Hualong Yu

Updating multigranulation rough approximations with increasing of granular structures

Dynamic updating of the rough approximations is a critical factor for the success of the rough set theory since data is growing at an unprecedented rate in the information-explosion era. Though many updating schemes have been proposed to study such problem, few of them were carried out in a multigranulation environment. To fill such gap, the updating of the multigranulation rough approximations is firstly explored in this paper. Both naive and fast algorithms are presented for updating the multigranulation rough approximations with the increasing of the granular structures. Different from the naive algorithm, the fast algorithm is designed based on the monotonic property of the multigranulation rough approximations. Experiments on six microarray data sets show us that the fast algorithm can effectively reduce the computational time in comparison with the naive algorithm when facing high dimensional data sets. Moreover, it is also shown that fast algorithm is useful in decreasing the computational time of finding both traditional reduct and attribute clustering based reduct.

Decision-theoretic rough set

We propose a DTRS by a set of cost matrices.Optimistic and pessimistic cases are two special models of our approach.Two criterions based reducts are calculated by two different algorithms. By introducing the misclassification and delayed decision costs into the probabilistic approximations of the target, the model of decision-theoretic rough set is then sensitive to cost. However, traditional decision-theoretic rough set is proposed based on one and only one cost matrix, such model does not take the characteristics of multiplicity and variability of cost into consideration. To fill this gap, a multicost strategy is developed for decision-theoretic rough set. Firstly, from the viewpoint of the voting fusion mechanism, a parameterized decision-theoretic rough set is proposed. Secondly, based on the new model, the smallest possible cost and the largest possible cost are calculated in decision systems. Finally, both the decision-monotocity and cost criteria are introduced into the attribute reductions. The heuristic algorithm is used to compute decision-monotonicity reduct while the genetic algorithm is used to compute the smallest and the largest possible cost reducts. Experimental results on eight UCI data sets tell us: 1. compared with the raw data, decision-monotocity reduct can generate greater lower approximations and more decision rules; 2. the smallest possible cost reduct is much better than decision-monotocity reduct for obtaining smaller costs and more decision rules. This study suggests new research trends concerning decision-theoretic rough set theory.

α-Dominance relation and rough sets in interval-valued information systems

Though rough set has been widely used to study systems characterized by insufficient and incomplete information, its performance in dealing with initial interval-valued data needs to be seriously considered for improving the suitability and scalability. The aim of this paper is to present a parameterized dominance-based rough set approach to interval-valued information systems. First, by considering the degree that an interval-valued data is dominating another one, we propose the concept of α-dominance relation. Second, we present the α-dominance based rough set model in interval-valued decision systems. Finally, we introduce lower and upper approximate reducts into α-dominance based rough set for simplifying decision rules, we also present the judgement theorems and discernibility functions, which describe how lower and upper approximate reducts can be calculated. This study suggests potential application areas and new research trends concerning rough set approach to interval-valued information systems.

Multi-label learning with label-specific feature reduction

We propose two multi-label learning approaches with LIFT reduction.The idea of fuzzy rough set attribute reduction is adopted in our approaches.Sample selection improves the efficiency in feature dimension reduction. In multi-label learning, since different labels may have some distinct characteristics of their own, multi-label learning approach with label-specific features named LIFT has been proposed. However, the construction of label-specific features may encounter the increasing of feature dimensionalities and a large amount of redundant information exists in feature space. To alleviate this problem, a multi-label learning approach FRS-LIFT is proposed, which can implement label-specific feature reduction with fuzzy rough set. Furthermore, with the idea of sample selection, another multi-label learning approach FRS-SS-LIFT is also presented, which effectively reduces the computational complexity in label-specific feature reduction. Experimental results on 10 real-world multi-label data sets show that, our methods can not only reduce the dimensionality of label-specific features when compared with LIFT, but also achieve satisfactory performance among some popular multi-label learning approaches.

ODOC-ELM

The reason of the damage caused by class imbalance for ELM is analyzed in theory.The influence factors about the performance of ELM on skewed data are investigated.An optimal decision outputs compensation-based ELM called ODOC-ELM is presented.Exploring prior data distributions helps improve quality of ELM.Statistical results indicate the superiority of the proposed ODOC-ELM algorithm. Extreme learning machine (ELM) has been one widely used learning paradigm to train single hidden layer feedforward network (SLFN). However, like many other classification algorithms, ELM may learn undesirable class boundaries from data with unbalanced classes. This paper first tries to analyze the reason of the damage caused by class imbalance for ELM, and then discusses the influence of several data distribution factors for the damage. Next, we present an optimal decision outputs compensation strategy to deal with the class imbalance problem in the context of ELM. Specifically, the outputs of the minority classes in ELM are properly compensated. For a binary-class problem, the compensation can be regarded as a single variable optimization problem, thus the golden section search algorithm is adopted to find the optimal compensation value. For a multi-class problem, the particle swarm optimization (PSO) algorithm is used to solve the multivariate optimization problem and to provide the optimal combination of compensations. Experimental results on lots of imbalanced data sets demonstrate the superiority of the proposed algorithm. Statistical results indicate that the proposed approach not only outperforms the original ELM, but also yields better or at least competitive results compared with several widely used and state-of-the-art class imbalance learning methods.

Cost-sensitive rough set approach

We consider test cost and decision cost simultaneously.Cost-sensitive rough set was proposed and explored.Attribute reductions based on three different criteria were investigated. Cost sensitivity is an important problem, which has been addressed by many researchers around the world. As far as cost sensitivity in the rough set theory is concerned, two types of important costs have been seriously considered. On the one hand, the decision cost has been introduced into the modeling of decision-theoretic rough set. On the other hand, the test cost has been taken into account in attribute reduction. However, few researchers pay attention to the construction of rough set model with test cost and decision cost simultaneously. To fill such a gap, a new cost-sensitive rough set approach is proposed, in which the information granules are sensitive to test costs and approximations are sensitive to decision costs, respectively. Furthermore, with respect to different criteria of positive region preservation, decision-monotonicity and cost decrease, three heuristic algorithms are designed to compute reducts, respectively. The comparisons among these three algorithms show us: (1) positive region preservation based algorithm can keep the decision rules supported by lower approximation region unchanged; (2) decision-monotonicity based heuristic algorithm can obtain a reduct with more positive decision rules and higher classification accuracy; (3) cost minimum based algorithm can generate a reduct with minor cost. This study suggests potential application areas and new research trends concerning rough set theory.

Multigranulation rough set: A multiset based strategy

A simple multigranulation rough set approach is to approximate the target through a family of binary relations. Optimistic and pessimistic multigranulation rough sets are two typical examples of such approach. However, these two multigranulation rough sets do not take frequencies of occurrences of containments or intersections into account. To solve such problem, by the motivation of the multiset, the model of the multiple multigranulation rough set is proposed, in which both lower and upper approximations are multisets. Such two multisets are useful when counting frequencies of occurrences such that objects belong to lower or upper approximations with a family of binary relations. Furthermore, not only the concept of approximate distribution reduct is introduced into multiple multigranulation rough set, but also a heuristic algorithm is presented for computing reduct. Finally, multiple multigranulation rough set approach is tested on eight UCI (University of California–Irvine) data sets. Experimental results show: 1. the approximate quality based on multiple multigranulation rough set is between approximate qualities based on optimistic and pessimistic multigranulation rough sets; 2. by comparing with optimistic and pessimistic multigranulation rough sets, multiple multigranulation rough set needs more attributes to form a reduct.

Hierarchies on fuzzy information granulations: A knowledge distance based lattice approach

Hierarchy plays a crucial role in the development of the granular computing(GrC). Presently, a lot of hierarchies have been studied for characterizing the finer or coarser relationships among information granulations, which are derived from the crisp binary relations. To further improve the existing results, not only the fuzzy information granulations derived from the fuzzy binary relations are presented in this paper, but also the three orderings are explored for expressing the hierarchies on fuzzy information granulations. Furthermore, we also introduce the concepts of the global and local knowledge distances into fuzzy information granulations, which can be used to construct the knowledge distance lattices. It shows that the derived partial orderings through those lattices are corresponding to the three different hierarchies on fuzzy information granulations, respectively. The theoretical results provide us a more comprehensible perspective for the study of granular computing(GrC).

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Decision-theoretic rough set is a special rough set approach, which includes both misclassification and delayed decision costs. Though the property of monotonicity does not always hold in decision-theoretic rough set, the decision-monotonicity reduct may help us to increase both lower approximation and upper approximation. The experimental results in this paper tell us that by comparing with the original decision system, more cost is required with decision-monotonicity reduct. The implied philosophy is: if you want to get more, you should pay more!

δ-Cut Decision-Theoretic Rough Set Approach: Model and Attribute Reductions

Decision-theoretic rough set is a quite useful rough set by introducing the decision cost into probabilistic approximations of the target. However, Yaos decision-theoretic rough set is based on the classical indiscernibility relation; such a relation may be too strict in many applications. To solve this problem, a δ-cut decision-theoretic rough set is proposed, which is based on the δ-cut quantitative indiscernibility relation. Furthermore, with respect to criterions of decision-monotonicity and cost decreasing, two different algorithms are designed to compute reducts, respectively. The comparisons between these two algorithms show us the following: (1) with respect to the original data set, the reducts based on decision-monotonicity criterion can generate more rules supported by the lower approximation region and less rules supported by the boundary region, and it follows that the uncertainty which comes from boundary region can be decreased; (2) with respect to the reducts based on decision-monotonicity criterion, the reducts based on cost minimum criterion can obtain the lowest decision costs and the largest approximation qualities. This study suggests potential application areas and new research trends concerning rough set theory.