The Discernibility Matrices and Functions in Information Systems

Świniarski

2004

Rough-Neural Computing

Self Cite

Summary. We discuss information granulation applications in pattern recognition. The chapter consists of two parts. In the first part, we present applications of rough set methods for feature selection in pattern recognition. We emphasize the role of different forms of reducts that are the basic constructs of the rough set approach in feature selection. In the overview of methods for feature selection, we discuss feature selection criteria based on the rough set approach and the relationships between them and other existing criteria. Our algorithm for feature selection used in the application reported is based on an application of the rough set method to the result of principal component analysis used for feature projection and reduction. Finally, the first part presents numerical results of face recognition experiments using a neural network, with feature selection based on proposed principal component analysis and rough set methods. The second part consists of an outline of an approach to pattern recognition with the application of background knowledge specified in natural language. The approach is based on constructing approximations of reasoning schemes. Such approximations are called approximate reasoning schemes and rough neural networks.

Section: Discernibility and Boolean Reasoningmentioning

confidence: 99%

Information Granulation and Pattern Recognition

Świniarski

2004

Rough-Neural Computing

Self Cite

“…In other words, a reduct is a minimal set of attributes from A that preserves the original classification defined by the set A of attributes. Finding a minimal reduct is NP-hard [111]. One can also show that the number of reducts of an information system with m attributes can be equal to m ⌊m/2⌋…”

Section: Reduct and Corementioning

confidence: 99%

“…Construction of the decision-relative discernibility function from this matrix follows the construction of the discernibility function from the discernibility matrix. It has been shown [111] that the set of prime implicants of f d M (A) defines the set of all decision-relative reducts of A.…”

Section: Reduct and Corementioning

confidence: 99%

“…[110]). High computational complexity of analyzed problems (like NP-hardness of minimal reduct computation problem [111]) is not due to their formulation using Boolean reasoning framework but it is the intrinsic property of these problems. In some sense one cannot expect that by using other formalization the computational complexity of these problems can be decreased.…”

Section: Reduct and Corementioning

confidence: 99%

See 1 more Smart Citation

Rough Sets and Rough Logic: A KDD Perspective

Pawlak

Polkowski

Rough Set Methods and Applications

2000

Self Cite

Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85,86] in the early 1980's. In the ensuing years, we have witnessed a systematic, world-wide growth of interest in rough sets and their applications.The main goal of rough set analysis is induction of approximations of concepts. This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete. A fortiori, we have to describe concepts of interest (features, properties, relations etc.) not completely but by means of their reflections (i.e. approximations) in the chosen language. The most important issues in this induction process are:-construction of relevant primitive concepts from which approximations of more complex concepts are assembled, -measures of inclusion and similarity (closeness) on concepts, -construction of operations producing complex concepts from the primitive ones.Basic tools of rough set approach are related to concept approximations. They are defined by approximation spaces. For many applications, in particular for KDD problems, it is necessary to search for relevant approximation spaces in the large space of parameterized approximation spaces. Strategies for tuning parameters of approximation spaces are crucial for inducing concept approximations of high quality.Methods proposed in rough set approach are kin to general methods used to solve Knowledge Discovery and Data Mining (KDD) problems like feature selection, feature extraction (e.g. discretization or grouping of symbolic value),

“…Information granules in the form of rules are extracted from decision tables using rough set methods. Discovery of decider neuron rules stems from an application of the rule derivation method given in [13]- [14]. This characterization of a decider neuron is based on the identification of information granules based on decision rules [15].…”

Section: Introductionmentioning

confidence: 99%

Towards Rough Neural Computing Based on Rough Membership Functions: Theory and Application

Peters

Rough Sets and Current Trends in Computing

Lai

et al. 2001

Abstract. This paper introduces a neural network architecture based on rough sets and rough membership functions. The neurons of such networks instantiate approximate reasoning in assessing knowledge gleaned from input data. Each neuron constructs upper and lower approximations as an aid to classifying inputs. Rough neuron output has various forms. In this paper, rough neuron output results from the application of a rough membership function. A brief introduction to the basic concepts underlying rough membership neural networks is given.An application of rough neural computing is briefly considered in classifying the waveforms of power system faults. Experimental results with rough neural classification of waveforms are also given.