LAUSR

The study is concerned with a problem of relational factorization which engages fuzzy relational calculus. It forms an interesting alternative to the method of non-negative matrix factorization that has been commonly discussed and found in numerous applications. The relational factorization takes n-dimensional data located in the unit hypercube and factors it into data of lower dimensionality and some fuzzy relation. Owing to the logic nature of processing delivered by relational calculus, the dimensionality reduction exhibits transparency as the reduction itself is described in terms of logic expressions. Two types of factorizations are investigated by using s-t and t-s composition operators where t and s are triangular norms and conforms, respectively. A two-level process of factorization is designed. A gradient-based learning scheme is developed. The quantification of the performance of the factorization process is realized by bringing a concept of information granularity: the obtained fuzzy relations are made granular constructs and the quality of the produced factorization is assessed in terms of the coverage and specificity of the obtained granular results. A collection of experiments is included to present the performance of factorization and its parametric analysis.