Roman W. Swiniarski

Rough set methods in feature selection and recognition

We present applications of rough set methods for feature selection in pattern recognition. We emphasize the role of the basic constructs of rough set approach in feature selection, namely reducts and their approximations, including dynamic reducts. In the overview of methods for feature selection we discuss feature selection criteria, including the rough set based methods. Our algorithm for feature selection is based on an application of a rough set method to the result of principal components analysis (PCA) used for feature projection and reduction. Finally, the paper presents numerical results of face and mammogram recognition experiments using neural network, with feature selection based on proposed PCA and rough set methods.

Modeling rough granular computing based on approximation spaces

The results reported in this paper create a step toward the rough set-based foundations of data mining and machine learning. The approach is based on calculi of approximation spaces. In this paper, we present the summarization and extension of our results obtained since 2003 when we started investigations on foundations of approximation of partially defined concepts (see, e.g., [2,3,7,37,20,21,5,42,39,38,40]). We discuss some important issues for modeling granular computations aimed at inducing compound granules relevant for solving problems such as approximation of complex concepts or selecting relevant actions (plans) for reaching target goals. The problems discussed in this article are crucial for building computer systems that assist researchers in scientific discoveries in many areas such as biology. In this paper, we present foundations for modeling of granular computations inside of system that is based on granules called approximation spaces. Our approach is based on the rough set approach introduced by Pawlak [24,25]. Approximation spaces are fundamental granules used in searching for relevant complex granules called as data models, e.g., approximations of complex concepts, functions or relations. In particular, we discuss some issues that are related to generalizations of the approximation space introduced in [33,34]. We present examples of rough set-based strategies for the extension of approximation spaces from samples of objects onto a whole universe of objects. This makes it possible to present foundations for inducing data models such as approximations of concepts or classifications analogous to the approaches for inducing different types of classifiers known in machine learning and data mining. Searching for relevant approximation spaces and data models are formulated as complex optimization problems. The proposed interactive, granular computing systems should be equipped with efficient heuristics that support searching for (semi-)optimal granules.

Rough sets as a front end of neural-networks texture classifiers

Abstract The paper describes an application of rough sets method to feature selection and reduction as a front end of neural-network-based texture images recognition. The methods applied include singular-value decomposition (SVD) for feature extraction, principal components analysis (PCA) for feature projection and reduction, and rough sets methods for feature selection and reduction. For texture classification the feedforward backpropagation neural networks were applied. The numerical experiments show the ability of rough sets to select reduced set of patterns features (minimizing the pattern size), while providing better generalization of neural-network texture classifiers.

Rough sets and vague concept approximation: from sample approximation to adaptive learning

We present a rough set approach to vague concept approximation. Approximation spaces used for concept approximation have been initially defined on samples of objects (decision tables) representing partial information about concepts. Such approximation spaces defined on samples are next inductively extended on the whole object universe. This makes it possible to define the concept approximation on extensions of samples. We discuss the role of inductive extensions of approximation spaces in searching for concept approximation. However, searching for relevant inductive extensions of approximation spaces defined on samples is infeasible for compound concepts. We outline an approach making this searching feasible by using a concept ontology specified by domain knowledge and its approximation. We also extend this approach to a framework for adaptive approximation of vague concepts by agents interacting with environments. This paper realizes a step toward approximate reasoning in multiagent systems (MAS), intelligent systems, and complex dynamic systems (CAS).

Approximation Spaces in Rough-Granular Computing

We discuss some generalizations of the approximation space definition introduced in 1994 [24, 25]. These generalizations are motivated by real-life applications. Rough set based strategies for extension of such generalized approximation spaces from samples of objects onto their extensions are discussed. This enables us to present the uniform foundations for inducing approximations of different kinds of granules such as concepts, classifications, or functions. In particular, we emphasize the fundamental role of approximation spaces for inducing diverse kinds of classifiers used in machine learning or data mining.

Information Granulation and Pattern Recognition

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.

Rough sets and higher order vagueness

We present a rough set approach to vague concept approximation within the adaptive learning framework. In particular, the role of extensions of approximation spaces in searching for concept approximation is emphasized. Boundary regions of approximated concepts within the adaptive learning framework are satisfying the higher order vagueness condition, i.e., the boundary regions of vague concepts are not crisp. There are important consequences of the presented framework for research on adaptive approximation of vague concepts and reasoning about approximated concepts. An illustrative example is included showing the application of Boolean reasoning in adaptive learning.

Independent Component Analysis, Principal Component Analysis and Rough Sets in Face Recognition

The paper contains description of hybrid methods of face recognition which are based on independent component analysis, principal component analysis and rough set theory. The feature extraction and pattern forming from face images have been provided using Independent Component Analysis and Principal Component Analysis. The feature selection/reduction has been realized using the rough set technique. The face recognition system was designed as rough-sets rule based classifier.

Perspectives on Uncertainty and Risk in Rough Sets and Interactive Rough-Granular Computing

We discuss an approach for dealing with uncertainty in complex systems. The approach is based on interactive computations over complex objects called here complex granules c-granules, for short. Any c-granule consists of a physical part and a mental part linked in a special way. We begin from the rough set approach and next we move toward interactive computations on c-granules. From our considerations it follows that the fundamental issues of intelligent systems based on interactive computations are related to risk management in such systems. Our approach is a step toward realization of the Wisdom Technology WisTech program. The approach was developed over years of work on different real-life projects.

Rough Set Based Reasoning About Changes

We consider several issues related to reasoning about changes in systems interacting with the environment by sensors. In particular, we discuss challenging problems of reasoning about changes in hierarchical modeling and approximation of transition functions or trajectories. This paper can also be treated as a step toward developing rough calculus.