Incremental non-negative matrix factorization is an unsupervised learning algorithm based on subspace dimensionality reduction technology. In this paper, the idea of fisher discriminant analysis is introduced into incremental non-negative matrix factorization, and an incremental learning algorithm of non-negative matrix factorization with discriminative information and constraints is proposed. Firstly, prior information of original training samples is utilized to initialize the incremental coefficient matrix through an index matrix. Secondly, the object function of incremental non-negative matrix factorization is improved to be a batch-incremental learning algorithm with the constraints of maximizing between-class scatter and minimizing within-class scatter. Finally, the factor matrices are calculated by the method of multiplicative iteration. Experimental results on ORL, Yale B and PIE face databases show the effectiveness of the proposed method.

Inspired by the ideas of factorization and attribute reduction, the concept reduction preserving binary relations is proposed. Firstly, the definition of concept reduction preserving binary relations is given and the judgment theorems of corresponding consistent sets and reduct are proposed. Secondly, according to the roles of formal concepts in the process of concept reduction preserving binary relations, formal concepts are classified into three types: core concepts, relative necessary concepts and unnecessary concepts. Finally, the characteristics of three types of concepts are discussed, and the related conclusions about three types of concepts are given from the perspective of binary relations and operators. The results in this paper provide a research basis for the further study in algorithm,application and deeper theoretical analysis.

Since the interaction of different types of amino acid has an influence on the prediction of protein structure, convolutional neural networks and long short-term memory neural networks are integrated. A convolutional long short-term memory neural network is proposed to predict 8-class protein secondary structures. Firstly, the protein sequence is represented based on the amino acid sequence class feature and the amino acid structure profile feature. The local correlation characteristics between amino acid residues are extracted by the convolutional operations, and then the long-range interactions between the residues on protein sequences are extracted by the bi-directional long short-term memory network. Finally, the local correlation characteristics and long-range interactions between amino acid residues are employed to predict protein secondary structures. Experimental results show that the proposed model achieves a higher accuracy than the baselines and the framework has good scalability.

In the inconsistent decision table, the generalized decision reduction is not fully consistent with the relative reduction. The definitions of generalized decision reduction and the relative reduction are given in both partition-based and covering-based belief structures respectively. Then, the evidence structure characteristic of the two reduction methods are intensively studied. The results show that the generalized decision reduction set is the minimal attribute set maintaining the sum of the plausibility functions of the generalized decision unchanged, while the relative reduction set is the minimal attribute set maintaining the sum of the belief functions of the generalized decision unchanged. On the basis of those, the generalized belief reduction is defined in partition-based and covering-based belief structures, respectively. The consistency among generalized decision reduction, generalized belief reduction and relative reduction are further analyzed. The results verify that the generalized decision reduction set must be a relative consistent reduction set and the generalized decision reduction is equivalent to the generalized belief reduction. It is proved that the generalized decision reduction of a given decision table must be its relative coordination set, and the core set of the relative reduction is included in the generalized decision reduction. The necessary and sufficient condition that the generalized reduction is identical with the relative reduction is given in two different belief structures respectively.