49,887 research outputs found
The Binary Space Partitioning-Tree Process
The Mondrian process represents an elegant and powerful approach for space
partition modelling. However, as it restricts the partitions to be
axis-aligned, its modelling flexibility is limited. In this work, we propose a
self-consistent Binary Space Partitioning (BSP)-Tree process to generalize the
Mondrian process. The BSP-Tree process is an almost surely right continuous
Markov jump process that allows uniformly distributed oblique cuts in a
two-dimensional convex polygon. The BSP-Tree process can also be extended using
a non-uniform probability measure to generate direction differentiated cuts.
The process is also self-consistent, maintaining distributional invariance
under a restricted subdomain. We use Conditional-Sequential Monte Carlo for
inference using the tree structure as the high-dimensional variable. The
BSP-Tree process's performance on synthetic data partitioning and relational
modelling demonstrates clear inferential improvements over the standard
Mondrian process and other related methods
Approximations from Anywhere and General Rough Sets
Not all approximations arise from information systems. The problem of fitting
approximations, subjected to some rules (and related data), to information
systems in a rough scheme of things is known as the \emph{inverse problem}. The
inverse problem is more general than the duality (or abstract representation)
problems and was introduced by the present author in her earlier papers. From
the practical perspective, a few (as opposed to one) theoretical frameworks may
be suitable for formulating the problem itself. \emph{Granular operator spaces}
have been recently introduced and investigated by the present author in her
recent work in the context of antichain based and dialectical semantics for
general rough sets. The nature of the inverse problem is examined from
number-theoretic and combinatorial perspectives in a higher order variant of
granular operator spaces and some necessary conditions are proved. The results
and the novel approach would be useful in a number of unsupervised and semi
supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings,
Springe
Class Association Rules Mining based Rough Set Method
This paper investigates the mining of class association rules with rough set
approach. In data mining, an association occurs between two set of elements
when one element set happen together with another. A class association rule set
(CARs) is a subset of association rules with classes specified as their
consequences. We present an efficient algorithm for mining the finest class
rule set inspired form Apriori algorithm, where the support and confidence are
computed based on the elementary set of lower approximation included in the
property of rough set theory. Our proposed approach has been shown very
effective, where the rough set approach for class association discovery is much
simpler than the classic association method.Comment: 10 pages, 2 figure
Knowledge Engineering from Data Perspective: Granular Computing Approach
The concept of rough set theory is a mathematical approach to uncertainly and vagueness in data analysis, introduced by Zdzislaw Pawlak in 1980s. Rough set theory assumes the underlying structure of knowledge is a partition. We have extended Pawlak’s concept of knowledge to coverings. We have taken a soft approach regarding any generalized subset as a basic knowledge. We regard a covering as basic knowledge from which the theory of knowledge approximations and learning, knowledge dependency and reduct are developed
- …