Development of Adaptive Fuzzy-Neuro Generalized Learning-Vector Quantization Using PI Membership Function (AFNGLVQ-PI)

Abstract

In a real-world environment, there are several difficult obstacles to overcome in classification. Those obstacles are data overlapping and skewness of data distribution. Overlapping data occur when many data from different classes overlap with each other; this condition often occurs when there are many classes in a data set. On other hand, skewness of data distribution occurs when the data distribution is not a Gaussian (normal) distribution. To overcome these two problems, a new method called Adaptive Fuzzy-Neuro Generalized Learning Vector Quantization using PI membership function (AFNGLVQ-PI) is proposed in this study. AFNGLVQ-PI is derived from Fuzzy-Neuro Generalized Learning Vector Quantization using the PI membership function (FNGLVQ-PI). In FNGLVQ-PI, the updated values for minimum and maximum variables in the fuzzy membership function are set based on the mean of the updated values. Whereas, in the newly proposed AFNGLVQ-PI, updated values for minimum, maximum, and mean variables are derived based on the differential equations to approximate the data distribution better. In this study, the newly proposed AFNGLVQ-PI algorithm was tested and verified on twelve different data sets. Two of the data sets are synthetic data sets where we could compare the performance of the data sets in different overlapping conditions and levels of skewness. The rest of the data sets were chosen and used as a benchmark to compare the performance of the proposed algorithm. In the experiment, AFNGLVQ-PI took first place in 18 out of 29 experiments. Furthermore, AFNGLVQ-PI also achieved positive improvements for all data sets used in the experiments, which could not be achieved by the Learning Vector Quantization (LVQ), Generalized Learning Vector Quantization (GLVQ), and other commonly used algorithms, such as SVM, kNN, and MLP.

Keywords

• AFNGLVQ-PI
• classification
• FNGLVQ
• GLVQ
• Fuzzy