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# A classification algorithm with Linear Discriminant Analysis and Axiomatic Fuzzy Sets

• * Corresponding author: Xiaodong Liu
The work is supported by National Natural Science Foundation of China under grants 61673082 and 61533005.
• In exploratory data mining, most classifiers pay more attention on the accuracy and speed of learned models, but they are lacking of the interpretability. In this paper, an interpretable and comprehensible classifier is proposed based on Linear Discriminant Analysis (LDA) and Axiomatic Fuzzy Sets (AFS). The algorithm utilizes LDA to extract features with the largest inter-class variance. Besides, the proposed approach aims to explore a transformation from the selected feature space to a semantic space where the samples in the same class are made as close as possible to one another, whereas the samples in the different class are as far as possible from one another. Moreover, the descriptions of each class can be obtained by the proposed approach. When compared with well-known classifiers such as LogisticR, C4.5Tree, SVM and KNN, the proposed method not only can achieve better performance in terms of accuracy but also has the capability of interpretability and comprehension.

Mathematics Subject Classification: Primary: 03B52, 03E72, 28E10, 94D05.

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• Figure 1.  The proposed classifier flow chart

Figure 2.  Samples in abstract features space

Figure 3.  The membership degree of $m_1$ on all data

Figure 4.  The membership degree of description Class 1

Figure 5.  The membership degree of description Class 2

Figure 6.  The membership degree of description Class 3

Figure 7.  The membership degree of three class descriptions on all samples

Table 1.  The maximum, average and minimum of each abstract feature

 feature $f_1$ $f_2$ minimum -1.73 -2.36 average 0.00 0.00 maximum 1.61 2.44

Table 2.  The experiments results-accuracy rates(standard deviation)

 dataset LogisticR C4.5Tree SVM KNN Our method wine 0.9556$\pm$0.0032 0.9364$\pm$0.0127 0.7900$\pm$0.0118 0.7074$\pm$0.0141 0.9666$\pm$0.0005 iris 0.9593$\pm$0.0021 0.9520$\pm$0.0053 0.9826$\pm$0.0071 0.9647$\pm$0.0032 0.9867$\pm$0.0000 heart 0.8399$\pm$0.0038 0.7544$\pm$0.0230 0.6918$\pm$0.0181 0.6604$\pm$0.0118 0.8407$\pm$0.0000 breast_C 0.7220$\pm$0.0209 0.7142$\pm$0.0209 0.6034$\pm$0.0241 0.5405$\pm$0.0118 0.7753$\pm$0.0038 seeds 0.9228$\pm$0.0020 0.9286$\pm$0.0089 0.9271$\pm$0.0055 0.8828$\pm$0.0088 0.8590$\pm$0.0093 USD 0.7309$\pm$0.0052 0.9321$\pm$0.0090 0.9510$\pm$0.0017 0.8247$\pm$0.0133 0.7912$\pm$0.0090 column_2c 0.8258$\pm$0.0030 0.8067$\pm$0.0205 0.8625$\pm$0.0031 0.8280$\pm$0.0064 0.7697$\pm$0.0040 caesarian 0.6741$\pm$0.0189 0.5263$\pm$0.0341 0.6551$\pm$0.0161 0.5589$\pm$0.0326 0.7253$\pm$0.0125 immunotherapy 0.7973$\pm$0.0139 0.8073$\pm$0.0262 0.7897$\pm$0.0000 0.7235$\pm$0.0208 0.7617$\pm$0.0091 SHS2015 0.5572$\pm$0.0133 0.6126$\pm$0.0133 0.6443$\pm$0.0213 0.5445$\pm$0.0561 0.6498$\pm$0.0028
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