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Ensemble clustering helps achieve fast clustering under abundant computing resources by constructing multiple base clusterings. Compared with the standard single clustering algorithm, ensemble clustering integrates the advantages of multiple clustering algorithms and has stronger robustness and applicability. Nevertheless, most ensemble clustering algorithms treat each base clustering result equally and ignore the difference of clusters. If a cluster in a base clustering is reliable/unreliable, it should play a critical/uncritical role in the ensemble process. Fuzzy-rough sets offer a high degree of flexibility in enabling the vagueness and imprecision present in real-valued data. In this paper, a novel fuzzy-rough induced spectral ensemble approach is proposed to improve the performance of clustering. Specifically, the significance of clusters is differentiated, and the unacceptable degree and reliability of clusters formed in base clustering are induced based on fuzzy-rough lower approximation. Based on defined cluster reliability, a new co-association matrix is generated to enhance the effect of diverse base clusterings. Finally, a novel consensus spectral function is defined by the constructed adjacency matrix, which can lead to significantly better results. Experimental results confirm that the proposed approach works effectively and outperforms many state-of-the-art ensemble clustering algorithms and base clustering, which illustrates the superiority of the novel algorithm. [ABSTRACT FROM AUTHOR]

Background: The performance of nearest‐neighbour classification is highly sensitive to the quality of data. In order to reduce the impact of the inevitable existence of irrelevant features in data, this paper employs the information learned by neural networks to implement a feature weighting technique and associated weighted multi‐functional nearest‐neighbour classification method. Method: The non‐iterative neural networks are easy to implement while enjoying remarkable computational efficiency. In this paper, four non‐iterative neural networks (ELM, E‐ELM, RAWN and RVFL) are employed to evaluate the significance of features to decisions learned and stored in the parameters of neural networks. Moreover, the bias of the significance of features is comforted by using cross‐validation. The resulting feature significance is converted into feature weights to further implement weighted multi‐functional nearest‐neighbour classification. Result: The experimental results demonstrate that the proposed neuro‐weighted feature weighting strategy can effectively reduce the impact of irrelevant features and enhance the performance of multi‐functional nearest‐neighbour classification. Contribution: The proposed algorithm explores an avenue to efficiently utilize the learned knowledge of neural networks to reduce the role of irrelevant feature in nearest‐neighbour classification. [ABSTRACT FROM AUTHOR]

Knowledge reduction is a crucial topic in formal concept analysis. There always exists uncertain, symmetric linguistic-evaluation information in social life, which leads to high complexity in the process of knowledge representation. In order to overcome this problem, we are focused on studying the linguistic-concept-reduction methods in an uncertain environment with fuzzy linguistic information. Based on three-way decisions and an attribute-oriented concept lattice, we construct a fuzzy-object-induced three-way attribute-oriented linguistic (FOEAL) concept lattice, which provides complementary conceptual structures of a three-way concept lattice with symmetric linguistic-evaluation information. Through the granular concept of the FOEAL lattice, we present the corresponding linguistic concept granular consistent set and granular reduction. Then, we further employ the linguistic concept discernibility matrix and discernibility function to calculate the granular reduction set. A similar issue on information entropy is investigated to introduce a method of entropy reduction for the FOEAL lattice, and the relation between the linguistic concept granular reduction and entropy reduction is discussed. The efficiency of the proposed method is depicted by some examples and comparative analysis. [ABSTRACT FROM AUTHOR]