An Efficient Algorithm for Pawlak Reduction Based on Simplified Discernibility Matrix

Firstly, the concept of simplified information system is introduced, the notion of simplified discerniblity matrix is put forward and the method for computing core based on the simplified discerniblity matrix, which can well deal with inconsistent information system. And it is proved that core based on the simplified discernibility matrix is equivalent to that based on the previous one, on the basis of that, an efficient algorithm incremental updating for core is presented, which only need to analyze the updating parts of discernibility matrix and doesn’t need to re-calculate discerniblily matrix, when a new object is added to information system. Finally, Theoretical analysis and example results show that the algorithm is efficient and feasible.

Some scholars provided the discernibility matrix based on the positive region. The time complexity of the algorithm for computing core with this discernibility matrix is O(|CparU|2 ). For cutting down the time complexity of the algorithm, the definition of simplified discernibility matrix based on the positive region and the corresponding definition of the core are provided. At the same time, it is proved that this core is equivalent to the core based on the positive region. Since the partition of U/C is the key process for computing simplified discernibility matrix, a quick algorithm for computing U/C is designed with the idea of radix sorting. Its time complexity is O(|CparU|). On this condition, a new algorithm for computing core based on the positive region is designed with the simplified discernibility. Its time complexity is cut down to max{O(|CparU'posparU/C|), O(|CparU|)}.

Knowledge reduction is one of challenging problems in rough set theory, many static knowledge reduction algorithms have been proposed, however, since the objects in the actual information system are often changed, these static algorithms are computationally time-consuming. In order to overcome this shortcoming, the concept of simplified information system is introduced, and it is proved that knowledge reduction based on the simplified discernibility matrix is equivalent to that based on skowron’s discernibility matrix, On this condition, an efficient incremental updating algorithm for knowledge reduction is designed, which can be used to improve the efficiency of knowledge reduction, when a new object is added to information system. Finally, Theoretical analysis and example results show that illustrate the efficiency and feasibility of the algorithm.

Attribute reduction plays an important role in knowledge discovery and data mining. Confronted with data characterized by the interval and missing values in many data analysis tasks, it is interesting to research the attribute reduction for interval-valued data with missing values. Uncertainty measures can supply efficient viewpoints, which help us to disclose the substantive characteristics of such data. Therefore, this paper addresses the attribute reduction problem based on uncertainty measure for interval-valued data with missing values. At first, an uncertainty measure is provided for measuring candidate attributes, and then an efficient attribute reduction algorithm is developed for the interval-valued data with missing values. To improve the efficiency of attribute reduction, the objects that fall within the positive region are deleted from the whole object set in the process of selecting attributes. Finally, experimental results demonstrate that the proposed algorithm can find a subset of attributes in much shorter time than existing attribute reduction algorithms without losing the classification performance.

An improved attribute reduction scheme with covering based rough sets

Rough set theory is emerging as a powerful toll for reasoning about data. Attribute reduction is one of important topics in the research on the rough set theory. Heuristic, discernibility matrix and matrix method are three usually methods for designing attribute reduction algorithm in attribute reduction based on rough set. Some researchers use matrix method to design attribute reduction algorithm. The time complexity of the algorithm is O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> |U| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), and the computation of the algorithm is time consuming. To lower the time complexity, it was first proposed a new matrix, and provided an attribute reduction definition based on the new matrix. Then it was proved that the new attribute reduction definition is the same as the old reduction. At last, we used the matrix of attribute to define the significance of attribute, and designed a new attribute reduction algorithm, which time complexity is cut to O(|C||U|)+O(|C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> |U/C| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). At the same time, an example was used to illustrate the new algorithm.

A systematic study on attribute reduction with rough sets based on general binary relations

This paper addresses a modified dynamic programming parallel algorithm, and its associated architecture of temporal and spatial complexity of O(N), with N number of processing elements involved in computation. The modification consists of the algorithm adaptation to image interest point matching and architecture optimization. The parallel algorithm simulates the designed architecture, validates it functionally, and allows temporal performance prediction. The proposed algorithm of low spatial and temporal complexities is very suitable for real time on board applications (autonomous robot guidance, trajectory matching, blind vision guidance...).

Knowledge reduction is an important issue when dealing with huge amounts of data. Rough set theory provides two fundamental concepts to deal with this special problem: attribute reduction and core, where attribute reduction is the key problem. There are a lot of methods available for attribute reduction, but very little work has been done for attribute reduction for the cases of deleting and modifying. Therefore, in this paper, we introduce a new updating method based on discernibility matrix for attribute reduction for the case of deleting. When a few old objects are deleted from a decision information system, a core and a new attribute reduction can be obtained quickly because it only deletes a few old rows and columns, or inserts a few rows and updates corresponding columns when updating the discernibility matrix.

The attribute reduction and relative attribute reduction were discussed in this paper. They are the core of KDD. The information view and the algebra view of rough set theory were combined and a novel attribute reduction algorithm was proposed. In the algorithm, the core attribute set which is the initial candidate reduction set is obtained from the discernibility matrix. The frequency of attributes, got from the filtered discernibility matrix, is used as the heuristic information of attributes selection. The algorithmpsilas terminal condition is realized by the conditional entropy. Taking the climatic factor reduction in load forecasting as an example, it has proved that the algorithm requires less computation, has high efficiency and can reduce the redundant attribute in the relative reduction set to a certain extent.

A novel method for attribute reduction of covering decision systems

In view of too many attributes in hoisting motor state recognition of quayside container crane. Attribute reduction method based on discernibility matrix is introduced to attribute reduction of lifting motor state information table. A method of attribute reduction based on the combination of rough set and genetic algorithm is proposed to deal with the hoisting motor state decision table. Under the condition that the information system's decision-making ability is unchanged, the redundant attribute is deleted. Which reduces the complexity and computation of the recognition process of the hoisting motor. It is possible to realize the fast state recognition.

Attribute reduction is a popular topic in research on rough sets. In the classical model, much progress has been made in the study of the attribute reduction of indiscernibility and discernibility relations. To enhance the fault tolerance of the model, concepts of both indiscernibility and discernibility relations involving uncertain or imprecise information are proposed in this paper. The attribute reductions of the relative β -indiscernibility relation and relative β -discernibility relation and their algorithms are proposed. When the precision satisfies certain conditions, the reduction of two relation concepts can be converted into a positive region reduction. Therefore, the discernibility matrix is used to construct the reductions of the two relation concepts and the positive region. Furthermore, the corresponding algorithm of the relative β -indiscernibility (discernibility) relation reduction can be optimized when the precision is greater than 0.5, and this is used to develop an optimization algorithm that constructs the discernibility matrix more efficiently. Experiments show the feasibility of the two relation reduction algorithms. More importantly, the reduction algorithms of the two relations and the optimization algorithm are compared to demonstrate the feasibility of the optimization algorithm proposed in this paper.

Calcium signals have been implicated in the regulation of many diverse cellular processes. The problem of how information from extracellular signals is delivered with specificity and fidelity using fluctuations in cytosolic Ca2+ concentration remains unresolved. The capacity of cells to generate Ca2+ signals of sufficient spatial and temporal complexity is the primary constraint on their ability to effectively encode information through Ca2+. Over the past decade, a large body of literature has dealt with some basic features of Ca2+-handling in cells, as well as the multiplicity and functional diversity of intracellular Ca2+ stores and extracellular Ca2+ influx pathways. In principle, physiologists now have the necessary information to attack the problem of function- and agonist-specificity in Ca2+ signal transduction. This review explores the data indicating that Ca2+ release from diverse sources, including many types of intracellular stores, generates Ca2+ signals with sufficient complexity to regulate the vast number of cellular functions that have been reported as Ca2+-dependent. Some examples where such complexity may relate to neuroendocrine regulation of hormone secretion/synthesis are discussed. We show that the functional and spatial heterogeneity of Ca2+ stores generates Ca2+ signals with sufficient spatiotemporal complexity to simultaneously control multiple Ca2+-dependent cellular functions in neuroendocrine systems.

Calcium signals have been implicated in the regulation of many diverse cellular processes. The problem of how information from extracellular signals is delivered with specificity and fidelity using fluctuations in cytosolic Ca2+ concentration remains unresolved. The capacity of cells to generate Ca2+ signals of sufficient spatial and temporal complexity is the primary constraint on their ability to effectively encode information through Ca2+. Over the past decade, a large body of literature has dealt with some basic features of Ca2+-handling in cells, as well as the multiplicity and functional diversity of intracellular Ca2+ stores and extracellular Ca2+ influx pathways. In principle, physiologists now have the necessary information to attack the problem of function- and agonist-specificity in Ca2+ signal transduction. This review explores the data indicating that Ca2+ release from diverse sources, including many types of intracellular stores, generates Ca2+ signals with sufficient complexity to regulate the vast number of cellular functions that have been reported as Ca2+-dependent. Some examples where such complexity may relate to neuroendocrine regulation of hormone secretion/synthesis are discussed. We show that the functional and spatial heterogeneity of Ca2+ stores generates Ca2+ signals with sufficient spatiotemporal complexity to simultaneously control multiple Ca2+-dependent cellular functions in neuroendocrine systems.