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The L-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L-median are available. Problem specific algorithms can be used, but also general optimization routines. The aim is to compare different algorithms with respect to their precision and runtime. This is possible because all considered algorithms have been implemented in a standardized manner in the open source environment R. In most situations, the algorithm based on the optimization routine NLM (non-linear minimization) clearly outperforms other approaches. Its low computation time makes applications for large and high-dimensional data feasible. [ABSTRACT FROM AUTHOR]

Abstract: This note extends to the continuous-time case the “tube-based” approach for the design of discrete-time robust model predictive control (MPC) algorithms developed in . This extension is of interest in view of the simplicity and popularity of the method as well as of the industrial relevance of continuous-time implementations of MPC. The proposed robust control law is composed of two terms: (1) a sampled-data MPC control law and (2) a continuous-time state feedback term. [Copyright &y& Elsevier]

Abstract: To explore multi-way data, different methods have been proposed. Here, we study the popular PARAFAC (Parallel factor analysis) model, which expresses multi-way data in a more compact way, without ignoring the underlying complex structure. To estimate the score and loading matrices, an alternating least squares procedure is typically used. It is however well known that least squares techniques suffer from outlying observations, making the models useless when outliers are present in the data. In this paper, we present a robust PARAFAC method. Essentially, it searches for an outlier-free subset of the data, on which we can then perform the classical PARAFAC algorithm. An outlier map is constructed to identify outliers. Simulations and examples show the robustness of our approach. [Copyright &y& Elsevier]

Krishnapuram and Keller [IEEE Trans. Fuzzy Syst., vol. 1, no. 2, pp. 98–110, May 1993] proposed a possibilistic c-means (PCM) clustering by relaxing the constraint in fuzzy c-means (FCMs) that the memberships of a data point across classes sum to 1. The PCM algorithm has a tendency to produce coincident clusters. This can be a merit of PCM as a good mode-seeking algorithm if initials and parameters are suitably chosen. However, the performance of PCM heavily depends on initializations and parameter selection. In this paper, we propose a mechanism of robust automatic merging. We then create an automatic merging possibilistic clustering method (AM-PCM), where the proposed algorithm does not only solve these parameter-selection and initialization problems but also obtains an optimal cluster number. The proposed AM-PCM algorithm first uses all data points as initial cluster centers and then automatically merges these surrounding points around each cluster mode such that it can self-organize data groups according to the original data structure. The AM-PCM can exhibit the robustness to parameter, noise, cluster number, different volumes, and initializations. The computational complexity of AM-PCM is also analyzed. Comparisons between AM-PCM and other clustering methods are made. Some numerical data and real datasets are used to show these good aspects of AM-PCM. Experimental results and comparisons actually demonstrate that the proposed AM-PCM is an effective and parameter-free robust clustering algorithm. [ABSTRACT FROM AUTHOR]

Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction. [ABSTRACT FROM AUTHOR]