Guoyin Wang

An automatic method to determine the number of clusters using decision-theoretic rough set

Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. Determining the number of clusters in a data set is one of the most challenging and difficult problems in cluster analysis. To combat the problem, this paper proposes an efficient automatic method by extending the decision-theoretic rough set model to clustering. A new clustering validity evaluation function is designed based on the risk calculated by loss functions and possibilities. Then a hierarchical clustering algorithm, ACA-DTRS algorithm, is proposed, which is proved to stop automatically at the perfect number of clusters without manual interference. Furthermore, a novel fast algorithm, FACA-DTRS, is devised based on the conclusion obtained in the validation of the ACA-DTRS algorithm. The performance of algorithms has been studied on some synthetic and real world data sets. The algorithm analysis and the results of comparison experiments show that the new method, without manual parameter specified in advance, is more valid to determine the number of clusters and more efficient in terms of time cost.

A tree-based incremental overlapping clustering method using the three-way decision theory

Existing clustering approaches are usually restricted to crisp clustering, where objects just belong to one cluster; meanwhile there are some applications where objects could belong to more than one cluster. In addition, existing clustering approaches usually analyze static datasets in which objects are kept unchanged after being processed; however many practical datasets are dynamically modified which means some previously learned patterns have to be updated accordingly. In this paper, we propose a new tree-based incremental overlapping clustering method using the three-way decision theory. The tree is constructed from representative points introduced by this paper, which can enhance the relevance of the search result. The overlapping cluster is represented by the three-way decision with interval sets, and the three-way decision strategies are designed to updating the clustering when the data increases. Furthermore, the proposed method can determine the number of clusters during the processing. The experimental results show that it can identifies clusters of arbitrary shapes and does not sacrifice the computing time, and more results of comparison experiments show that the performance of proposed method is better than the compared algorithms in most of cases.

Generic normal cloud model

Abstract Cloud model is a cognitive model which can realize the bidirectional cognitive transformation between qualitative concept and quantitative data based on probability statistics and fuzzy set theory. It uses the forward cloud transformation (FCT) and the backward cloud transformation (BCT) to implement the cognitive transformations between the intension and extension of a concept. As one of the most important cloud models, the normal cloud models, especially the 2 nd -order normal cloud model based on normal distribution and Gaussian membership function has been extensively researched and successfully applied to many fields. In this paper, a 2 nd -order generic normal cloud model, which establishes a relationship between normal cloud and normal distribution, is proposed, and the 2 nd -order generic forward normal cloud transformation algorithm ( 2 nd -GFCT) is presented. Whereafter, an ideal backward cloud transformation algorithm of the 2 nd -order generic normal cloud model ( 2 nd -GIBCT) is designed based on the mutually inverse features of FCT and BCT, in which the distribution of all the cloud drops generated in 2 nd -GFCT is used. Meanwhile, a 2 nd -order generic backward cloud transformation algorithm ( 2 nd -GBCT), which does not use the distribution of cloud drops, is also proposed to solve real life problems since it is impossible to know the distribution of all the cloud drops in advance in real life applications. The relationships between the generic backward cloud transformation algorithms are further studied, which help reach the finding that the two backward cloud transformation algorithms presented by Wang and Xu [26,34] are two special cases of the 2 nd -GBCT. In addition, the 2 nd -order generic normal cloud model is further generalized to p th -order generic normal cloud model, and the p th -order generic forward normal cloud transformation algorithm ( p th -GFCT) and the backward cloud transformation algorithm ( p th -GBCT) are presented. Finally, the performances of the 2 nd -GIBCT and the 2 nd -GBCT are illustrated by simulation experiment. The effectiveness of the 2 nd -GBCT is shown by the results of image segmentation.

RRIA: A Rough Set and Rule Tree Based Incremental Knowledge Acquisition Algorithm

As a special way in which the human brain is learning new knowledge, incremental learning is an important topic in AI. It is an object of many AI researchers to find an algorithm that can learn new knowledge quickly, based on original knowledge learned before, and in such way that the knowledge it acquires is efficient in real use. In this paper, we develop a rough set and rule tree based incremental knowledge acquisition algorithm. It can learn from a domain data set incrementally. Our simulation results show that our algorithm can learn more quickly than classical rough set based knowledge acquisition algorithms, and the performance of knowledge learned by our algorithm can be the same as or even better than classical rough set based knowledge acquisition algorithms. Besides, the simulation results also show that our algorithm outperforms ID4 in many aspects.

Incremental attribute reduction based on elementary sets

In the research of knowledge acquisition based on rough sets theory, attribute reduction is a key problem. Many researchers proposed some algorithms for attribute reduction. Unfortunately, most of them are designed for static data processing. However, many real data are generated dynamically. In this paper, an incremental attribute reduction algorithm is proposed. When new objects are added into a decision information system, a new attribute reduction can be got by this method quickly.

Decision region distribution preservation reduction in decision-theoretic rough set model

Abstract In the Pawlak rough set model, the positive region, the boundary region and the non-negative region are monotonic with respect to the set inclusion of attributes. However, the monotonicity property of the decision regions (positive region, boundary region or non-negative region) with respect to the set inclusion of attributes does not hold in the decision-theoretic rough set model. Therefore, the decision regions may be changed after attribute reduction based on quantitative preservation or qualitative preservation of decision regions. This effect is observed partly because three decision regions are defined by introducing the probabilistic threshold values. In addition, heuristic reduction algorithms based on decision regions may find super reducts because of the non-monotonicity of decision regions. To address the above issues, this paper proposes solutions to the attribute reduction problem based on decision region preservation in the decision-theoretic rough set model. First, the ( α , β ) positive region distribution preservation reduct, the ( α , β ) boundary region distribution preservation reduct and the ( α , β ) negative region distribution preservation reduct are introduced into the decision-theoretic rough set model. Second, three new monotonic measures are constructed by considering variants of the conditional information entropy, from which we can obtain the heuristic reduction algorithms. The results of the experimental analysis validate the monotonicity of new measures and verify the effectiveness of decision region distribution preservation reducts.

A Decision-Theoretic Rough Set Approach for Dynamic Data Mining

Uncertainty and fuzziness generally exist in real-life data. Approximations are employed to describe the uncertain information approximately in rough set theory. Certain and uncertain rules are induced directly from different regions partitioned by approximations. Approximation can further be applied to datamining-related task, e.g., attribute reduction. Nowadays, different types of data collected from different applications evolve with time, especially new attributes may appear while new objects are added. This paper presents an approach for dynamic maintenance of approximations w.r.t. objects and attributes added simultaneously under the framework of decision-theoretic rough set (DTRS). Equivalence feature vector and matrix are defined first to update approximations of DTRS in different levels of granularity. Then, the information system is decomposed into subspaces, and the equivalence feature matrix is updated in different subspaces incrementally. Finally, the approximations of DTRS are renewed during the process of updating the equivalence feature matrix. Extensive experimental results verify the effectiveness of the proposed methods.

Monotonic uncertainty measures for attribute reduction in probabilistic rough set model

Attribute reduction is one of the most fundamental and important topics in rough set theory. Uncertainty measures play an important role in attribute reduction. In the classical rough set model, uncertainty measures have the monotonicity with respect to the granularity of partition. However, the monotonicity of uncertainty measures does not hold when uncertainty measures in classical rough set model are directly extended into probabilistic rough set model, which makes it not so reasonable to use them to evaluate the uncertainty in probabilistic rough set model. Moreover, the monotonicity is very important for constructing attribute reduction algorithms because the monotonicity of uncertainty measures can simplify the algorithm design. This paper focuses on constructing monotonic uncertainty measures in probabilistic rough set model. Firstly, we analyze the non-monotonicity problem of uncertainty measures in probabilistic rough set model. Secondly, we propose three basic uncertainty measures and three expected granularity-based uncertainty measures, the monotonicity of these measures is proved to be held and the relationship between these measures and corresponding uncertainty measures in classical rough set model is also obtained. Finally, a new attribute reduct is defined based on the proposed monotonic uncertainty measure, and the corresponding heuristic reduction algorithms are developed. The results of experimental analysis are included to validate the effectiveness of the proposed uncertainty measures and new reduct definition. The non-monotonicity of uncertainty measures is studied in probabilistic rough set model.Three basic uncertainty measures and three expected granularity-based uncertainty measures are proposed.The proposed uncertainty measures have the monotonicity with respect to the granularity of partitions.The monotonic uncertainty measure based attribute reduction methods are constructed.

Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts

Incomplete contexts are a kind of formal contexts in which the relationship between some objects and some attributes is unavailable or lost. Knowledge discovery in incomplete contexts is of interest because such databases are frequently encountered in the real world. This paper mainly focuses on two issues: approximate concept construction with three-way decisions and attribute reduction in incomplete contexts. The theory of three-way decisions is formulated based on the notions of acceptance, rejection and non-commitment. It is an extension of the commonly used binary-decision model with an added third option. Based on three-way decisions, we propose two models to construct approximate concepts in incomplete contexts, and the equivalence of the two is revealed. To simplify the representation of the approximate concept lattices, we further present the attribute reduction approaches.

Attribute reduction for massive data based on rough set theory and MapReduce

Data processing and knowledge discovery for massive data is always a hot topic in data mining, along with the era of cloud computing is coming, data mining for massive data is becoming a highlight research topic. In this paper, attribute reduction for massive data based on rough set theory is studied. The parallel programming mode of MapReduce is introduced and combined with the attribute reduction algorithm of rough set theory, a parallel attribute reduction algorithm based on MapReduce is proposed, experiment results show that the proposed method is more efficiency for massive data mining than traditional method, and it is a effective method effective method effective method for data mining on cloud computing platform.