# Combining Fuzzy C-Means Clustering with Fuzzy Rough Feature Selection
## 1 Introduction  
We live in an age of data explosion--dealing with the growth of datasets usually requires much time and expense if we use the existing computers and algorithms. We want the dataset to contain more and more features to increase the likelihood of distinguishing different categories. Unfortunately, it may not be right. A higher-dimensional dataset increases the possibility of discovering incompletely valid false patterns. An effective way of resolving this problem is to select some of the most relevant and informative features from the dataset and eliminate redundant or irrelevant features. Unlike other dimensional reduction methods, feature selection retains the original meaning of features. This method can effectively reduce the size of a dataset without influencing the information expressed by the data, thus reducing cost and saving time. Researchers have carried out different definitions of feature selection. Ideally, feature selection is to find the minimum feature subset which is necessary and sufficient to identify the target [1]. The definition of feature selection from the angle of improving the prediction accuracy is a process which can increase the classification accuracy or reduce the characteristic dimension without lowering the classification accuracy [2]. The basic method of feature selection is to generate a feature subset (search algorithm) and then evaluate the subset (evaluation criteria). The selection algorithm and evaluation criteria are two important parts of feature selection; an excellent search algorithm can speed up the search of features to find the optimal solution. The normal search algorithms contain global optimization, random search, and heuristic search. Evaluation criteria are defined as to evaluatethe feature subset which is selected with some evaluation criterions. The evaluation decides directly the output of algorithm and performance of a classification model. An excellent evaluation criterion ensures the chosen subset contains a large amount of information and tiny redundancy. Evaluation functions can be divided into filter (evaluation function is independent of classifier), wrapper (the error probability of classifier is used as evaluation function), and embedding (a mixture of the first two). Common feature selection methods include Relief (relevant features), LVW (Las Vegas wrapper), LARS (least angle regression), and attribute reduction of rough set. Fuzzy rough set is the extension of rough set. Two important applications of rough set are rule induction and attribute reduction (the meaning is the same as feature selection, but in rough set theory it is often called attribute reduction). However, rough set feature selection can only reduce the dataset of discrete data, and to overcome the drawback, people combined fuzzy set to rough set. Fuzzy rough feature selection (FRFS) provides a method which can effectively reduce the datasets of real value or discrete noise data (or both) without users' information. In addition, the technology can be applied to data with a continuous or nominal decision attribute, thus it can be used in the regression and classification dataset, and only requires additional information for each feature of fuzzy partition which can be automatically derived from the data. An important problem of FRFS is the determination of the similarity relations between objects. The existing methods are not flexible nor pertinent. In this paper, a method combines the membership function generation method based on fuzzy c-means clustering and fuzzy equivalence is proposed. The improving FRFS can automatically generate a membership function based on the knowledge of the dataset itself and complete feature selection. This paper is structured as follows: Section 2 is literature review. The theoretical background is given in Section 3, introducing the rough set attribute reduction, membership function, and fuzzy rough feature selection. In Section 4, the improved fuzzy rough feature selection is presented, and an experiment is provided in Section 5.