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1

GrDBSCAN: A granular density-based clustering algorithm

Suchy Dawid, Siminski Krzysztof

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 2

297--312

EN

Density-based spatial clustering of applications with noise (DBSCAN) is a commonly known and used algorithm for data clustering. It applies a density-based approach and can produce clusters of any shape. However, it has a drawback-its worst-case computational complexity is O(n2) with regard to the number of data items n. The paper presents GrDBSCAN: a granular modification of DBSCAN with reduced complexity. The proposed GrDBSCAN first granulates data into fuzzy granules and then runs density-based clustering on the resulting granules. The complexity of GrDBSCAN is linear with regard to the input data size and higher only for the number of granules. That number is, however, a parameter of the GrDBSCAN algorithm and is (significantly) lower than that of input data items. This results in shorter clustering time than in the case of DBSCAN. The paper is accompanied by numerical experiments. The implementation of GrDBSCAN is freely available from a public repository.

2

GrNFS: A granular neuro-fuzzy system for regression in large volume data

Siminski Krzysztof

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 3

445--459

EN

Neuro-fuzzy systems have proved their ability to elaborate intelligible nonlinear models for presented data. However, their bottleneck is the volume of data. They have to read all data in order to produce a model. We apply the granular approach and propose a granular neuro-fuzzy system for large volume data. In our method the data are read by parts and granulated. In the next stage the fuzzy model is produced not on data but on granules. In the paper we introduce a novel type of granules: a fuzzy rule. In our system granules are represented by both regular data items and fuzzy rules. Fuzzy rules are a kind of data summaries. The experiments show that the proposed granular neuro-fuzzy system can produce intelligible models even for large volume datasets. The system outperforms the sampling techniques for large volume datasets.

3

Fuzzy number division and the multi-granularity phenomenon

Piegat A., Pluciński M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 4

497--511

EN

The paper presents difficulties connected with fuzzy and interval division. If operations such as fuzzy addition, subtraction and multiplication provide as a result one compact, multidimensional granule, then a result of the fuzzy division can consists of few separated granules. Such results are more difficult to use in next calculations. The paper shows that the number of solution granules can be higher than 2 and that in certain problems division does not occur explicitly. In certain problems, separation of particular solution granules can be considerable. The paper also shows how to realize the fuzzy division when its denominator contains zero. Most types of fuzzy arithmetics forbid such operation. However, the paper shows that it is possible. Multidimensional fuzzy RDM arithmetic and horizontal membership functions which facilitate detecting of solution granules are also described. The considered problems are visualized by examples.

4

Granule based multiple objects tracking in wireless sensor and actor networks

Bernaś M., Płaczek B.

Studia Informatica

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2016

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Vol. 37, nr 2

5--14

EN

In proposed method sensor nodes provide data that allow actors to track and catch moving targets. Interval granules are used to take into account uncertain target positions and velocities. The wireless sensor nodes report position of a target only if length or direction of optimal actor's path to the target changes significantly. The effectiveness of the introduced method was experimentally evaluated in a simulation environment.

PL

W zaproponowanej metodzie węzły czujników dostarczają dane, które umożliwiają śledzenie ruchomych celów przez węzły mobilne (aktorów). Zastosowano ziarna informacji w formie przedziałów, aby uwzględnić niepewność danych (pozycji oraz prędkości celu). Węzły sieci sensorowej wysyłają informację o położeniu celu do aktora tylko wtedy, gdy odległość lub kierunek aktora odbiega znacząco od optymalnego. Skuteczność metody potwierdzono eksperymentalnie w środowisku symulacyjnym.

5

Relations of granular worlds

Pedrycz W., Vukovich G.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 3

347-357

EN

In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such it is very much oriented towards coping with the underlying relational aspects of the experimental data. The second goal deals with a formation of a mapping between information granules constructed in two spaces (thus it concentrates on the directional aspect of information granulation). The quality of the mapping is directly affected by the information granules over which it operates, so in essence we are interested in the granules that not only reflect the data but also contribute to the performance of such a mapping. The optimization of information granules is realized through a collaboration occurring at the level of the data and the mapping between the data sets. The operational facet of the problem is cast in the realm of fuzzy clustering. As the standard techniques of fuzzy clustering (including a well-known approach of FCM) are aimed exclusively at the first objective identified above, we augment them in order to accomplish sound mapping properties between the granules. This leads to a generalized version of the FCM (and any other clustering technique for this matter). We propose a generalized version of the objective function that includes an additional collaboration component to make the formed information granules in rapport with the mapping requirements (that comes with a directional component captured by the information granules). The additive form of the objective function with a modifiable component of collaborative activities makes it possible to express a suitable level of collaboration and to avoid a phenomenon of potential competition in the case of incompatible structures and the associated mapping. The logic-based type of the mapping (that invokes the use of fuzzy relational equations) comes ...