## Two new operations over extended index matrices and their applications in Big Data

### Krassimir Atanassov, Veselina Bureva

DOI: http://dx.doi.org/10.15439/2022F300

Citation: Proceedings of the 17th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 30, pages 1–6 (2022)

Abstract. The Index Matrices (IMs) are extensions of the matrices of algebra. Over the IMs different operations, relations and operators are defined. In the present paper, two new operations over IMs are defined and some of their properties are studied. An application of these operations for describing of Big Data procedure is discussed. Hortonworks Data Platform (HDP) is used to provide capabilities for data warehouse processing in the Big Data environment. Apache Hive is selected for data warehouse construction and querying. Firstly, data warehouse for product sells is implemented. The tables for employees, customers, products and product sells are created. Thereafter the new index matrix operations for difference between two IMs are executed for the first time in the Big Data environment. SQL queries are written to demonstrate the operations. The new index matrix operations are executed using SQL JOIN notation and logical operator NOT EXISTS.

### References

- Apache Hive, https://hive.apache.org/
- Atanassov K. Generalized index matrices, Comptes rendus de l’Academie Bulgare des Sciences, Vol. 40, 1987, No. 11, 15–18.
- Atanassov, K., Index Matrices: Towards an Augmented Matrix Calculus, Springer, Cham, 2014. 11
- Atanassov, K., Extended index matrices, Proc. of the 7-th IEEE Conference “Intelligent Systems”, Warsaw, 24-26 Sept. 2014 (P. Angelov, K. Atanassov, L. Doukovska, M. Hadjiski, V. Jotsov, J. Kacprzyk, N. Kasabov, S. Sotirov, E. Szmidt, S. Zadrozny, Eds.), Springer, Cham, 2015, 305-317.
- Hortonworks Data platform, https://www.cloudera.com/products/hdp.html
- Lankaster, P. Theory of Matrices, Academic Press, New York, 1969.
- Zhang, F. Matrix Theory. Springer, New York, 2011.