Cluster Anlaysis in Multiset Spaces
نویسنده
چکیده
The paper considers techniques for grouping objects that are described with many quantitative and qualitative attributes and may exist in several copies. Such multi-attribute objects may be represented as multisets or sets with repeating elements. Multiset characteristics and operations under an arbitrary number of multisets are determined. The various options for the objects’ aggregation (addition, union, intersection) and the main features of hierarchical and non hierarchical cluster analysis in multiset metric spaces are discussed.
منابع مشابه
REDUNDANCY OF MULTISET TOPOLOGICAL SPACES
In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.
متن کاملA Comparison between Strand Spaces and Multiset Rewriting for Security Protocol Analysis
Formal analysis of security protocols is largely based on a set of assumptions commonly referred to asthe Dolev-Yao model. Two formalisms that state the basic assumptions of this model are related here:strand spaces and multiset rewriting with existential quantification. Strand spaces provide a simple andeconomical approach to analysis of completed protocol runs by emphasizing causa...
متن کاملTopological approximations of multisets
athemat s.2012.1 Abstract Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset bas...
متن کاملAlgorithms of nonlinear document clustering based on fuzzy multiset model
Fuzzy multiset is applicable as a model of information retrieval because it has the mathematical structure which expresses the number and the degree of attribution of an element simultaneously. Therefore fuzzy multisets can be used also as a suitable model for document clustering. This paper aims at developing clustering algorithms based on a fuzzy multiset model for document clustering. The st...
متن کاملIndependent Subspaces of Gene Expression Data
Independent subspace anlaysis (ISA) is a linear modelbased method which generalizes independent component analysis (ICA) by incorporating the invariant feature subspace into multidimensional ICA. In this paper we apply ISA to the problem of gene expression data analysis and show the useful behavior of the independent subspaces of gene expression data in the task of gene clustering and gene-gene...
متن کامل