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A classification algorithm with Linear Discriminant Analysis and Axiomatic Fuzzy Sets

  • * Corresponding author: Xiaodong Liu

    * Corresponding author: Xiaodong Liu 
The work is supported by National Natural Science Foundation of China under grants 61673082 and 61533005.
Abstract Full Text(HTML) Figure(7) / Table(2) Related Papers Cited by
  • 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.

    Citation:

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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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV
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