The Research Of Attribute Reduction Method Based On Fuzzy Rough Sets

Attribute reduction is an effective method for dealing with high dimensional data. Its aim to remove redundant features under the premise of keeping the classification ability unchanged. It can get useful information from high dimensional data with attribute reduction. This simplifies the process of knowledge processing. Fuzzy rough set model is one of the popular rough set methods used for attribute reduction. It is widely used in the fields of machine learning, data mining and pattern recognition. In this thesis we construct four kinds of attribute reduction algorithms base on fuzzy rough set model.1. Fuzzy rough set model basd on distance measure first introduces a distance measure into fuzzy rough sets. Then, we present a class of fuzzy similarity relations based on distance measures and construct a fuzzy rough set model with fixed distance parameter. However, the discrimination of membership degrees of different fuzzy similarity relations may be very small in a high dimensional feature space due to the fixed distance parameter. In order to solve the problem, the fixed distance parameter is replaced by a variable distance parameter. Some iterative formulas for computing fuzzy rough dependency and attribute significance are presented and an iterative computation method based on variable distance parameter is proposed, using which a greedy convergent algorithm for attribute reduction can be designed.2. Fuzzy neighbor rough set model first defines the fuzzy decisions of samples by using the concept of fuzzy neighborhood. A parameterized fuzzy information granule is introduced to characterize fuzzy decision. Then, we construct a new rough set model: fuzzy neighborhood rough set model. Based on this model, the definitions of upper and lower approximation, boundary region and positive region are given and the effects of feature subset and parameters on them are discussed. In order to make the new model tolerate noises in data, we introduce a variable precision fuzzy neighborhood rough set model. This model can decrease the possibility that a sample is classified into a wrong category. Finally, we define the dependency between fuzzy decision and condition attributes and employ the dependency to evaluate the significance of a candidate feature, by which a greedy feature subset selection algorithm is designed.3. Fitted fuzzy rough model first introduces the fuzzy decision of a sample by using the concept of fuzzy neighborhood. Then, a parameterized fuzzy relation is introduced for data clustering, by which fuzzy information granules are formed. The fuzzy lower and upper approximations of a decision are reconstructed based on the maximum membership fuzzy decision principle. Thus, a new fuzzy rough set model, the fitted fuzzy rough set is introduced. The model can fit a given data set well and guarantee the membership degree of a sample belonging to its own category reaches the maximal value. It is effective to avoid the samples being misclassified. Finally, we define the dependency function between condition attribute and decision attribute. It is used to measure the significance of a candidate attribute and then a greedy forward algorithm for attribute reduction is designed.4. Fuzzy rough set model based on discrete space first introduces a parameterized similarity measure to characterize the similarity between the samples in discrete space. Then, the definitions of upper and lower approximation, positive region and fuzzy dependency between condition attribute and fuzzy decision are given and the effects of the parameters on them are discussed. Based on this, a fuzzy rough set model in discrete sample space is constructed. However, the discrimination of membership degrees of different fuzzy similarity relations may be very small in a high dimensional feature space due to the fixed similarity measure parameter. We adopt an increasing sequence as the gradual value of the fixed similarity measure parameter. Some iterative formulas for computing fuzzy rough dependency and attribute significance based on variable similarity measure parameter are presented. We prove the convergence of these iterative formulas. A greedy forward algorithm for attribute reduction is designed based on iterative computation formulas.The data sets selected from UCI are used to compare these algorithms with some existing algorithms, and the experimental results show these proposed reduction algorithms are feasible and effective.