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3 International Journal of Applied Mathematics and Computer Science

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GrDBSCAN: A granular density-based clustering algorithm

Suchy Dawid, Siminski Krzysztof

International Journal of Applied Mathematics and Computer Science

2023

Vol. 33, no. 2

297--312

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.

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

Siminski Krzysztof

International Journal of Applied Mathematics and Computer Science

2021

Vol. 31, no. 3

445--459

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.

An outlier-robust neuro-fuzzy system for classification and regression

Siminski Krzysztof

International Journal of Applied Mathematics and Computer Science

2021

Vol. 31, no. 2

303--319

Real life data often suffer from non-informative objects—outliers. These are objects that are not typical in a dataset and can significantly decline the efficacy of fuzzy models. In the paper we analyse neuro-fuzzy systems robust to outliers in classification and regression tasks. We use the fuzzy c-ordered means (FCOM) clustering algorithm for scatter domain partition to identify premises of fuzzy rules. The clustering algorithm elaborates typicality of each object. Data items with low typicalities are removed from further analysis. The paper is accompanied by experiments that show the efficacy of our modified neuro-fuzzy system to identify fuzzy models robust to high ratios of outliers.