Performance Comparison between Two Interpretations of Missing Data using Matrix-Characterized Approximations

Nowadays, the veracity related with data quality such as incomplete, inconsistent, vague or noisy data creates a major challenge to data mining and data analysis. Rough set theory presents a special tool for handling the incomplete and imprecise data in information systems. In this paper, rough set based matrix-represented approximations are presented to compute lower and upper approximations. The induced approximations are conducted as inputs for data analysis method, LERS (Learning from Examples based on Rough Set) used with LEM2 (Learning from Examples Module, Version2) rule induction algorithm. Analyzes are performed on missing datasets with “do not care” conditions and missing datasets with lost values. In addition, experiments on missing datasets with different missing percent by using different thresholds are also provided. The experimental results show that the system outperforms when missing data are characterized as “do not care” conditions than represented as lost values

Rough sets based matrix approaches with dynamic attribute variation in set-valued information systems

AbstractSet-valued information systems are generalized models of single-valued information systems. The attribute set in the set-valued information system may evolve over time when new information arrives. Approximations of a concept by rough set theory need updating for knowledge discovery or other related tasks. Based on a matrix representation of rough set approximations, a basic vector H(X) is induced from the relation matrix. Four cut matrices of H(X), denoted by H[μ,ν](X), H(μ,ν](X), H[μ,ν)(X) and H(μ,ν)(X), are derived for the approximations, positive, boundary and negative regions intuitively. The variation of the relation matrix is discussed while the system varies over time. The incremental approaches for updating the relation matrix are proposed to update rough set approximations. The algorithms corresponding to the incremental approaches are presented. Extensive experiments on different data sets from UCI and user-defined data sets show that the proposed incremental approaches effectively reduce the computational time in comparison with the non-incremental approach