Algorithms for Projection - Pursuit robust principal component analysis.

The results of a standard principal component analysis (PCA) can be affected by the presence of outliers. Hence robust alternatives to PCA are needed. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit-based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in the presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real data sets. (c) 2007 Elsevier B.V. All rights reserved.multivariate statistics; optimization; numerical precision; outliers; robustness; scale estimators; estimators; regression;

Algorithms for projection-pursuit robust principal component analysis.

Principal Component Analysis (PCA) is very sensitive in presence of outliers. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real datasets.Algorithms; Data; Field; IT; Methods; Outliers; Performance; Principal component analysis; Principal components analysis; Projection-pursuit; Robustness; Simulation; Space; Variables; Variance;

Robust compositional data analysis

Many practical data sets contain outliers or other forms of data inhomogeneities. Robust statistics offers concepts how to deal with these situations where the data do not follow strict model assumptions. These concepts are designed for the usual Euclidean space, and they can be easily applied to compositional data if they are represented in this space as well. It turns out that the isometric logratio (ilr) transformation is best suitable in the context of robust estimation. Depending on the method applied, an interpretation of result is usually done in a back-transformed space

Analysis of compositional data using robust methods. The R-package robCompositons

The free and open-source programming language and software environment R (R Development Core Team, 2010) is currently both, the most widely used and most popular software for statistics and data analysis. In addition, R becomes quite popular as a (programming) language, ranked currently (February 2011) on place 25 at the TIOBE Programming Community Index (e.g., Matlab: 29, SAS: 30, see http://www.tiobe.com). The basic R environment can be downloaded from the comprehensive R archive network (http://cran.rproject.org). R is enhanceable via packages which consist of code and structured standard documentation including code application examples and possible further documents (so called vignettes) showing further applications of the packages. Two contributed packages for compositional data analysis comes with R, version 2.12.1.: the package compositions (van den Boogaart et al., 2010) and the package robCompositions (Templ et al., 2011). Package compositions provides functions for the consistent analysis of compositional data and positive numbers in the way proposed originally by John Aitchison (see van den Boogaart et al., 2010). In addition to the basic functionality and estimation procedures in package compositions, package robCompositions provides tools for a (classical) and robust multivariate statistical analysis of compositional data together with corresponding graphical tools. In addition, several data sets are provided as well as useful utility functions

Classical and robust imputation of missing values for compositional data using balances

Classical and Robust Imputation of Missing Values for Compositional Data using Balance

Simplicial principal component analysis for density functions in Bayes spaces

Probability density functions are frequently used to characterize the distributional properties of large-scale database systems. As functional compositions, densities primarily carry relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. The specific features of density functions are accounted for in Bayes spaces, which result from the generalization to the infinite dimensional setting of the Aitchison geometry for compositional data. The aim is to build up a concise methodology for functional principal component analysis of densities. A simplicial functional principal component analysis (SFPCA) is proposed, based on the geometry of the Bayes space B2 of functional compositions. SFPCA is performed by exploiting the centred log-ratio transform, an isometric isomorphism between B2 and L2 which enables one to resort to standard FDA tools. The advantages of the proposed approach with respect to existing techniques are demonstrated using simulated data and a real-world example of population pyramids in Upper Austria

BIM in teaching — lessons learned from exploratory study

Building Information Technology bears promise to bring integration into fragmented AEC industry, as well as large potentials for optimization and management of building performance along life cycle. However, the adoption in Central Europe is much slower than in the USA or Scandinavia; the designers and planners are sceptical about BIM benefits. In order to build up capabilities and thus support BIM adoption in the practice, BIM skills have be built up already in university teaching. This endeavour is the central aim of the BIM_sustain project accomplished at the Vienna University of Technology. In winter term 2012/13 and winter term 2013/14 we accomplished interdisciplinary BIM-supported design labs with student participants from architecture, civil engineering and building science. The teams used different modelling and simulation software constellations for building design and analysis. The software-constellations were evaluated in terms of BIMinteroperability, and the design process was documented by means of time and activity assessment, surveys on team performance, process satisfaction and technology acceptance and focus group interviews. In this paper we will present the results of the evaluation of both courses and analyse the differences resulting from the different course design in the two consequent terms. The first course was dominated by the issue of interfaces, whereas the second course, where better functioning software combinations in terms of data transfer were used, was dominated by the issues related to the collaboration and teamwork. Our results are not only informative for the configuration of interdisciplinary BIM-supported university teaching, but can be derived for the practice as well, especially in the areas of project management, software usage, modelling conventions or incentive systems

Directional outlyingness applied to distances between genomic words

The detection of outlier curves/images is crucial in many areas, such as environmental, meteorological, medical, or economic contexts. In the functional framework, outlying observations are not only those that contain atypically high or low values, but also curves that present a different shape or pattern from the rest of the curves in the sample. In this short paper, we mention some recent methods for outlier detection in functional data and apply a recently proposed measure, the directional outlyingness, and the functional outlier map to detect words with outlying distance distribution in the human genome.publishe