Adapted variable precision rough set approach for EEG analysis

Summary

Objective

Rough set theory (RST) provides powerful methods for reduction of attributes and creation of decision rules, which have successfully been applied in numerous medical applications. The variable precision rough set model (VPRS model), an extension of the original rough set approach, tolerates some degree of misclassification of the training data. The basic idea of the VPRS model is to change the class information of those objects whose class information cannot be induced without contradiction from the available attributes. Thereafter, original methods of RST are applied.

An approach of this model is presented that allows uncertain objects to change class information during the process of attribute reduction and rule generation. This method is referred to as variable precision rough set approach with flexible classification of uncertain objects (VPRS(FC) approach) and needs only slight modifications of the original VPRS model.

Methods and material

To compare the VPRS model and VPRS(FC) approach both methods are applied to a clinical data set based on electroencephalogram of awake and anesthetized patients. For comparison, a second data set obtained from the UCI machine learning repository is used. It describes the shape of different vehicle types. Further well known feature selection methods were applied to both data sets to compare their results with the results provided by rough set based approaches.

Results

The VPRS(FC) approach requires higher computational effort, but is able to achieve better reduction of attributes for noisy or inconsistent data and provides smaller rule sets.

Conclusion

The presented approach is a useful method for substantial attribute reduction in noisy and inconsistent data sets.

Introduction

Rough Set Theory (RST), as introduced by Pawlak [1], [2], provides methods for knowledge reduction and induction of decision rules which have successfully been applied in numerous medical applications [3], [4], [5], [6], [7], [8]. Analysis of electroencephalogram (EEG) data has also been subject of rough set applications [9], [10], [11]. EEG signals are electrical potentials generated by brain activity and measured on the scalp by non-invasive electrodes. These signals have amplitudes of typically some 10 μV. EEG is usually distorted by a high level of noise and by different types of artifacts. Therefore, the analysis of EEG-based data is a particular challenge for methods of artificial intelligence.

The original RST is able to handle inconsistent granular data, but does not tolerate noise or inexact attribute values. The variable precision rough set (VPRS) model overcomes this drawback by allowing a previously defined degree of misclassification.

The VPRS model considers some objects of the given data set as misclassified or uncertain. In a first step, the full attribute set is used to evaluate which objects are regarded as misclassified. The class information (decision) of these objects is changed resulting in a data set that can be handled by methods of the original RST. So, the initial definition of misclassified objects is preserved throughout the entire process.

We present an approach of the VPRS model referred to as variable precision rough set approach with flexible classification of uncertain objects (VPRS(FC) approach). In contrast to the VPRS model, misclassified objects are identified during the reduction process: First a reduced attribute set is selected, then misclassified objects are identified. This procedure ignores the information of removed attributes completely and may be advantageous when removed attributes are noisy.

The VPRS(FC) approach satisfies largely the main definitions of the VPRS model, only slight modifications have to be done. As a result, the VPRS(FC) approach can achieve a better reduction of attributes and smaller sets of decision rules, which are easier to interpret and allow a faster classification of new objects.

However, some fundamental assumptions of the original RST are no longer valid. As a consequence, it is not possible to apply techniques for the limitation of the computational effort.

In the next section some fundamentals of the original RST are introduced with a focus on those statements, which are affected by the VPRS(FC) approach. Section 3 gives a survey of the VPRS model. In Section 4 the VPRS(FC) approach is introduced and related work is reviewed. Particularly similar investigations from Mi [12] and Inuiguchi [13] also allowing flexible classification are considered. Section 5 states the relation of rough set based attribute reduction to other feature selection methods. In Section 6 the VPRS model and the VPRS(FC) approach are applied to a clinical data set based on EEG signals from anesthetized unconscious and awake patients. To prove that the VPRS(FC) approach performs well on different types of data, it is applied to a vehicle database from the university of California Irvine (UCI) machine learning repository and results are compared with VPRS model. Alternatively, common feature selection methods are applied on the identical data sets and resulting classification rates are presented in Section 8. In Section 9 the results are summarized and discussed.