Discernibility matrix based incremental feature selection on fused decision tables

Abstract In rough set philosophy, each set of data can be seen as a fuzzy decision table. Since a decision table dynamically increases with time and space, these decision tables are integrated into a new one called fused decision table. In this paper, we focus on designing an incremental feature selection method on fused decision table by optimizing the space constraint of storing discernibility matrix. Here discernibility matrix is a known way of discernibility information measure in rough set theory. This paper applies the quasi/pseudo value of discernibility matrix rather than the true value of discernibility matrix to design an incremental mechanism. Unlike those discernibility matrix based non-incremental algorithms, the improved algorithm needs not save the whole discernibility matrix in main memory, which is desirable for the large data sets. More importantly, with the increment of decision tables, the discernibility matrix-based feature selection algorithm could constrain the computational cost by applying efficient information updating techniques—quasi/pseudo approximation operators. Finally, our experiments reveal that the proposed algorithm needs less computational cost, especially less occupied space, on the condition that the accuracy is limitedly lost.

[1]  Shi-Jinn Horng,et al.  Matrix-based dynamic updating rough fuzzy approximations for data mining , 2017, Knowl. Based Syst..

[2]  Jiye Liang,et al.  The Information Entropy, Rough Entropy And Knowledge Granulation In Rough Set Theory , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  Qiang Shen,et al.  Dynamic feature selection with fuzzy-rough sets , 2013, 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[4]  Hui Xiong,et al.  IDR/QR: An Incremental Dimension Reduction Algorithm via QR Decomposition , 2005, IEEE Trans. Knowl. Data Eng..

[5]  Ming-Wen Shao,et al.  Attribute reduction based on k-nearest neighborhood rough sets , 2019, Int. J. Approx. Reason..

[6]  Z. Pawlak Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[7]  Jiye Liang,et al.  Ieee Transactions on Knowledge and Data Engineering 1 a Group Incremental Approach to Feature Selection Applying Rough Set Technique , 2022 .

[8]  Jianzhong Li,et al.  Incremental Detection of Inconsistencies in Distributed Data , 2012, IEEE Transactions on Knowledge and Data Engineering.

[9]  Qinghua Hu,et al.  A Fitting Model for Feature Selection With Fuzzy Rough Sets , 2017, IEEE Transactions on Fuzzy Systems.

[10]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[11]  Wai Keung Wong,et al.  Granular maximum decision entropy-based monotonic uncertainty measure for attribute reduction , 2019, Int. J. Approx. Reason..

[12]  Degang Chen,et al.  The Model of Fuzzy Variable Precision Rough Sets , 2009, IEEE Transactions on Fuzzy Systems.

[13]  Da Ruan,et al.  Neighborhood rough sets for dynamic data mining , 2012, Int. J. Intell. Syst..

[14]  Wenhao Shu,et al.  An incremental approach to attribute reduction from dynamic incomplete decision systems in rough set theory , 2015, Data Knowl. Eng..

[15]  Xiaojun Xie,et al.  A novel incremental attribute reduction approach for dynamic incomplete decision systems , 2018, Int. J. Approx. Reason..

[16]  Yiyu Yao,et al.  Interpreting Concept Learning in Cognitive Informatics and Granular Computing , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Yi Cheng,et al.  The incremental method for fast computing the rough fuzzy approximations , 2011, Data Knowl. Eng..

[18]  Jianhua Dai,et al.  Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification , 2013, Appl. Soft Comput..

[19]  Pan Yunhe,et al.  A Parallel Approximate Rule Extracting Algorithm Based on the Improved Discernibility Matrix , 2004 .

[20]  Guoyin Wang,et al.  RRIA: A Rough Set and Rule Tree Based Incremental Knowledge Acquisition Algorithm , 2003, Fundam. Informaticae.

[21]  Hongmei Chen,et al.  Dynamic maintenance of approximations in set-valued ordered decision systems under the attribute generalization , 2014, Inf. Sci..

[22]  Zhang Yi,et al.  Incremental rough set approach for hierarchical multicriteria classification , 2018, Inf. Sci..

[23]  Dun Liu,et al.  A fuzzy rough set approach for incremental feature selection on hybrid information systems , 2015, Fuzzy Sets Syst..

[24]  Wojciech Ziarko,et al.  DATA‐BASED ACQUISITION AND INCREMENTAL MODIFICATION OF CLASSIFICATION RULES , 1995, Comput. Intell..

[25]  Qinghua Hu,et al.  On Robust Fuzzy Rough Set Models , 2012, IEEE Transactions on Fuzzy Systems.

[26]  Hui Wang,et al.  Fuzzy rough set based incremental attribute reduction from dynamic data with sample arriving , 2017, Fuzzy Sets Syst..

[27]  Guoyin Wang,et al.  A Decision-Theoretic Rough Set Approach for Dynamic Data Mining , 2015, IEEE Transactions on Fuzzy Systems.

[28]  Isabelle Guyon,et al.  An Introduction to Variable and Feature Selection , 2003, J. Mach. Learn. Res..

[29]  Marzena Kryszkiewicz,et al.  FUN: Fast Discovery of Minimal Sets of Attributes Functionally Determining a Decision Attribute , 2008, Trans. Rough Sets.

[30]  Tianrui Li,et al.  Dynamical updating fuzzy rough approximations for hybrid data under the variation of attribute values , 2017, Inf. Sci..

[31]  Min Chen,et al.  Rough Cluster Quality Index Based on Decision Theory , 2009, IEEE Transactions on Knowledge and Data Engineering.

[32]  Tianrui Li,et al.  An incremental attribute reduction approach based on knowledge granularity under the attribute generalization , 2016, Int. J. Approx. Reason..

[33]  Shang Gao,et al.  Pseudo-label neighborhood rough set: Measures and attribute reductions , 2019, Int. J. Approx. Reason..

[34]  Qinghua Hu,et al.  Feature Selection Based on Neighborhood Discrimination Index , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Qinghua Hu,et al.  Feature selection based on maximal neighborhood discernibility , 2018, Int. J. Mach. Learn. Cybern..

[36]  Da Ruan,et al.  Probabilistic model criteria with decision-theoretic rough sets , 2011, Inf. Sci..

[37]  Ming-Wen Shao,et al.  Feature subset selection based on fuzzy neighborhood rough sets , 2016, Knowl. Based Syst..

[38]  Wang Guo-ying An incremental rule acquisition algorithm based on variable precision rough set model , 2005 .

[39]  Guoyin Wang,et al.  Incremental Attribute Reduction Based on Elementary Sets , 2005, RSFDGrC.

[40]  Witold Pedrycz,et al.  Data-Distribution-Aware Fuzzy Rough Set Model and its Application to Robust Classification , 2016, IEEE Transactions on Cybernetics.

[41]  Yi Pan,et al.  A Parallel Matrix-Based Method for Computing Approximations in Incomplete Information Systems , 2015, IEEE Transactions on Knowledge and Data Engineering.

[42]  Maria E. Orlowska,et al.  Maintenance of Knowledge in Dynamic Information Systems , 1992, Intelligent Decision Support.

[43]  Hong-Ying Zhang,et al.  Feature selection and approximate reasoning of large-scale set-valued decision tables based on α-dominance-based quantitative rough sets , 2017, Inf. Sci..

[44]  Dun Liu,et al.  Dynamic Maintenance of Approximations in Dominance‐Based Rough Set Approach under the Variation of the Object Set , 2013, Int. J. Intell. Syst..

[45]  Tianrui Li,et al.  Composite rough sets for dynamic data mining , 2014, Inf. Sci..

[46]  Ivo Düntsch,et al.  Uncertainty Measures of Rough Set Prediction , 1998, Artif. Intell..

[47]  Xizhao Wang,et al.  Attributes Reduction Using Fuzzy Rough Sets , 2008, IEEE Transactions on Fuzzy Systems.

[48]  Rajen B. Bhatt,et al.  On fuzzy-rough sets approach to feature selection , 2005, Pattern Recognit. Lett..

[49]  Fan Min,et al.  Cost-sensitive approximate attribute reduction with three-way decisions , 2019, Int. J. Approx. Reason..

[50]  Tianrui Li,et al.  Fast algorithms for computing rough approximations in set-valued decision systems while updating criteria values , 2015, Inf. Sci..

[51]  Wei Wei,et al.  Discernibility matrix based incremental attribute reduction for dynamic data , 2018, Knowl. Based Syst..

[52]  Qiang Shen,et al.  Centre for Intelligent Systems and Their Applications Fuzzy Rough Attribute Reduction with Application to Web Categorization Fuzzy Rough Attribute Reduction with Application to Web Categorization Fuzzy Sets and Systems ( ) – Fuzzy–rough Attribute Reduction with Application to Web Categorization , 2022 .

[53]  Chien-Chung Chan,et al.  A Rough Set Approach to Attribute Generalization in Data Mining , 1998, Inf. Sci..

[54]  Hamido Fujita,et al.  An incremental attribute reduction approach based on knowledge granularity with a multi-granulation view , 2017, Inf. Sci..

[55]  Xue Rong Zhao,et al.  Cost-sensitive three-way class-specific attribute reduction , 2019, Int. J. Approx. Reason..

[56]  Shi-Jinn Horng,et al.  A Group Incremental Reduction Algorithm with Varying Data Values , 2017, Int. J. Intell. Syst..

[57]  Richard Jensen,et al.  Towards scalable fuzzy-rough feature selection , 2015, Inf. Sci..

[58]  Jiye Liang,et al.  A new method for measuring uncertainty and fuzziness in rough set theory , 2002, Int. J. Gen. Syst..

[59]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[60]  Ge Yu,et al.  i2MapReduce: Incremental mapreduce for mining evolving big data , 2015, 2016 IEEE 32nd International Conference on Data Engineering (ICDE).

[61]  Wei-Zhi Wu,et al.  Maximal-Discernibility-Pair-Based Approach to Attribute Reduction in Fuzzy Rough Sets , 2018, IEEE Transactions on Fuzzy Systems.

[62]  Geert Wets,et al.  A rough sets based characteristic relation approach for dynamic attribute generalization in data mining , 2007, Knowl. Based Syst..

[63]  Qinghua Hu,et al.  Information-preserving hybrid data reduction based on fuzzy-rough techniques , 2006, Pattern Recognit. Lett..

[64]  Tran Cao Son,et al.  Incremental Information Extraction Using Relational Databases , 2012, IEEE Transactions on Knowledge and Data Engineering.

[65]  Zeung nam Bien,et al.  Incremental Inductive Learning Algorithm in the Framework of Rough Set Theory and its Application , 1998 .

[66]  Yee Leung,et al.  Granular Computing and Knowledge Reduction in Formal Contexts , 2009, IEEE Transactions on Knowledge and Data Engineering.

[67]  Baoli Wang,et al.  An incremental attribute reduction method for dynamic data mining , 2018, Inf. Sci..

[68]  Da Ruan,et al.  Rough sets based matrix approaches with dynamic attribute variation in set-valued information systems , 2012, Int. J. Approx. Reason..

[69]  Ronald R. Yager,et al.  Participatory Learning With Granular Observations , 2009, IEEE Transactions on Fuzzy Systems.

[70]  Lei Zhu,et al.  Incremental and Decremental Max-Flow for Online Semi-Supervised Learning , 2016, IEEE Transactions on Knowledge and Data Engineering.

[71]  Liang Li,et al.  Particle swarm optimization algorithm for the location of the critical non-circular failure surface in two-dimensional slope stability analysis , 2007 .

[72]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

[73]  Jonathan Lawry,et al.  Granular Knowledge Representation and Inference Using Labels and Label Expressions , 2010, IEEE Transactions on Fuzzy Systems.

[74]  Degang Chen,et al.  An incremental algorithm for attribute reduction with variable precision rough sets , 2016, Appl. Soft Comput..

[75]  Qiang Shen,et al.  Selecting informative features with fuzzy-rough sets and its application for complex systems monitoring , 2004, Pattern Recognit..

[76]  Liu Zong,et al.  An Incremental Arithmetic for the Smallest Reduction of Attributes , 1999 .

[77]  Jianzhong Li,et al.  Incremental Detection of Inconsistencies in Distributed Data , 2014, IEEE Trans. Knowl. Data Eng..

[78]  Lu Wang,et al.  Multi-objective attribute reduction in three-way decision-theoretic rough set model , 2019, Int. J. Approx. Reason..

[79]  Witold Pedrycz,et al.  Positive approximation: An accelerator for attribute reduction in rough set theory , 2010, Artif. Intell..

[80]  Xizhao Wang,et al.  On the generalization of fuzzy rough sets , 2005, IEEE Transactions on Fuzzy Systems.

[81]  Degang Chen,et al.  Active Sample Selection Based Incremental Algorithm for Attribute Reduction With Rough Sets , 2017, IEEE Transactions on Fuzzy Systems.

[82]  Xizhao Wang,et al.  Dynamic ensemble extreme learning machine based on sample entropy , 2012, Soft Comput..

[83]  Wei Wei,et al.  Accelerating incremental attribute reduction algorithm by compacting a decision table , 2018, Int. J. Mach. Learn. Cybern..

[84]  Yang Ming An Incremental Updating Algorithm for Attribute Reduction Based on Improved Discernibility Matrix , 2007 .