Dimensionality reduction - A soft set-theoretic and soft graph approach

Abstract

Due to the digitization of information, organizations have abundant data in databases. Large-scale data are equally important and complex hence gathering, storing, understanding, and analyzing data is a problem for organizations. To extract information from this superfluous data, the need for dimensionality reduction increases. Soft set theory has been efficaciously applied and solved problems of dimensionality, which saves the cost of computation, reduces noise, and redundancy in data. Different methods and measures are developed by researchers for the reduction of dimensions, in which some are probabilistic, and some are non-probabilistic. In this paper, a non-probabilistic approach is developed by using soft set theory for dimensionality reduction. Further, an algorithm of dimensionality reduction through bipartite graphs is also described. Lastly, the proposed algorithm is applied to a case study, and a comparison of results indicates that the proposed algorithm is better than the existing algorithms.

Keywords

• dimensionality reduction
• soft set
• grade membership
• binary-valued information system
• soft graph