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Ellipticity and Circularity Measuring via Kullback–Leibler Divergence

reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Jacek Tabor received

Extreme entropy machines: robust information theoretic classification

Most existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach the classification problem by applying entropy measures as a model objective function. We focus on quadratic Renyi’s entropy and connected Cauchy–Schwarz Divergence which leads to the ...

Expansivity and Cone-fields in Metric Spaces

ukasz Struski Jacek Tabor Mathematics Subject Classification Due to the results of Lewowicz and Tolosa expansivity can be characterized with the aid of Lyapunov function. In this paper we study a

Conditionally δ-midconvex functions

Jacek Chudziak 0 Jacek Tabor 0 Jozef Tabor 0 0 Mathematics Subject Classification. 26A51, 26B25, 39B62 Let X be a real linear space, V be a nonempty subset of X and be a nonnegative real number. A

Asymmetric Clustering Index in a Case Study of 5-HT1A Receptor Ligands

The automatic clustering of chemical compounds is an important branch of chemoinformatics. In this paper the Asymmetric Clustering Index (Aci) is proposed to assess how well an automatically created partition reflects the reference. The asymmetry allows for a distinction between the fixed reference and the numerically constructed partition. The introduced index is applied to ...

Midconvexity for finite sets

Let X be a finite subset of a real vector space. We study Jensen-type convexity on subsets of X. In particular for subsets of X, we introduce the definition of X-midconvex sets. We show that such a notion corresponds well to the classical notion of a convex set. Moreover, we prove that a function X-midconvex set is a midconvex hull of all its extremal points. Other analogues of ...