Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches

Abstract—Semantics-preserving dimensionality reduction refers to the problem of selecting those input features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition, and signal processing. This has found successful application in tasks that involve data sets containing huge numbers of features (in the order of tens of thousands), which would be impossible to process further. Recent examples include text processing and Web content classification. One of the many successful applications of rough set theory has been to this feature selection area. This paper reviews those techniques that preserve the underlying semantics of the data, using crisp and fuzzy rough set-based methodologies. Several approaches to feature selection based on rough set theory are experimentally compared. Additionally, a new area in feature selection, feature grouping, is highlighted and a rough set-based feature grouping technique is detailed. Index Terms—Dimensionality reduction, feature selection, feature transformation, rough selection, fuzzy-rough selection.

Fuzzy-Rough Sets Assisted Attribute Selection

Attribute selection (AS) refers to the problem of selecting those input attributes or features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition and signal processing. Unlike other dimensionality reduction methods, attribute selectors preserve the original meaning of the attributes after reduction. This has found application in tasks that involve datasets containing huge numbers of attributes (in the order of tens of thousands) which, for some learning algorithms, might be impossible to process further. Recent examples include text processing and web content classification. AS techniques have also been applied to small and medium-sized datasets in order to locate the most informative attributes for later use. One of the many successful applications of rough set theory has been to this area. The rough set ideology of using only the supplied data and no other information has many benefits in AS, where most other methods require supplementary knowledge. However, the main limitation of rough set-based attribute selection in the literature is the restrictive requirement that all data is discrete. In classical rough set theory, it is not possible to consider real-valued or noisy data. This paper investigates a novel approach based on fuzzy-rough sets, fuzzy rough feature selection (FRFS), that addresses these problems and retains dataset semantics. FRFS is applied to two challenging domains where a feature reducing step is important; namely, web content classification and complex systems monitoring. The utility of this approach is demonstrated and is compared empirically with several dimensionality reducers. In the experimental studies, FRFS is shown to equal or improve classification accuracy when compared to the results from unreduced data. Classifiers that use a lower dimensional set of attributes which are retained by fuzzy-rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method. In addition, it is shown that FRFS is more powerful than the other AS techniques in the comparative study

A temporal semantics for Nilpotent Minimum logic

In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by {\L}3: a completeness theorem will be shown. This is the prosecution of the work initiated in [AGM08] and [ABM09], in which the authors construct a temporal semantics for the many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table

"Possible Definitions of an ’A Priori’ Granule\ud in General Rough Set Theory" by A. Mani

We introduce an abstract framework for general rough set theory from a mereological perspective and consider possible concepts of ’a priori’ granules and granulation in the same. The framework is ideal for relaxing many of the\ud relatively superfluous set-theoretic axioms and for improving the semantics of many relation based, cover-based and dialectical rough set theories. This is a\ud relatively simplified presentation of a section in three different recent research papers by the present author.\u