STORM - a novel information fusion and cluster interpretation technique

Analysis of data without labels is commonly subject to scrutiny by unsupervised machine learning techniques. Such techniques provide more meaningful representations, useful for better understanding of a problem at hand, than by looking only at the data itself. Although abundant expert knowledge exists in many areas where unlabelled data is examined, such knowledge is rarely incorporated into automatic analysis. Incorporation of expert knowledge is frequently a matter of combining multiple data sources from disparate hypothetical spaces. In cases where such spaces belong to different data types, this task becomes even more challenging. In this paper we present a novel immune-inspired method that enables the fusion of such disparate types of data for a specific set of problems. We show that our method provides a better visual understanding of one hypothetical space with the help of data from another hypothetical space. We believe that our model has implications for the field of exploratory data analysis and knowledge discovery.

Spectral synthesis and topologies on ideal spaces for Banach *-algebras

This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G).