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EN
Emerging intelligent information systems are pushing existing mathematical foundations into new directions. Generalized covering approximation spaces present abstract data model useful in development of new data analysis methods. The paper introduces construction of rough classifiers in generalized covering approximation spaces. The main idea comes from generation of rough coverings in feature space and calculation of rough covering descriptor. Data are divided into data blocks and each data block statistic and bounding block is calculated . Feature space is divided into feature blocks. For each data bounding block, its inclusion into feature block is calculated and rough covering descriptor is created. Rough covering descriptor is embedded in the generalized covering approximation spaces with standard, fuzzy and probabilistic coverings giving robust theoretical framework in design, implementation and application of classification algorithms.
PL
W pracy przedstawiono nowy sposób konstrukcji klasyfikatorów w uogólnionych aproksymacyjnych przestrzeniach pokryć, definiowanych jako przestrzenie aproksymacyjne zawierające przestrzeń obiektów, pokrycia w tej przestrzeni, oraz pokrycia w przestrzeni atrybutów wraz z zdefiniowaną funkcją zawierania się zbiorów zastosowaną dla pokryć.
EN
Mathematical foundations are steadily extended and pushing rough set theory into incorporating new data analysis methods and data models. Generalized approximation spaces present abstract model useful in understanding unknown and undefined data structure leading into creation many new robust and intelligent approaches. Covering approximation spaces present data by means of coverings of the universe. In the paper, these two approaches have been put together introducing the concept of generalized covering approximation space. Further rough coverings model for generalized covering approximation spaces has been presented. Proposed rough covering models are based upon clustering and thresholding of feature space, are embedded in generalized approximation spaces, simultaneously spanning standard, fuzzy and probabilistic data models.
PL
Tematem pracy jest przedstawienie modelu grupowania w rozszerzenym pojęciu uogólnionych przestrzeni aproksymacyjnych, polegającym na zdefiniowaniu pokryć 9 w tych przestrzeniach. W ten sposób uogólniona przestrzeń aproksymacyjna, posiadająca z definicji sąsiedztwa oraz funkcję zawierania się zbiorów, posiada dodatkowo zdefiniowany system pokryć - czyli jest także przestrzenią pokryć. Praca wprowadza model grupowania w uogólnionych aproksymacyjnych przestrzeniach pokryć obejmujący pokrycia standardowe, rozmyte oraz probabilistyczne. W części prezentacyjnej przedstawione zostały przykłady wybranych uogólnionych aproksymacyjnych przestrzeni pokryć.
3
Content available remote Adaptive Rough Entropy Clustering Algorithms in Image Segmentation
EN
High quality performance of image segmentation methods presents one leading priority in design and implementation of image analysis systems. Incorporating the most important image data information into segmentation process has resulted in development of innovative frameworks such as fuzzy systems, rough systems and recently rough - fuzzy systems. Data analysis based on rough and fuzzy systems is designed to apprehend internal data structure in case of incomplete or uncertain information. Rough entropy framework proposed in [12, 13] has been dedicated for application in clustering systems, especially for image segmentation systems. We extend that framework into eight distinct rough entropy measures and related clustering algorithms. The introduced solutions are capable of adaptive incorporation of the most important factors that contribute to the relation between data objects and makes possible better understanding of the image structure. In order to prove the relevance of the proposed rough entropy measures, the evaluation of rough entropy segmentations based on the comparison with human segmentations from Berkeley and Weizmann image databases has been presented. At the same time, rough entropy based measures applied in the domain of image segmentation quality evaluation have been compared with standard image segmentation indices. Additionally, rough entropy measures seem to comprehend properly properties validated by different image segmentation quality indices.
4
Content available remote GRASS
5
Content available remote 3D data visualization of chaotic dynamic systems
EN
Dynamical systems are often haracterized by difficult to comprehend internal structure. Their understanding requires much effort as well as much insight. Visualization process in low - dimensional spaces can contribute better data presentation together with following better apprehension of intrinsic data relations. This publication is a summary of authors' experience concerning visualization of chaotic systems in 3D spaces by means of modern graphic hardware and software. The OpenGL and DirectX technology and animation techniques have been discussed. Examples of 3D visualization are presented.
6
Content available remote GIS za darmo
7
Content available remote GIS za darmo
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