Feature selection in mixed data

Attribute selection with fuzzy decision reducts

A fuzzy rough set is an important rough set model used for feature selection. It uses the fuzzy rough dependency as a criterion for feature selection. However, this model can merely maintain a maximal dependency function. It does not fit a given dataset well and cannot ideally describe the differences in sample classification. Therefore, in this study, we introduce a new model for handling this problem. First, we define the fuzzy decision of a sample using the concept of fuzzy neighborhood. Then, a parameterized fuzzy relation is introduced to characterize the fuzzy information granules, using which the fuzzy lower and upper approximations of a decision are reconstructed and a new fuzzy rough set model is introduced. This can guarantee that the membership degree of a sample to its own category reaches the maximal value. Furthermore, this approach can fit a given dataset and effectively prevents samples from being misclassified. Finally, we define the significance measure of a candidate attribute and design a greedy forward algorithm for feature selection. Twelve datasets selected from public data sources are used to compare the proposed algorithm with certain existing algorithms, and the experimental results show that the proposed reduction algorithm is more effective than classical fuzzy rough sets, especially for those datasets for which different categories exhibit a large degree of overlap.

A Fitting Model for Feature Selection With Fuzzy Rough Sets

Rough set theory has been extensively discussed in machine learning and pattern recognition. It provides us another important theoretical tool for feature selection. In this paper, we construct a novel rough set model for feature subset selection. First, we define the fuzzy decision of a sample by using the concept of fuzzy neighborhood. A parameterized fuzzy relation is introduced to characterize fuzzy information granules for analysis of real-valued data. Then, we use the relationship between fuzzy neighborhood and fuzzy decision to 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 parameters on these concepts are discussed. 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, using which a greedy feature subset selection algorithm is designed. The proposed algorithm is compared with some classical algorithms. The experiments show that the proposed algorithm gets higher classification performance and the numbers of selected features are relatively small.

Feature subset selection based on fuzzy neighborhood rough sets

Two fuzzy covering rough set models and their generalizations over fuzzy lattices

Generalized fuzzy rough sets determined by a triangular norm

Multi-label decision data serve as an important extension of decision data, where several labels associate with each object. In classical multi-granulation rough set models, granulation selection is always related to positive region. However, some positive region reducts are not appropriate for multi-label data due to the fact that the uncertainties implied by labels are not totally considered. To overcome this deficiency in this paper, we propose the optimal granulation selection in multi-granulation and multi-label decision table. First, two kinds of fine and coarse decision functions are introduced, which represent all certainly and all possibly associated labels for the objects in the same class from optimistic and pessimistic viewpoints, respectively. Some relevant propositions and theorems are also carefully examined. Based on granular significance, a novel approach of optimal granulation selection is discussed. Finally, a heuristic algorithm is designed and an illustrative example is given to show the effectiveness of this algorithm. The main contribution of this paper is to extend the attribute reduction of multi-label data based on rough set theory, and overcome the limitation of the positive region reducts, in which the uncertainties implied by labels are not totally considered.

Optimal granulation selection for multi-label data based on multi-granulation rough sets

Optimal granulation selection for similarity measure-based multigranulation intuitionistic fuzzy decision-theoretic rough sets

Rough set theory has become well-established as a mechanism for uncertainty management in a wide variety of applications. This paper studies the measurement of uncertainty in generalized fuzzy rough sets determined by a triangular norm. Based on information theory, the entropy of a generalized fuzzy approximation space is introduced, which is similar to Shannon's entropy. To measure uncertainty in generalized fuzzy rough sets, a notion of fuzziness is introduced. Some basic properties of this measure are examined. For a special triangular norm T= min , it is proved that the measure of fuzziness of a generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable.

Information-Theoretic Measure of Uncertainty in Generalized Fuzzy Rough Sets

Granular computing (
$$ GrC $$

) is one of the key issues in the field of information sciences. Research on the theory and algorithms of granular computing has very important practical significance in huge amounts of information. In multi-granulation rough set theory, two subsets are calculated to approximate the target concept, which are extremely time-consuming for large-scale data. In this paper, to address the issue above, we propose efficient algorithms for updating the lower approximation when a single object is added into or deleted from the target concept in an incomplete information system. Firstly, adjustable multi-granulation rough sets (
$$ AMGRSs $$

) are introduced in an incomplete information system, and the related properties and theorems are explored. Secondly, it is proved that local-
$$ AMGRSs $$

 and 
$$ AMGRSs $$

 are equivalent in an incomplete information system. Finally, dynamic algorithms for updating the lower approximation are proposed, and the efficiency of these algorithms is verified by an experiment.

Tao Feng

Papers

Generalized fuzzy rough sets determined by a triangular norm

Optimal granulation selection for multi-label data based on multi-granulation rough sets

Optimal granulation selection for similarity measure-based multigranulation intuitionistic fuzzy decision-theoretic rough sets

Information-Theoretic Measure of Uncertainty in Generalized Fuzzy Rough Sets

A dynamic approach for updating the lower approximation in adjustable multi-granulation rough sets