知识矩阵表示

doi:10.16088/j.issn.1001-6600.2022031004

摘要/Abstract

摘要： 知识表示是一切人工智能算法得以运行的基础,它能够把人类知识表示成机器可以处理的数据结构。本文介绍知识矩阵表示,它可以从知识表示的根本上简化算法的运行过程并提高算法的运行效率。具体地,本文首先将时态推理中的13种区间关系表示转化成5×5矩阵,在此基础上,时态关系演算与传播可以通过矩阵计算获得。然后,将产生式规则的相互关系转化成矩阵,并编码成一个计算公式,它是一个不确定性推理的数学模型。最后,将样本关系表示成矩阵,一次计算就可以获得K值和K个最近邻点,它可以将KNN分类的懒惰学习部分模型化,即转化成数学模型。除此之外,本文展望知识矩阵表示未来的工作,提出知识矩阵表示需要针对不同的应用定义不同的演算方法。

关键词: 知识表示, 矩阵表示, 关系演算, 时态推理, KNN分类

Abstract: Knowledge representation is the basis of all artificial intelligence algorithms. It can represent human knowledge as a data structure that can be processed by machines. This paper shows the knowledge matrix representation, which can fundamentally simplify the operation process of the algorithm and improve the operation efficiency of the algorithm. Specifically, this paper first transforms 13 kinds of interval relationship representations in temporal reasoning into 5×5 matrix. On this basis, the calculation and propagation of temporal relations can be obtained through matrix calculation. Then, the relationship between production rules is transformed into a matrix and encoded into a calculation formula, which is a mathematical model of uncertain reasoning. Finally, the sample relationship is expressed as a matrix, and K values and K nearest neighbors can be obtained in one step calculation. It can model the lazy learning part of KNN classification, i.e., transform it into a mathematical model. In addition, this paper also looks forward to the future work of knowledge matrix representation, and points out that knowledge matrix representation needs to define different calculation methods for different applications.

Key words: knowledge representation, matrix representation, relation calculus, temporal reasoning, KNN classification

中图分类号:

TP181

张师超, 李佳烨. 知识矩阵表示[J]. 广西师范大学学报（自然科学版）, 2022, 40(5): 36-48.

ZHANG Shichao, LI Jiaye. Knowledge Matrix Representation[J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(5): 36-48.

参考文献

[1]MESKE C, BUNDE E, SCHNEIDER J, et al. Explainable artificial intelligence: objectives, stakeholders, and future research opportunities[J]. Information Systems Management, 2022, 39(1): 53-63. DOI: 10.1080/10580530.2020.1849465.
[2]LONGONI C, CIAN L. Artificial intelligence in utilitarian vs. hedonic contexts: the “word-of-machine” effect[J]. Journal of Marketing, 2022, 86(1): 91-108. DOI: 10.1177/0022242920957347.
[3]YANG Y, LIU Y, LÜ X Y, et al. Anthropomorphism and customers’ willingness to use artificial intelligence service agents[J]. Journal of Hospitality Marketing & Management, 2022, 31(1): 1-23. DOI: 10.1080/19368623.2021.1926037.
[4]ZHANG K, CHEN K Z. Artificial intelligence: opportunities in lung cancer[J]. Current Opinion in Oncology, 2022, 34(1): 44-53. DOI: 10.1097/CCO.0000000000000796.
[5]ALBAWI S, MOHAMMED T A, AL-ZAWI S. Understanding of a convolutional neural network[C]// 2017 International Conference on Engineering and Technology (ICET). Piscataway, NJ: IEEE Press, 2017: 1-6. DOI: 10.1109/ICEngTechnol.2017.8308186.
[6]ZHANG C X, SONG D J, HUANG C, et al. Heterogeneous graph neural network[C]// Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. New York, NY: Association for Computing Machinery, 2019: 793-803. DOI: 10.1145/3292500.3330961.
[7]苗旭鹏, 周跃, 邵蓥侠, 等. GSO: 基于图神经网络的深度学习计算图子图替换优化框架[J]. 计算机科学, 2022, 49(3): 86-91. DOI: 10.11896/jsjkx.210700199.
[8]黄春, 姜浩, 全哲, 等. 面向深度学习的批处理矩阵乘法设计与实现[J]. 计算机学报, 2022, 45(2): 225-239. DOI: 10.11897/SP.J.1016.2022.00225.
[9]LIU H W, LI X L, ZHANG S C, et al. Adaptive hashing with sparse matrix factorization[J]. IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(10): 4318-4329. DOI: 10.1109/TNNLS.2019.2954856.
[10]ZHU X F, ZHANG S C, HE W, et al. One-step multi-view spectral clustering[J]. IEEE Transactions on Knowledge and Data Engineering, 2019, 31(10): 2022-2034. DOI: 10.1109/TKDE.2018.2873378.
[11]ZHU X F, YANG J Y, ZHANG C Y, et al. Efficient utilization of missing data in cost-sensitive learning[J]. IEEE Transactions on Knowledge and Data Engineering, 2021, 33(6): 2425-2436. DOI: 10.1109/TKDE.2019.2956530.
[12]ZHAO L, SUN Q, YE J P, et al. Multi-task learning for spatio-temporal event forecasting[C]// Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY: Association for Computing Machinery, 2015: 1503-1512. DOI: 10.1145/2783258.2783377.
[13]FENG W, ZHANG C, ZHANG W, et al. STREAMCUBE: hierarchical spatio-temporal hashtag clustering for event exploration over the Twitter stream[C]// 2015 IEEE 31st International Conference on Data Engineering. Piscataway, NJ: IEEE Press, 2015: 1561-1572. DOI: 10.1109/ICDE.2015.7113425.
[14]张师超. 一个预测模型及性质[J]. 计算机学报, 1992, 15(4): 318-320.
[15]张师超. 时态关系代数与元组演算的等价性[J]. 计算机学报, 1993, 16(12): 936-939.
[16]张师超, 罗旭东. 一个模糊时态关系代数[J]. 软件学报, 1994, 5(9): 59-64.
[17]张师超, 张钹. 间断区间时态逻辑的语义[J]. 计算机学报, 1996, 19(12): 948-952. DOI: 10.3321/j.issn:0254-4164. 1996.12.010.
[18]ZHANG S C, LI J Y, ZHANG W Z, et al. Hyper-class representation of data[EB/OL]. (2022-01-28)[2022-03-10]. https://arxiv.org/abs/2201.13317. DOI: 10.48550/arXiv.2201.13317.
[19]YUE W C, LIU X, LI S Y, et al. Knowledge representation and reasoning with industrial application using interval-valued intuitionistic fuzzy Petri nets and extended TOPSIS[J]. International Journal of Machine Learning and Cybernetics, 2021, 12(4): 987-1013. DOI: 10.1007/s13042-020-01216-1.
[20]MOROZ O V. Model of self-organizing knowledge representation and organizational knowledge transformation[J]. American Journal of Artificial Intelligence, 2020, 4(1): 1-19. DOI: 10.11648/j.ajai.20200401.11.
[21]HUANG W M, HARRIE L. Towards knowledge-based geovisualisation using Semantic Web technologies: a knowledge representation approach coupling ontologies and rules[J]. International Journal of Digital Earth, 2020, 13(9): 976-997. DOI: 10.1080/17538947.2019.1604835.
[22]ALLEN J F. Maintaining knowledge about temporal intervals[J]. Communications of the ACM, 1983, 26(11): 832-843. DOI: 10.1145/182.358434.
[23]ALLEN J F. Towards a general theory of action and time[J]. Artificial Intelligence, 1984, 23(2): 123-154. DOI: 10.1016/0004-3702(84)90008-0.
[24]ZHANG S C, ZHANG C Q. IMC: a method for interval calculus in matrix[J]. Knowledge and Information Systems, 1999, 1(2): 257-268. DOI: 10.1007/BF03325100.
[25]ZHANG S C, ZHANG C Q. Propagating temporal relations of intervals by matrix[J]. Applied Artificial Intelligence, 2002, 16(1): 1-27.
[26]ZHANG C Q, ZHANG S C, ZHANG Z L. Temporal constraint satisfaction in matrix method[J]. Applied Artificial Intelligence, 2003, 17(2): 135-154. DOI: 10.1080/713827103.
[27]YANG T M, SHADLEN M N. Probabilistic reasoning by neurons[J]. Nature, 2007, 447(7148): 1075-1080.
[28]SANTOS Jr E. On linear potential functions for approximating Bayesian computations[J]. Journal of the ACM, 1996, 43(3): 399-430. DOI: 10.1145/233551.233552.
[29]ZHANG S C, ZHANG C Q. Encoding probability propagation in belief networks[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2002, 32(4): 526-531. DOI: 10.1109/TSMCA.2002.804784.
[30]ZHANG S C, LI X L, ZONG M, et al. Learning k for kNN classification[J]. ACM Transactions on Intelligent Systems and Technology, 2017, 8(3): 43. DOI: 10.1145/2990508.
[31]ZHANG S C, LI X L, ZONG M, et al. Efficient kNN classification with different numbers of nearest neighbors[J]. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(5): 1774-1785. DOI: 10.1109/TNNLS.2017.2673241.
[32]ZHANG S C, LI J Y. KNN classification with one-step computation[J/OL]. IEEE Transactions on Knowledge and Data Engineering[2022-03-10]. https://ieeexplore.ieee.org/document/9566737. DOI: 10.1109/TKDE.2021.3119140.
[33]NIE F P, HUANG H, CAI X, et al. Efficient and robust feature selection via joint l_2,1-norms minimization[C]// Advances in Neural Information Processing Systems 23(NIPS 2010). Red Hook, NY: Curran Associates Inc., 2010: 1813-1821.
[34]LI J Y, ZHANG S C, ZHANG L Y,et al. Unsupervised nonlinear feature selection algorithm via kernel function[J]. Neural Computing and Applications, 2020, 32(11): 6443-6454. DOI: 10.1007/s00521-018-3853-y.
[35]YUN H W, YU J H, LEE S B. Three dimensional disaster monitoring of the Pohang earthquake in the Republic of Korea by Sentinel-L[C]// IGARSS 2018-2018 IEEE International Geoscience and Remote Sensing Symposium. Piscataway, NJ: IEEE Press, 2018: 2228-2230. DOI: 10.1109/IGARSS.2018.8517289.
[36]BEYER K, GOLDSTEIN J, RAMAKRISHNAN R,et al. When is “nearest neighbor” meaningful?[C]// Database Theory-ICDT’99: LNCS Volume 1540. Berlin: Springer, 1999: 217-235. DOI: 10.1007/3-540-49257-7_15.
[37]ILESANMI A E, ILESANMI T O. Methods for image denoising using convolutional neural network: a review[J]. Complex & Intelligent Systems, 2021, 7(5): 2179-2198. DOI: 10.1007/s40747-021-00428-4.
[38]XIE J, COLONNA J G, ZHANG J L. Bioacoustic signal denoising: a review[J]. Artificial Intelligence Review, 2021, 54(5): 3575-3597. DOI: 10.1007/s10462-020-09932-4.
[39]KIM J H, KIM T S, CHOI J H, et al. End-to-end multi-task learning of missing value imputation and forecasting in time-series data[C]// 2020 25th International Conference on Pattern Recognition (ICPR). Los Alamitos, CA: IEEE Computer Society, 2021: 8849-8856. DOI: 10.1109/ICPR48806.2021.9412112.
[40]DONG W L, GAO S, YANG X B, et al. An exploration of online missing value imputation in non-stationary data stream[J]. SN Computer Science, 2021, 2(2): 57. DOI: 10.1007/s42979-021-00459-1.

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