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Classical attribute reduction algorithms based on attribute significance initiate too many jobs ( O(| C|2)) when they run in MapReduce. To improve the efficiencies of these algorithms, we proposed a novel reduction algorithm. Instead of focusing on attribute significance, the notion of a core attribute was applied to construct a new heuristic reduction algorithm, and only | C| jobs were considered to obtain a reduct. The algorithm only included two basic operations: compare and sort. The latter was optimised using the shuffle mechanism in MapReduce, which provided an efficient sorting ability for big data. In particular, we connected jobs in an iterative form to transfer the processing result of the former job to the latter job. Finally, experimental results demonstrated that the proposed attribute reduction algorithm was efficient and significantly improved upon the classical algorithms in runtime and number of jobs.

Attribute reduction is one of the challenging problems in rough set theory. To accomplish an efficient reduction algorithm, this paper analyzes the shortcomings of the traditional methods based on attribute significance, and suggests a novel reduction way where the traditional attribute significance calculation is replaced by a special core attribute calculation. A decision table called the positive region sort ascending decision table (PR-SADT) is defined to optimize some key steps of the novel reduction method, including the special core attribute calculation, positive region calculation, etc. On this basis, a fast reduction algorithm is presented to obtain a complete positive region reduct. Experimental tests demonstrate that the novel reduction algorithm achieves obviously high computational efficiency.

In this paper, we introduce the principle of identifying state transition based on the Van der Pol-Duffing oscillator in weak signal detection, which demonstrate the importance to indicate external perturbation existence and detect weak signal accurately. Starting from analyzing the insufficiency of employing classical identification methods occurring in the detecting process, we put forward a novel identification method named region analyzation method to improve the deficiency. Then, an establishment and feasibility analysis of this proposed method are described exhaustively. Numerical experiments on merits of this proposed method that is compared with the classical methods are carried out. The results indicate that this proposed method has better identifying capability than the classical methods and provides extendibility to engineering application.

Effective and fast attribute reduction algorithm on high-dimensional dataset is one of the most important issues of big data, and several parallel attribute reduction algorithms were implemented by using MapReduce. However, MapReduce is not suitable for iterative computing, which causes low calculation efficiency in many cases. In this paper, we proposed a novel parallel attribute reduction algorithm by considering the new generation distributed computing framework Apache Spark. First, the core attribute decision strategy is proposed to replace the traditional attribute significance calculation, and the number of iterations is reduced from C R − R 2 ∕ 2 + | R | ∕ 2 to C ( C represents the number of condition attributes and R represents the number of attributes in the reduct result). Furthermore, for high-dimensional datasets, we designed a batch processing strategy to reduce the number of iterations exponentially. Second, the proposed algorithm was speeded up with three techniques, including: (1) the network data transmission is minimized based on the localized operation; (2) a single cache iteration method is suggested to reduce disk I/O cost; (3) some calculations are skipped by an interruption strategy. In the experimental analysis, we succeeded with various types of real big datasets and random datasets in a real distributed computing environment and compared with the classic MapReduce-based parallel attribute reduction algorithm PAAR_PR in various aspects. Experimental conclusions proved that the computing efficiency of our algorithm has been improved by more than 98% compared to the classic parallel attribute reduction algorithm PAAR_PR.

In order to resolve the degradation phenomenon of the classical three-way decisions model based on rough set three-regions, the notion of decision trap is proposed to make a novel three-way decisions model for decision tables (3WD-D). 3WD-D adopts the trisection-acting frame, and redefines three types of strategies in acting component as accept right decisions, reject decision traps and non-commitment, respectively. Based on the new strategies, the universe is divided into three new regions. They are acceptance region (AR), rejection region (RR), and delay region (DR), respectively. The related theory analysis and experiments show that 3WD-D resolve the degradation phenomenon and is effective in decision tables.

The orthogonal frequency division multiplexing (OFDM) modulation technique has been used widely in visible light communications (VLC) systems to combat intersymbol interference. At the same time, the inherent drawback of OFDM with a high peak-to-average power ratio (PAPR) is brought into OFDM visible light communications (VLC-OFDM). Furthermore, considering the limited dynamic range characteristics of light-emitting diodes, the performance degradation caused by a high PAPR is more serious in VLC-OFDM. In this paper, we propose a partial transmit sequence (PTS) technique based on the combination of a genetic algorithm (GA) and a hill-climbing algorithm (GH-PTS) to solve the problem of high PAPR. GH-PTS is a modified PTS technique based on GA-PTS. Essentially, GH-PTS is a local optimization of GA-PTS. Simulation results show that the optimized technique is able to reduce PAPR more effectively without any loss of bit error rate performance than the GA-PTS technique in VLC-OFDM system.