Research on Identification of Consumer Product Quality Safety Factors Based on Improved FCM Algorithm

In view of the shortcomings of FCM algorithm, the membership degree and the cluster category number are improved to perfect the FCM algorithm. The performance of the improved algorithm is verified by a case of consumer product quality as a data source, and the results show that with the improved algorithm, both clustering accuracy rate and F value are improved.


Introduction
The consumer product quality safety has become a hot issue in the society, which is related to the people's physical and mental health and social harmony and stability. At present, the research in the field of consumer product quality safety in China is still in its initial stage, and the systematic method for identifying and analyzing the impact factors of consumer product quality safety has yet to be established. Based on the improved FCM clustering algorithm, the impact factors of consumer product quality safety can be effectively identified and extracted, and the scientificity and effectiveness of the supervision on consumer product quality safety can be further improved.

Another Section of Your Paper FCM clustering algorithm is a fuzzy clustering algorithm proposed by Dunn and developed by
Bezdek. To some extent, the reliability of FCM algorithm on clustering effect and stability depends on the initial setting of parameters. Reasonable selection of the cluster number and the initial value of fuzzy weighted index will affect the clustering results. In addition, FCM algorithm has some shortcomings [1][2][3]: (1) FCM algorithm has certain limitations in the reasonable identification of outlier data; (2) Whether in the FCM algorithm can be reasonably selected will directly affect the clustering results.
In order to overcome the above two shortcomings, this paper will improve the reasonable selection of cluster number and weighted index and the optimization of data identification of outliers in the following two aspects: firstly, FCM algorithm is sensitive to the outlier data, so it is necessary to 2 modify the membership degree of the data, i.e. modify the membership degree of the outlier data which deviates from the cluster center, so that it will have less impact on the clustering effect in the process of continuous update of the cluster center; secondly, the cluster number c should be reasonably selected. It is necessary to introduce the fuzzy division validity function. By this theory, we can compare the advantages and disadvantages of different cluster numbers, so that the number of categories can be determined automatically.

Weighted Membership Degree
In order to reduce the impact of such outlier X on the clustering effect, an improved membership method is proposed in this paper. The basic idea of this method is as follows [3][4][5][6]: For a given dataset , add a weighted value  to the fuzzy membership degree tk u of the dataset D studied, so as to reduce the impact of the outlier on the cluster center i P and improve the clustering analysis. The purpose of this method is to increase the impact of data point t d with high membership degree tk u on the cluster center position i P by introducing the weighted membership value  , and to reduce the impact of data point t d with small membership degree tk u on the cluster center position i P . The improved formula is shown below: As can be seen from the above formula, the value range of has been reduced to a certain extent compared with the original value of ( ) a tk U (the smaller the degree of membership, the more obvious the corresponding reduction). It can be clearly seen from the above formula that the impact of data point t d with small membership degree on the cluster center i P is reduced.  is the weighting coefficient, which is generally in the range of [0,1] . The larger  is, the smaller the adjustment range of membership degree tk u will be, and the result is relatively accurate; the smaller  is, the greater the adjustment range of membership degree tk u will be, and the result is better. Its advantage lies in speeding up the adjustment of membership degree tk u and improving the efficiency of the whole algorithm.

Steps of algorithm
The steps of improved FCM algorithm are as follows: (1) Given the cluster category number c ( 1 c n   , n is the number of samples) and the fuzzy index (1 ) m m    , the cluster center matrix is 1 2 [ , , , , , ] i c P P P P P    . Set the iteration stop threshold (1)  , the cluster prototype i P and the iteration counter (2) Update the division matrix ( ) a U with the iterative formula below. The iterative formula of membership degree is a mapping from a point to a set. In practical calculation, the following membership degree updating formula is usually adopted [6]: We can improve the membership degree to reduce the impact of the outlier on the cluster center: (3) The cluster prototype ( 1) v i

Data sources
It uses IRIS dataset as a test set to verify the improved FCM algorithm, and applies the "consumer product quality safety accident cases" as the data source to complete the identification and analysis of consumer product quality safety factors. The IRIS dataset uses the characteristics of iris as the data source, and the dataset contains 150 datasets. There are 200 cases of consumer product quality safety accidents, the data of which comes from consumer complaints, online public opinion and injury surveillance.   . Performance Comparison with Improved FCM Algorithm By importing the IRIS dataset, consumer product quality safety accident case dataset and idea algorithm into MATLAB, we can get clustering results before and after FCM algorithm improvement based on the IRIS dataset (as shown in Figure 2). The clustering results before and after FCM algorithm improvement based on the consumer product quality safety accident cases are shown in Figure 3. By calculating the accuracy rate and F value of the improved algorithm, we can get algorithm performance comparison data (as shown in Figure 4).

Conclusion
In view of the defects of the existing FCM algorithm, this paper suggests improvement in the following two aspects: firstly the weighted membership degree; secondly the optimal selection of cluster category number. After introducing new weight variables into the membership degree and putting forward a new membership degree update function, the impact of the outlier on the cluster center begins to decrease. According to the clustering validity function, this paper proposes a new method to discriminate the clustering validity function. In the experimental process, the IRIS dataset is used to verify the performance of the improved algorithm, and factor clustering analysis is carried out in combination with the dataset of typical consumer product quality safety accident cases. The results show that the clustering results based on the improved FCM algorithm are obviously better than those based on the unimproved FCM algorithm.