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Uniform Cross-entropy Clustering

100%

Brzeski M. , Spurek P.

tom Vol. 25

117--126

Robust mixture models approaches, which use non-normal distributions have recently been upgraded to accommodate data with fixed bounds. In this article we propose a new method based on uniform distributions and Cross- Entropy Clustering (CEC). We combine a simple density model with a clustering method which allows to treat groups separately and estimate parameters in each cluster individually. Consequently, we introduce an effective clustering algorithm which deals with non-normal data.

Watching steps of a grand tour implementation

88%

Bartkowiak A. , Szustalewicz A.

tom Vol. 7, No. 3

655-680

Bartkowiak and Szustalewicz, 1997 (B&Sz), have proposed an implementation of the grand tour algorithm designed specially to detect outliers in multivariate data. The algorithm work by performing a sequence of rotations and projections onto a specific 2D-plane (Π proj). This is equivalent to perform a series of rotations yielding transformed coordinates of the data: X(tr) = XA, with A being the rotation matrix, while X and X,sup>(tr) denote the data matrices before and after the rotation appropriately. A superimposed concentration ellipse indicates the outstanding points. We complement the paper of B&Sz by considering some details and variants of the implementation of the grand tour algorithm. In particular we watch the trajectories of the projected points. Our concern is the denseness of the watched projctions. We look at the trajectories of the projected point visible in the Π proj plane and the frequencies of thier appearing in various sectors of that plane. In the Appendix we present the derivation of the formula for the rotation matrix A employed in each step of the algorithm for obtaining the transformed data coordinates.

On the factorization of the Haar measure on finite Coxeter groups

75%

Urban R.

tom Vol. 31, Fasc. 1

141--148

Let W be a finite Coxeter group and let λW be the Haar measure on W; i.e., λW(ω) = |W|−1 for every ω ∈ W: We prove that there exist a symmetric set T ̸= W of generators of W consisting of elements of order not greater than 2 and a finite set of probability measures {μ1..., μk} with their supports in T such that their convolution product μ1 ∗ ...∗ μk = λW:

Interval shrinkage estimation of the parameter of exponential distribution in the presence of outliers under loss functions

75%

Nasiri P.

tom 23

nr 3

65-78

In this paper, we studied estimators based on an interval shrinkage with equal weights point shrinkage estimators for all individual target points θ¯ ∈ (θ0, θ1) for exponentially distributed observations in the presence of outliers drawn from a uniform distribution. Estimators obtained from both shrinkage and interval shrinkage were compared, showing that the estimators obtained via the interval shrinkage method perform better. Symmetric and asymmetric loss functions were also used to calculate the estimators. Finally, a numerical study and illustrative examples were provided to describe the results.