融合计算智能的蛋白质结构预测研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
后基因组时代生命科学中最重大的研究课题之一是蛋白质组研究,对蛋白质空间结构预测研究在整个蛋白质组计划中占有着极其重要的地位。蛋白质预测结构研究内容包括:序列预处理、二级结构预测、超二级结构预测、关联图预测、三级结构预测等。本文对其中的序列预处理、二级结构预测及关联图预测进行了深入研究。
     蛋白质序列由DNA序列翻译而来, DNA序列的质量高低决定了蛋白质结构预测的准确性。现有的DNA序列预处理工具对垃圾碱基信息的过滤和清除效率不高,且随着DNA序列长度的增加出错概率会显著升高。因此,本文对DNA序列的预处理进行了研究。
     BP神经网络广泛应用在蛋白质二级结构预测中,但是BP算法有其明显的缺陷,如训练速度慢、容易陷入局部极值等,这对蛋白质二级结构预测精度有重要影响,因此有必要对应用于蛋白质结构预测的神经网络算法进行改进;目前二级结构预测研究在特征表达上有缺陷,仅仅考虑氨基酸基本组成成份,特征信息表达不完整,忽略氨基酸疏水性特征以及氨基酸之间的长程作用,因此,研究基于更完善特征表达的蛋白质二级结构分类方法是有必要的。
     蛋白质的三维空间结构与其功能紧密相关,目前,从蛋白质二级结构直接预测三维空间结构非常困难,蛋白质关联图预测是蛋白质三级结构和二级结构之间的重要桥梁,因此蛋白质关联图预测有着重要的研究意义。论文取得的主要成果与创新工作概括如下:
     ①提出一种新的融合智能检测的DNA序列预处理方法,它不需要预先给出载体序列、剪接位点和克隆适配片段等信息,通过统计分析、随机搜索和图操作等方法自动发现并定位垃圾信息。此新方法可以作为组件工具供DNA序列数据处理管道系统调用。
     ②提出一种用于蛋白质二级结构预测的改进型动态隧道神经网络算法。神经网络具有容易陷入局部极小的缺点,动态隧道神经网络通过“钻隧道”方式,让目标函数跳出局部最小,找到更小的可行域,从而避免神经网络陷入局部极小。传统的动态隧道技术隧道方向单一并且随意,因此具有不稳定性。为了有效提高动态隧道的搜索效率,提出了一种改进型动态隧道神经网络算法。该算法增加搜索的隧道数,引入夹角弹性系数控制隧道方向,考察隧道之间的相互影响。在蛋白质二级结构预测实验中,改进型动态隧道神经网络算法预测的效果优于神经网络算法和传统的动态隧道神经网络算法。
     ③针对氨基酸疏水性特征以及氨基酸之间的长程作用在蛋白质二级结构预测中的影响进行了比较试验分析。目前采用机器学习进行蛋白质二级结构预测的方法,忽略氨基酸疏水性特征以及氨基酸之间的长程作用,因此准确率不高。用氨基酸对应的疏水能值替换蛋白质中相应的氨基酸,可以得到一个疏水能值的序列。实验中发现,用长的疏水能值序列,训练BP网络,对长程作用起主导的E结构(β-折叠)的预测效果好。
     ④基于比较完善的蛋白质特征表达提出Co-training算法。比较试验分析表明,氨基酸的长程作用在二级结构预测中对E结构(β-折叠)有重要的作用。因此,提出基于Profile编码特征和疏水能值特征两个独立冗余视图的Co-training算法。该算法的主要步骤为:在Profile特征空间训练SVM分类器,在疏水性特征空间训练BP神经网络分类器,协同对氨基酸二级结构进行预测;对SVM分类器和BP分类器有分歧的样本,基于主动选择思想,给予两个分类器不同的优先级进行仲裁。实验表明,Co-training方法有较高的准确性,对长程作用起主导的E结构(β-折叠),短程作用起主导的H结构(α-螺旋)预测准确率都有提高。
     ⑤首次将马尔科夫逻辑网应用到蛋白质关联图预测研究中。Markov逻辑网是将Markov网与一阶逻辑相结合的一种全新的统计关系学习模型,该方法可以计算出世界的概率分布,进而为推理服务。本文利用该方法的这一优点,将蛋白质关联图预测问题形式化。具体采用了判别式训练的学习算法和MC-SAT推理算法,并详细阐述了如何用少量的谓词公式来描述蛋白质关联图预测中不同方面的本质特征,将Markov逻辑表示的各方面组合起来形成各种模型。实验结果表明基于Markov逻辑网的蛋白质关联图预测方法可以取得比基于神经网络的方法更好的效果,从而为Markov逻辑网解决实际的预测问题提供了有效途径。
Proteomics is becoming an important research domain in the life science with the approach of post-genome area. Prediction of protein structures research takes a significant role in the whole proteomics plan. The content of protein structures prediction research includes sequences preprocessing, protein secondary structures prediction, protein supersecondary structures prediction, protein contact maps prediction, protein 3D structures prediction, etc. This paper made an intensive study on sequences preprocessing, protein secondary structures prediction and protein contact maps prediction.
     Protein sequences are translated from DNA sequences, so the quality of DNA sequences is an important factor to prediction accuracy of protein structures. Existing DNA sequences preprocessing tools are still not efficient in noise segments filtering and cleaning. The probability of error will increase significantly with the increasement of the length of DNA.Thus, this paper made research in DNA sequences preprocessing.
     BP neural networks have been widely used in protein secondary structures prediction, but they have some defects, such as slow convergence speed and local optimum traps. These defects influence the accuracy of protein structures prediction and need to be improved. Meanwhile, existing available methods for protein secondary structures prediction are limited on feature representation. Only basic compositon of amino acids is considerd in these methods as a result they are incapable of representing necessary information completely. The hydrophobicity of amino acids and interaction between amino acids which are far away from each other have been ignored.In this paper,an improved classification method for protein secondary structures predition based on more complete feature representation need to be furtherly explored.
     The 3D structures of proteins are tightly associated with specific functions. Nowadays, it is very difficult to predict the 3D structures from the secondary protein sequences. Protein contact maps are possible connecting ties between 3D structures and secondary structures. There is thus a need to predict the contact maps of proteins.
     The main contributions of this paper are summarized as follows:
     First of all, a novel DNA preprocessing method merging intelligent detection is proposed. This approach finds and locates contaminants automatically using statistical methods, random search and graph-theoretic operations but with no extra background information such as vector sequences, splice sites and clone adapters. This new method can be applied in the DNA data processing pipe as an independent component tool.
     Secondly, an improved dynamic tunneling neural network algorithm, which is applied in protein secondary structures prediction, has been proposed. Neural networks suffer from a defect of easily immersing in local traps. The dynamic tunneling technique helps neural networks to eliminate the local traps by“tunneling”and jumping into lower valleys of object function. However, the traditional dynamic tunneling technique tries to search in a random and single direction, thus it is instable. In order to improve the searching efficiency, an improved dynamic tunneling neural network algorithm has been proposed to enhance the stability by increasing the directions of tunneling and controlling the interaction between trajectories of the tunneling system with an angle spring coefficient. Experimental results show that the improved algorithm outperforms both the traditional neural network and the traditional dynamic tunneling neural network in the prediction of protein secondary structures.
     Thirdly, comparative experiments, which test the influence of the amino acid hydrophobic property and the interaction between far away amino acids in protein secondary structures prediction, have been implemented. Existing machine learning based protein secondary structures prediction methods suffer from low prediction accuracy because they ignore the amino acid hydrophobic property and the interaction between far away amino acids. A sequence of hydrophobic value can be built by replacing the amino acid by its hydrophobic energy value. Experiments show that the BP neural network using long amino hydrophobic energy value sequences works well in prediction of E structure (β-strand) which is controlled mainly by long amino acid-amino acid interaction.
     Fourthly, this paper proposes a Co-training algorithm based on different protein features. The comparative experiments show that the long amino acid-amino acid interaction plays a significant role on predicting E structure (β-strand). Therefore, a Co-training algorithm is explored which is based on both the profile space and the hydrophobic energy value space. They are sufficient and redundant views. In the proposed algorithm, there are two classifiers. One is the SVM classifier trained in the profile space, and the other is the BP neural network classifier trained in the hydrophobic energy value space, and they predict one amino acid’s secondary structure independently. If these two classifiers have different prediction results with one amino acid, an arbitration rule proposed in this paper is employed to make the final decision which is based on an active selecting strategy according to the two classifiers’different priority levels. The experimental results show that the proposed algorithm has higher prediction accuracy both in E structure (β-strand) which controlled mainly by the long interaction and H structure (α-helix) which controlled mainly by the short interaction than existing algorithms.
     Fifthly, Markov Logic Networks are applied in protein contact maps prediction first time. Markov Logic Networks (MLNs) are new Statistical Relational Learning models in which Markov networks and first-order logic are combined together. They are able to compute the probability distribution of worlds and serve for the inference. In this paper, we introduce the theory, learning methods and inference algorithms of Markov Logic Networks and then apply them to the protein contact maps prediction. This research adopts discriminative learning algorithm for Markov Logic Networks weights learning, MC-SAT algorithm for inference. This paper also shows how to capture the essential features of different aspects in protein contact maps prediction with a small number of predicate rules and how to combine these rules together to compose different models. It is proved that the method based on Markov Logic Networks is better than the way based on conventional neural networks in protein contact maps prediction by experimental results.This research provide a new solution for such kind of practical prediction problems.
引文
[1]邹东升.蛋白质超二级结构预测[D].博士学位论文,重庆大学,2009.
    [2]孙啸,陆祖宏,谢建明.生物信息学基础[M].北京:清华大学出版社,2005.
    [3]刘桂霞.蛋白质关联图预测[D].博士学位论文,吉林大学,2007.
    [4] C.G. Anfinsen. Principles that govern folding chains[J]. Science. 1973. 181: 223-230.
    [5] J.M. Berg, J.L. Tymoczko, L. Stryer. Biochemistry[M].W.H.Freeman and Company New York,2002.
    [6] F. Sanger, et al.DNA sequenceing with chain-terminating inhibitors[J].Procceedings of the National Academy of Sciences,USA,1977,74:5463-5467.
    [7] H.H.Chou, M.H.Holmes. DNA sequence quality trimming and vector removal[J].Bioinformatics 2001,17:1093-1104.
    [8] Software tools are available for vector removal:Crossmatch[EB/OL],[2009] www.phrap.org/phredphrapconsed.html.
    [9] Software tools are available for vector removal:VecScreen[EB/OL],[2009] www.ncbi.nlm.nih.gov/VecScreen.
    [10] P.Y.Chou, G.D. Fasman. Prediction of protein conformation[J].Biochemistry,1974,13:222-245.
    [11] J. Carnier, D.J. Osguthorpe, B. Robson. Analysis of the accuracy and implications of simple methods for predicting the secondary structure of globular proteins[J].Journal of Molecular Biology,1978,120:97-120.
    [12] B. Rost, C. Sander. Prediction of protein secondary structure at better than 70% accuarcy. Journal of Molecular Biology,1993,232:584-599.
    [13] S.F. Atschul, et al.Gapped BLAST and PSI-BLAST:a new generation of protein database search programs[J].Nucleric Acids Research,1997,25:3389-3402.
    [14] J.A. Cuff, G.J. Barton. Evaluation and improvement of multiple sequence methods for protein secondary structure prediction,Proteins,1999,34:508-519.
    [15] A.A.Salamov, V.V.Solovyev. Prediction of protein secondary structure by combining nearest-neighbor algorithms and multiple sequence alignments[J].Journal of Molecular Biology,1995,247(1):11-15.
    [16] D.Frishman,P.Argos.75% accuracy in protein secondary structure prediction[J].Proteins,1997,27:329-335.
    [17] C.Bystroff, V. Thorsson, D. Baker. HMMSTR:A hidden markov model for local sequence e-structure correlations in proteins[J].Journal of Molecular Biology,2000,301:173-190.
    [18] K.J. Won, T. Hamelryck, A. Prugel-Bennett, et al. Evolving hidden markov models for proteinsecondary structure prediction[C].In Proceedings of IEEE Congress on Evolutionary Computation,Edinburgh,2005,33-40.
    [19] D.W. Mount. Bioinfomatics sequence and genome analysis[M].Cold Spring Harbor Laboratory Press,New York,2001.
    [20] N. Qian, T.J. Sejnowski. Predicting the secondary structure of globular proteins using neural network models[J].Journal of Molecular Biology,1988,202(4):856-84.
    [21] B. Rost, C. Sander. Combining evolutionary information and neural networks to predict protein secondary structrue[J].Proteins,1994,19:55-72.
    [22] S. Hua, Z. Sun.A novel method of protein secondary structure prediction with high segment overlap measure:support vector machine approach[J].Journal of Molecular Biology,2001,308:397-407.
    [23] H. Kim, H. Park. Prediction of protein relative solvent accessibility with support vector machines and long-range interaction 3D local descriptor[R].Department of Computer Science and Engineering,University of Minnesota,2003.
    [24] J. Guo, H. Chen, Z.R. Sun, et al.A novel method for protein secondary structure prediction usingdual-layer SVM and profiles,Proteins 2004,54:738-743.
    [25] B. Rost, C. Sander. Third generation prediction of secondary structure[M].Humana Press,2000,71-95.
    [26] V. Vapnik. Statistical learning theory[M]. John Wiley&Sons,Inc.,New York,1998.
    [27]解彬彬.蛋白质分子进化及其与分子内相互作用的关系[D].博士学位论文,山东大学,2009年.
    [28] L. Mirny, E. Domany. Protein fold recognition and dynamics in the space of contact maps[J]. Proteins:Struct. Funct. Genet. 1996,26.,391-410.
    [29] P. Fariselli, R. Casadio. Neural network based prediction of residue contacts in protein[J].Protein Eng 1999;12:15-21.
    [30] M.S. Singer, G. Vriend, R.P. Bywater. Prediction of protein residue contacts with a PDB-derived likelihood matrix[J]. Protein Eng 2002;15:721-725.
    [31] G. Pollastri, P. Baldi. Prediction of contact maps by GIOHMM and recurrent neural networks using lateral propagation from all four cardinal corners[J]. Bioinformatics.2002;18,Suppl 1:S62-70.
    [32] V. Alessandro, F. Paolo. A bi-recursive neural network architecture for the predictionof protein coarse contact maps[C]. CSB:Proceedings of the IEEE Computer Society Conference on Bioinformatics.2002,ISBN:0-695-1653-X.187-196.
    [33] V. Alessandro, F. Paolo. Prediction of protein coarse contact maps[J],Bioinform Comput Biol.2003,(2):411-31.
    [34] Y. Zhao, K. George. Prediction of contact maps using support vector machines[C],3rd IEEE International conference on Bioinformatics and Bioengineering(BIBE),2003.pp.26-33.
    [35] H. Nicholas, B. Kevin, A. Mark. Ragan and Thomas Huber. Protein contact predictionusing patterns of correlation[J]. PROTEINS:Structure,Function, and BioInformatics,2004,56:679-684.
    [36] R.M. MacCallum. Striped sheets and protein contact prediction[J]. Bioinformatics.2004 Aug 4;20 Suppl 1:I224-I231.
    [37] G.Z. Zhang, D.S. Huang.Prediction of inter-residue contacts map based on generic algorithm optimized radial basis function neural network and binary input encoding scheme[J]. Journal of Computer-Aided Molecular Design, Volume 18,Number 12,December 2004,pp.797-810.
    [38] N. Gupta, N. Mangal, S. Biswas. Evolution and similarity evaluation of protein structures in contact map space[J]. PROTEINS:Structure,Proteins. 2005 May 1,59(2):196-204.
    [39] M.Punta, B.Rost. PROFcon:novel prediction of long-range contacts[J]. Bioinforamtics.2005,2960-8.
    [40] V. Alessandro, W. Lan, P. Gianluca. A two-stage approach for improved prediction of residue contact maps[J]. BMC Bioinformatics,2006,7:180.
    [41] M.Venduscolo, E.Kussell, E. Domany. Recovery of protein sturctures through contact maps[J].Folding and Design.1997,2(5):295-306.
    [42] W.Kabsch, C.Sander.Dictionary of secondary structure pattern recognition of hydrogenbonded and geometric features[J].Biopolymers,1983,22:2577-2637.
    [43]刘桂霞,于哲舟,周春光.基于带偏差递归神经网络蛋白质关联图的预测[J].吉林大学学报., 2008(46): p265–270.
    [44] K. Park, M. Vendruscolo, E. Domany. Toward an energy function for the contact map representation of proteins[J]..Protein:Stucture,Function and Genetics,2000,40(2):237-248.
    [45]许忠能主编.生物信息学[M].北京:清华大学出版社,2008.
    [46] M.Margulies,et al.Genome sequencing in microfabricated high-density picolitre reactors[J].Nature,2005,437:376-380.
    [47] S.Richards,et al.Comparative genome sequencing of Drosophila pseudoobscura:chromosomal,gene and cis-element evolution[J].Genome Research,2007,15:1-18.
    [48] B. Ewing, L. Hillier, M.C. Wendl, et al. Base-calling of automated sequence traces using phred.I. Accuracy assessment[J].Genome Research,1998,8:175-185.
    [49] Paracel. TRACE TUNER,capturing the most information from the latest DNA sequencingsystems.[EB/OL][2009] http://www.paracel.com/htm/tracetuner.html.
    [50] P. Indyk, R. Motwani. Approximate nearest neighbors:towards removing the curse of dimmensionality[C].In ACM,editor,Proceedings of the thirtieth annual ACM Symposium on Theory of Computing:Dallas,Texas,May 23-26,1998,604-613,New York,NY,USA,1998.ACM Press.
    [51] X. Dong, S.Y. Sung, W.K. Sung, et al. Constrained based method for finding motif in DNA sequences[C].In Proc. Of IEEE 4th Sympon.
    [52] W.K. Sung, W.H. Lee. Fast and accurate probe selection algorithm for large genomes[C].In Proceedings of IEEE Computer Society Bioinform atics Conference(CSB),Stanford,CA,2003.
    [53] H. Rehbein, J. Bogerd. Identification of genetically modified zebrafish(Danio rerio) by Protein-and-DNA-Analysis[J],Journal für Verbraucherschutz und Lebensmittelsicherheit,2007,2(2):122-125.
    [54] H. Simon,叶世伟,史忠植. Neural tetworks:a comprehensive foundation.2nd Edition[M].北京.机械工业出版社.2004,1.Page(s):663-686.
    [55] Y. Keiichiro, K. Takahiko. Multi-trajectory dynamic tunneling algorithm[C].Systems,Man and Cybemetics.2002 IEEE International Conference on Volume 1.6-9 Oct.2002 Page(s):472-477.
    [56] R. Pinaki, Y.P. Singh, Chansarkar RA. Dynamic Tunneling Technique for Efficient Training of Multilayer Perceptrons[C]. IEEE Transaction on Neural Networks,Vol. 10,No.1. January 1999.
    [57]阮晓钢,孙海军.编码对蛋白质二级结构预测的影响[J].北京工业大学学报,2005,31(3):229-235.
    [58] C. Mark, M. George. A Co-training algorithm for multi-view data with applications in data fusion[J]. Chemometrics, 2009, 23(8): 294-303.
    [59] S. Tong, E. Chang. Support vector machine active learning for image retrieval [C].In:Proceedings of ACM International Conferece on Multimedia,pp.107-118.ACM Press,New York,NY(2001).
    [60] C. Cornelia, C. Doina, S. Adrian, et al. Semi-supervised Prediction of Protein Subcellular Localization Using Abstrction Augmented Markov Models [J/OL]. BMC Bioinformatics,2010, 11(8): 1471-2105[2010-10-29]. http://www.biomedcentral.com/1471-2105/11/S8/S6.
    [61] J. Cheng, K. Wang. Active learning for image retrieval with Co-SVM[J]. Pattern Recognition, 2007, 40(1): 330~334.
    [62] A.Blum, T.Mitchell. Combining labeled and unlabeled data with co-training[C].In:Proceedings of the 11th Annual Conference on Computational Learning Theory(COLT’98),Wisconsin,MI,1998,92-100.
    [63]周志华.半监督学习中的协同训练风范[EB/OL][2007] http://cs.nju.edu.cn/zhouzh/zhouzh.files/publication/mla07-cotraining.pdf.
    [64] K.Nigam,R.Ghani.Analyzing the effectiveness and applicability of co-training[C].In:Proceedingsof the 9th ACM International Conference on Information and Knowledge Management(CIKM’00),McLean,VA,2000,86-93.
    [65] S. Goldman, Y. Zhou. Enhancing supervised learning with unlabeled data[C].In:Proceedings of the17th International Conference on Machine Learning(ICML’00),San Francisco,CA,2000,327-334.
    [66] D. Angluin, P. Laird. Learning from noisy examples[J].Machine Learning,1988,2(4):343-370.
    [67] Y. Zhou, S. Goldman. Democratic co-learning[C].In:Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence(ICTAI’04),Boca Raton,FL,2004.594–602.
    [68] Z.H. Zhou, M. Li. Tri-training:Exploiting unlabeled data using three classifiers[J].IEEE Transactions on Knowledge and Data Engineering,2005,17(11):1529–1541.
    [69] T.G. Dietterich. Ensemble methods in machine learning[C].In:Proceedings of the 1st International Workshop on Multiple Classifier Systems(MCS’00),Cagliari,Italy,LNCS 1867,2000,1-15.
    [70] X. Zhu, Z. Ghahramani, J. Lafferty. Semi-supervised learning using Gaussian fields and harmonic functions[C]. In: Proceedings of the 20th International Conference on Machine Learning(ICML’03), Washington, DC, 2003, 912-919.
    [71] Z.H. Zhou, M. Li. Semi-supervised learning with co-training style algorithm[J]. IEEE Transactions on Knowledge and Data Engineering, 2007, 19(11).
    [72] M. Li, Z.H. Zhou. Improve computer-aided diagnosis with machine learning techniques using undiagnosed samples[J].IEEE Transactions on Systems,Man and Cybernetics–Part A,in press.
    [73] D. Mavroeidis, K. Chaidos, S. Pirillos, et al. Using tri-training and support vector machines for addressing the ECML/PKDD 2006 discovery challenge[C].In: Proceedings of the ECML-PKDD Discovery Challenge Workshop,Berlin,Germany,2006,39-47.
    [74] I. Cohen, F.G. Cozman, N. Sebe, et al. Semisupervised learning of classifiers: Theory, algorithm and their application to human-computer interaction[J].IEEE Transaction on Pattern Analysis and Machine Intelligence,2004,26(12):1553-1567.
    [75] F.G. Cozman, I. Cohen. Unlabeled data can degrade classification performance of generative Classifiers[C].In:Proceedings of the 15th International Conference of the Florida Artificial Intelligence Research Society(FLAIRS’02),Pensacola,FL,2002,327-331.
    [76] Q. Tian, J. Yu, Q. Xue, et al. A new analysis of the value of unlabeled data in semi-supervisedlearning for image retrieval[C].In:Proceedings of the IEEE International Conference on Multimedia Expo(ICME’04),Taibei,2004,1019-1022.
    [77] M. Li, Z.H. Zhou. SETRED:Self-training with editing[C].In:Proceedings of 9th Pacific-Asia Conference on Knowledge Discovery and Data Mining(PAKDD’05),Hanoi,Vietnam,LNAI 3518,2005,611-621.
    [78]龙平,殷建平,祝恩,赵文涛.主动学习研究综述[J].计算机研究与发展. 2008, 45(Suppl.): 300- 304.
    [79] Y.H. Freund, S. Seung, E. Shamir, et al. Selective sampling using the query by committee algorithm[J]. Machine Learning, 1997,28(223):133-168.
    [80] D.D. Lewis, W.A. Gail. A sequential algorithm for training text classifiers[C].In:Proc ofthe 17th ACM Int’1 Conf on Research and Development in Information Retrieval.Berlin:Springer,1994.3-12.
    [81] A.K. McCallum, K. Nigram. Employing EM in pool-based active learning for text classification[C].In:Proc of the 15th Int’1 Conf on Machine Learning.San Francisco,CA:Morgan Kaufmann,1998.
    [82] I .Muslea, S. Minton, C.A. Knoblock. Active learning with multiple view[J].Journal of ArtificialIntelligence Research,2006,27:203-233.
    [83] W. Kabsch, C. Sander. Dictionary of protein secondary structure:Pattern recognition of hydrogen-bonded and geometrical features[J].Biopolymers,1983,22:2577-2637.
    [84] D.Frishman,P.Argos.Knowledge-based protein secondary structure assignment[J].Proteins,1995,23:566-579.
    [85] F.M. Richards, C.E. Kundrot. Identification of structural motifs from protein coordinatedata:secondary structure and first-level super-secondary structure[J].Proteins,1988,3:71-84.
    [86] A.J. Mandell, K.A. Selz, M.F. Shlesinger. Wavelet transformation of protein hydrophoblicity sequences suggests their memberships in structural families [J]. Physica:A,1997,244:254~262.
    [87]吴晓明,王波,程敬之.基于小波分析法的蛋白质结构研究[J].西安交通大学学报, 2002, 36(4): 414~417.
    [88] H.M. Berman, J. Westbrook, Z. Feng, et al. The protein data bank[J].Nucleic Acids Research,28,235-242.
    [89]屈婉玲,耿素云,张立昂.离散数学[M].高等教育出版社, 2008. 43.
    [90] M. Genesereth, N. Nilsson. Logical foundations of artificial intelligence[M]. San Mateo,CA: Morgan Kaufmann, 1987. 44.
    [91] S.Z. Li. Markov random field modeling in computer vision[M]. London, UK: Springer-Verlag, 1995. 41.
    [92] R. Kindermann, J.L. Snell. Markov random fields and their applications[M]. American Mathematical Society, 1980. 42.
    [93]黄涛.马尔可夫逻辑网在Web中的应用[J].硕士学位论文,重庆大学, 2010年.
    [94] D. Lowd, P. Domingos. Efficient Weight Learning for Markov Logic Networks[A]. Proceedings of the eleventh european conference on principles and practice of knowledge discovery in databases. Warsaw, Poland: Springer, 2007. 200~211.
    [95] J. Whittaker. Graphical models in applied multivariate statistics[M]. John Wiley and Sons, 1990. 37
    [96]孙舒杨,刘大有,孙成敏.基于后验概率的Markov逻辑网参数学习方法[J].吉林大学学报(理学版), 2006, (06):946~950.
    [97] C. Andrieu, F.N. de, A. Doucet, et al. An introduction to MCMC for machine learning[J]. Machine Learning, 2003, : 5~43.
    [98] S. Kok, P. Singla, M. Richardson, et al. The alchemy system for statistical relational AI[R]. Seattle, WA: Department of Computer Science and Engineering, University of Washington, 2005.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700