Aiming at the problem of high time complexity of Conditional Preference networks (CP-nets) graph model in reasoning computation, a Generating CP-nets with Bounded Tree Width based on Dandelion code (BTW-CP-nets Gen) algorithm was proposed. First, through the principle of bidirectional mapping between Dandelion code and tree structure with tree width k ( k-tree), the decoding and encoding algorithms between Dandelion code and k-tree were derived to realize the one-to-one mapping between code and tree structure. Second, the k-tree was used to constrain the tree width of CP-nets structure, and the k-tree feature tree was used to obtain the directed acyclic graph structure of CP-nets. Finally, the bijection of discrete multi-valued functions was used to calculate the conditional preference table of each CP-nets node, and the dominant query test was executed to the generated bounded tree-width CP-nets. Theoretical analysis and experimental data show that, compared with the Pruffer code generating k-tree (Pruffer code) algorithm, BTW-CP-nets Gen algorithm has the running time on generating simple and complex structures reduced by 21.1% and 30.5% respectively,and the node traversal ratio of the graph model generated by BTW-CP-nets Gen in the dominant query is 18.48% and 29.03% higher on simple structure and complex structure respectively; the smaller the time consumed by BTW-CP-nets Gen algorithm, the higher the traversal node ratio of the dominant query. It can be seen that BTW-CP-nets Gen algorithm can effectively improve the algorithm efficiency in graph model reasoning.

Aiming at the problem that Overlapping Coalition Structure Generation (OCSG) in the Framework of cooperative games with Overlapping Coalitions (OCF games) is difficult to solve, an effective algorithm based on greedy method was proposed. First, the OCF games with number of coalition k constraints (kOCF games) was used to limit the scale of the OCSG problem. Then, a similarity measure was introduced to represent the similarity between any two coalition structures, and the property of monotonicity was defined based on the similarity measure, which means that the higher the similarity between a coalition structure and optimal coalition structure, the greater the monotonicity value of this coalition. Finally, for the kOCF games with monotonicity, the method of inserting player numbers one by one to approximate the optimal coalition structure was used to design the Coalition Constraints Greed (CCG) algorithm to solve the given OCSG problem, and the complexity of CCG algorithm was proved to be O( n2 ^k+1) theoretically. The influences of different parameters and coalition value distribution on the performance of the proposed algorithm were analyzed and verified through experiments, and this algorithm was compared with the algorithm proposed by Zick et al. (ZICK Y, CHALKIADAKIS G, ELKIND E, et al. Cooperative games with overlapping coalitions:charting the tractability frontier. Artificial Intelligence, 2019, 271:74-97) in the terms such as constraint condition. The results show that when the maximum number of coalitions k is constrained by a constant, the search times of the proposed algorithm increase linearly with the number of agents. It can be seen that CCG algorithm is tractable with the fixed-parameter k and has better applicability.

The traditional spectral clustering algorithm needs too much time to perform eigen-decomposition when the number of samples is very large. In order to solve the problem, a fast spectral clustering algorithm without eigen-decomposition was proposed to reduce the time overhead by multiplication update iteration. Firstly, the Nyström algorithm was used for random sampling in order to establish the relationship between the sampling matrix and the original matrix. Then, the indicator matrix was updated iteratively based on the principle of multiplication update iteration. Finally, the correctness and convergence analysis of the designed algorithm were given theoretically. The proposed algorithm was tested on five widely used real datasets and three synthetic datasets. Experimental results on real datasets show that:the average Normalized Mutual Information (NMI) of the proposed algorithm is 0.45, which is improved by 12.5% compared with that of the k-means clustering algorithm; the computing time of the proposed algorithm achieves 61.73 s, which is decreased by 61.13% compared with that of the traditional spectral clustering algorithm; and the performance of the proposed algorithm is superior to that of the hierarchical clustering algorithm, which verify the effectiveness of the proposed algorithm.

To solve the problem of low feature extraction efficiency in movie scoring, a Nyström method combined with QR decomposition was proposed. Firstly, sampling was performed using an adaptive method, QR decomposition of the internal matrix was performed, and the decomposed matrix was recombined with the internal matrix for feature decomposition. The approximate process of Nyström method was closely related to the number of selected landmarks and the process of selecting marker points. A series of point markers were selected to ensure the similarity after sampling. The adaptive sampling method can ensure the accuracy of approximation. QR decomposition can ensure the stability of the matrix and improve the accuracy of the preference feature extraction. The higher the accuracy of the preference feature extraction, the higher the stability of the recommendation system and the higher the accuracy of the recommendation. Finally, a feature extraction experiment was performed on a dataset of actual audience ratings of movies. The movie rating dataset contained 480189 users and 17770 movies. The experimental results show that when extracting the same number of landmarks, accuracy and efficiency of the improved Nyström method are improved to a certain degree, the time complexity is reduced from original O( n ³) to O( nc ²) ( c<< n) compared to pre-sampling. Compared with the standard Nyström method, the error is controlled below 25%.

To solve the problem that users and products can not be accurately selected in large data sets, and the problem that user behavior preference can not be predicted accurately, a new method of CUR (Column Union Row) matrix decomposition was proposed. A small number of columns were selected from the original matrix to form the matrix C, and a small number of rows were selected to form the matrix R. Then, the matrix U was constructed by Orthogonal Rotation (QR) matrix decomposition. The matrixes C and R were feature matrixes of users and products respectively, which were composed of real data, and enabled to reflect the detailed characters of both users as well as products. In order to predict behavioral preferences of users accurately, the authors improved the CUR algorithm in this paper, endowing it with greater stability and accuracy in terms of matrix recovery. Lastly, the experiment based on real dataset (Netflix dataset) indicates that, compared with traditional singular value decomposition, principal component analysis and other matrix decomposition methods, the CUR matrix decomposition algorithm has higher accuracy as well as better interpretability in terms of feature selection, as for matrix recovery, the CUR matrix decomposition also shows superior stability and accuracy, with a preciseness of over 90%. The CUR matrix decomposition has a great application value in the recommender system and traffic flow prediction.

In order to solve the problem that conditional constraints (context constraints) for personalized queries in database were not fully considered, a constraint model was proposed where the context i ^+≻i-| X means that the user prefers i ⁺ than i ^- based on the constraint of context X. Association rules mining algorithm based on MaxClique was used to obtain user preferences, and Conditional Preference Mining (CPM) algorithm combined with context obtained preference rules was proposed to obtain user preferences. The experimental results show that the context preference mining model has strong preference expression ability. At the same time, under the different parameters of minimum support, minimum confidence and data scale, the experimental results of preferences mining algorithm of CPM compared with Apriori algorithm and CONTENUM algorithm show that the proposed CPM algorithm can obviously improve the generation efficiency of user preferences.

Focusing on the issue that the traditional recommendation system requires users to give a clear preference matrix (U-I matrix) and then uses automation technology to capture the user preferences, a method for mining preference information of Agent from preference database was introduced. From the perspective of knowledge discovery, a k order preference mining algorithm named kPreM was proposed according to the Ceteris Paribus rules (CP rules). The k order CP rules were used to prune the information in the preference database, which decreased the database scanning times and increased the efficiency of mining preference. Then a general graph model named CP-nets (Conditional Preference networks) was used as a tool to reveal that the user preferences can be approximated by the corresponding CP-nets. The theoretical analysis and simulation results show that the user preferences are conditional preferences. In addition, the xcavation of CP-nets preference model provides a theoretical basis for designing personalized recommendation system.