{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:49Z","timestamp":1760242549770,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,11,6]],"date-time":"2017-11-06T00:00:00Z","timestamp":1509926400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673245","61573213","61703243"],"award-info":[{"award-number":["61673245","61573213","61703243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The decision tree algorithm is a core technology in data classification mining, and ID3 (Iterative Dichotomiser 3) algorithm is a famous one, which has achieved good results in the field of classification mining. Nevertheless, there exist some disadvantages of ID3 such as attributes biasing multi-values, high complexity, large scales, etc. In this paper, an improved ID3 algorithm is proposed that combines the simplified information entropy based on different weights with coordination degree in rough set theory. The traditional ID3 algorithm and the proposed one are fairly compared by using three common data samples as well as the decision tree classifiers. It is shown that the proposed algorithm has a better performance in the running time and tree structure, but not in accuracy than the ID3 algorithm, for the first two sample sets, which are small. For the third sample set that is large, the proposed algorithm improves the ID3 algorithm for all of the running time, tree structure and accuracy. The experimental results show that the proposed algorithm is effective and viable.<\/jats:p>","DOI":"10.3390\/a10040124","type":"journal-article","created":{"date-parts":[[2017,11,6]],"date-time":"2017-11-06T11:39:38Z","timestamp":1509968378000},"page":"124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Improvement of ID3 Algorithm Based on Simplified Information Entropy and Coordination Degree"],"prefix":"10.3390","volume":"10","author":[{"given":"Yingying","family":"Wang","sequence":"first","affiliation":[{"name":"School of Control Science and Engineering, Shandong University, Jinan 250061, China"}]},{"given":"Yibin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Shandong University, Jinan 250061, China"}]},{"given":"Yong","family":"Song","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai 264209, China"}]},{"given":"Xuewen","family":"Rong","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Shandong University, Jinan 250061, China"}]},{"given":"Shuaishuai","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Information Technology, Shandong University of Science and Technology, Jinan 250031, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,11,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1016\/j.eswa.2006.02.016","article-title":"Data Mining techniques for the detection of fraudulent financial statements","volume":"32","author":"Kirkos","year":"2007","journal-title":"Exp. Syst. Appl."},{"key":"ref_2","unstructured":"Witten, I.H., and Frank, E. (2000). Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations, Morgan Kaufmann Publisher."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gandhi, M., and Singh, S.N. (2015, January 25\u201327). Predictions in Heart Disease Using Techniques of Data Mining. Proceedings of the International Conference on Futuristic Trends on Computational Analysis and Knowledge Management, Noida, India.","DOI":"10.1109\/ABLAZE.2015.7154917"},{"key":"ref_4","unstructured":"Vishnubhotla, P.R. (2004). Storing Data Mining Clustering Results in a Relational Database for Querying and Reporting. (6,718,338), U.S. Patent."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1109\/TKDE.2003.1245283","article-title":"Benchmarking Attribute Selection Techniques for Discrete Class Data Mining","volume":"15","author":"Hall","year":"2003","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1017\/S0269888907001026","article-title":"A review of associative classification mining","volume":"22","author":"Thabtah","year":"2007","journal-title":"Knowl. Eng. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0898-1221(90)90354-M","article-title":"Parallelism and fast solution of linear systems","volume":"19","author":"Codenotti","year":"1990","journal-title":"Comput. Math. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2870","DOI":"10.1016\/j.eswa.2007.05.035","article-title":"Application of wrapper approach and composite classifier to the stock trend prediction","volume":"34","author":"Huang","year":"2008","journal-title":"Exp. Syst. Appl."},{"key":"ref_9","first-page":"2452","article-title":"Predicting stock returns by classifier ensembles","volume":"11","author":"Tsai","year":"2011","journal-title":"Appl. Comput."},{"key":"ref_10","unstructured":"Ahmadi, A., Omatu, S., and Kosaka, T. (2003, January 18\u201320). A PCA Based Method for Improving the Reliability of Bank Note Classifier Machines. Proceedings of the International Symposium on Image and Signal Processing and Analysis, Rome, Italy."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1108\/15265940710834753","article-title":"Prediction of bank failures in emerging financial markets: An ANN approach","volume":"8","author":"Ozkan","year":"2007","journal-title":"J. Risk Financ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3109\/00952999009001570","article-title":"Evaluation and treatment of adolescent substance abuse: A decision tree method","volume":"16","author":"Tarter","year":"1990","journal-title":"Am. J. Drug Alcohol. Abus."},{"key":"ref_13","unstructured":"Sekine, S., Grishman, R., and Shinnou, H. (1998, January 15\u201316). A Decision Tree Method for Finding and Classifying Names in Japanese Texts. Proceedings of the Sixth Workshop on Very Large Corpora, Montreal, QC, Canada."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/0893-6080(91)90012-T","article-title":"ARTMAP: Supervised real-time learning and classification of nonstationary data by a self-organizing neural network","volume":"4","author":"Carpenter","year":"1991","journal-title":"Neural Netw."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2298\/ACI0903065V","article-title":"International Statistical Classification of Diseases and Related Health Problems","volume":"56","author":"Vukasinovi","year":"2009","journal-title":"Acta Chir. Iugosl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1002\/sim.650","article-title":"A comparison of statistical methods for meta-analysis","volume":"20","author":"Brockwell","year":"2001","journal-title":"Stat. Med."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1007\/s10772-017-9429-x","article-title":"A decision tree using ID3 algorithm for English semantic analysis","volume":"20","author":"Phu","year":"2017","journal-title":"Int. J. Speech Technol."},{"key":"ref_18","first-page":"62","article-title":"In Defense of C4.5: Notes on Learning One-Level Decision Trees","volume":"254","author":"Elomaa","year":"1994","journal-title":"Mach. Learn. Proc."},{"key":"ref_19","first-page":"1137","article-title":"Rule-Based Classification Systems Using Classification and Regression Tree (CART) Analysis","volume":"67","author":"Lawrence","year":"2001","journal-title":"Photogr. Eng. Remote Sens."},{"key":"ref_20","first-page":"13","article-title":"A comparative study of decision tree ID3 and C4.5","volume":"4","author":"Hssina","year":"2014","journal-title":"Int. J. Adv. Comput. Sci. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Al-Sarem, M. (arXiv, 2015). Predictive and statistical analyses for academic advisory support, arXiv.","DOI":"10.5121\/ijcsit.2015.7510"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0165-1765(84)90126-5","article-title":"A note on the calculation and interpretation of the Gini index","volume":"15","author":"Lerman","year":"1984","journal-title":"Econ. Lett."},{"key":"ref_23","unstructured":"Fayyad, U.M., and Irani, K.B. (1992, January 12\u201316). The Attribute Selection Problem in Decision Tree Generation. Proceedings of the National Conference on Artificial Intelligence, San Jose, CA, USA."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1142\/S0218488504002631","article-title":"The Information Entropy, Rough Entropy and Knowledge Granulation in Rough Set Theory","volume":"12","author":"LIANG","year":"2008","journal-title":"Int. J. Uncertain. Fuzziness Knowl.-Based Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.artmed.2007.04.001","article-title":"A methodology for the automated creation of fuzzy expert systems for ischaemic and arrhythmic beat classification based on a set of rules obtained by a decision tree","volume":"40","author":"Exarchos","year":"2007","journal-title":"Artif. Intell. Med."},{"key":"ref_26","unstructured":"Quinlan, J.R. (1987, January 23\u201328). Generating Production Rules from Decision Trees. Proceedings of the International Joint Conference on Artificial Intelligence, Cambridge, MA, USA."},{"key":"ref_27","unstructured":"Sneyers, J., Schrijvers, T., and Demoen, B. (2005, January 2\u20135). The computational power and complexity of Constraint Handling Rules. Proceedings of the 2nd Workshop on Constraint Handling Rules, Sitges, Spain."},{"key":"ref_28","first-page":"1","article-title":"Coordination degree analysis of regional industry water use system","volume":"5","author":"Lei","year":"2004","journal-title":"J. Hydraul. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S1872-583X(09)60004-8","article-title":"Coordination Degree of Urban Population, Economy, Space, and Environment in Shenyang Since 1990","volume":"18","author":"Zhang","year":"2008","journal-title":"China Popul. Resour. Environ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1016\/j.datak.2007.05.005","article-title":"MMR: An algorithm for clustering categorical data using Rough Set Theory","volume":"63","author":"Parmar","year":"2007","journal-title":"Data Knowl. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Quinlan, J.R. (1986). Induction of Decision Trees, Kluwer Academic Publishers.","DOI":"10.1007\/BF00116251"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.ieri.2013.11.029","article-title":"Cascade Quality Prediction Method Using Multiple PCA+ID3 for Multi-Stage Manufacturing System","volume":"4","author":"Arif","year":"2013","journal-title":"Ieri Procedia"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1023\/A:1022694001379","article-title":"A Distance-Based Attribute Selection Measure for Decision Tree Induction","volume":"6","year":"1991","journal-title":"Mach. Learn."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1109\/12.863040","article-title":"Arithmetic on the European logarithmic microprocessor","volume":"49","author":"Coleman","year":"2001","journal-title":"IEEE Trans. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0893-6080(00)00093-9","article-title":"A pruning method for the recursive least squared algorithm","volume":"14","author":"Leung","year":"2001","journal-title":"Neural Netw."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1626","DOI":"10.1002\/2015WR017394","article-title":"Simulating California reservoir operation using the classification and regression-tree algorithm combined with a shuffled cross-validation scheme","volume":"52","author":"Yang","year":"2016","journal-title":"Water Resour. Res."},{"key":"ref_37","unstructured":"Kohavi, R. (1995, January 20\u201325). A study of Cross-Validation and Bootstrap for Accuracy Estimation And Model Selection. Proceedings of the International Joint Conference on Artificial Intelligence, Montreal, QC, Canada."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3735","DOI":"10.1016\/j.csda.2009.04.009","article-title":"Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap","volume":"53","author":"Kim","year":"2009","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Refaeilzadeh, P., Tang, L., and Liu, H. (2016). Cross-Validation. Encyclopedia of Database Systems, Springer.","DOI":"10.1007\/978-1-4899-7993-3_565-2"},{"key":"ref_40","unstructured":"Mumtaz, K., Sheriff, S.A., and Duraiswamy, K. (2009, January 4\u20136). Evaluation of three neural network models using Wisconsin breast cancer database. Proceedings of the International Conference on Control, Automation, Communication and Energy Conservation, Perundurai, India."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/4\/124\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:48:18Z","timestamp":1760208498000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/4\/124"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,6]]},"references-count":40,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["a10040124"],"URL":"https:\/\/doi.org\/10.3390\/a10040124","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2017,11,6]]}}}