstree function from the ade4-package to determine the minimum spanning tree (MST) of the data. The resulting MST is iteratively pruned by deleting edges (starting with the longest edge in the MST) until a connected subset with sufficient size (N) remains. Based on the robust subsample location and scatter are estimated. Value loc cov sample data Location estimate based on the robust subsample Covariance estimate based on the robust subsample Index of the observations in the robust subsample The input data set Thomas Kirschstein <thomas.kirschstein@wiwi.uni-halle.de> Kirschstein, T., Liebscher, S., and Becker, C. (2013): Robust estimation of location and scatter by pruning the minimum spanning tree, Journal of Multivariate Analysis, 120, , DOI: /j.jmva
8 8 rdela ## Determine subsample of minimal size #sub<-pmst(halle) ## Determine subsample of size=900 #extsub<-pmst(halle, N=900) rdela The RDELA Algorithm The function determines a robust subsample utilizing the Delaunay triangulation. rdela(data, N) data N At least a two-dimensional data matrix is required. Number of observations need to be greater than number of dimensions. No degenerated (i.e. collinear) data sets allowed. Size of the identified subsample. Default is (n+d+1)/2. The function first calls the delaunayn function within the geometry-package. The results are subsequently used to determine a robust subsample. Value data tri neigh radii center LiB LiN GeB drin The input data set. Vertices of all simplices of the Delaunay triangulation. Each row represents a simplex. Lists for every simplex the adjacent/neighboring simplices. Each list entry represents a simplex. Circum-(hypersphere-)radius of each simplex. Center coordinates of all simplices. List of all basins found. Index of simplices. Smallest subsample of size (n+d+1)/2. List of all neighboring simplices per basin. Index of simplices. Smallest subsample of size (n+d+1)/2. Number of associated data points per basin. Smallest subsample of size (n+d+1)/2. Robust subsample of minimal size.
9 rdela 9 Steffen Liebscher <steffen.liebscher@wiwi.uni-halle.de> Liebscher, S., Kirschstein, T., and Becker, C. (2013): RDELA - A Delaunay-Triangulation-based, Location and Covariance Estimator with High Breakdown Point, Statistics and Computing, DOI: /s #rdela(halle)
10 Index Topic datasets halle, 4 Topic robust flood, 2 plot.flood, 4 plot.pmst, 5 plot.rdela, 6 pmst, 7 rdela, 8 restlos-package, 2 flood, 2 halle, 4 plot.flood, 4 plot.pmst, 5 plot.rdela, 6 pmst, 7 rdela, 8 restlos (restlos-package), 2 restlos-package, 2 10
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