# VSFCM: A Novel Viewpoint-Driven Subspace Fuzzy C-Means Algorithm
## 5 Conclusions  
This paper has proposed a new subspace clustering algorithm, which is named viewpoint-driven subspace fuzzy c-means algorithm (VSFCM), and has achieved good clustering results. The main work and contributions of this paper are summarized as follows:  
First of all, in view of the problem that a large number of clustering algorithms are sensitive to the initialization of cluster centers, we propose a new cut-off distance under the system of the DPC algorithm and further provide a cut-off distance-induced clustering initialization method CDCI, which is used as an initialization strategy for cluster centers and also served as a new viewpoint selection strategy. It makes the initial cluster center closer to the true cluster center, which not only improves the clustering convergence speed, but also promotes the clustering accuracy to a certain extent.  
Secondly, by taking the viewpoint obtained by CDCI as being reflective of domain knowledge, the fuzzy clustering idea driven by knowledge and data is proposed. Subsequently, we introduce the subspace clustering mode and fuzzy feature weight processing mechanism and propose the separation formula between clusters, which is optimized with the viewpoint. On the basis of these, we establish the viewpoint-driven subspace fuzzy c-means algorithm (VSFCM). The viewpoint in it helps guide the clustering algorithm to discover the real data structure and thus get better clustering results. Additionally, the introduced separation term between clusters can maximize the distance between cluster centers in real time, achieve the maximum separation between clusters, and also optimize the internal mechanism of clustering.  
Finally, by applying our proposed VSFCM algorithm and comparison algorithms (V-FCM, SCAD, ESSC, FRPCM, and DVPFCM) to the three types of data sets, we can see that the proposed VSFCM algorithm performs best in terms of the five indicators, and exhibits stronger stability.  
Our clustering algorithm has a certain degree of noise resistance [5; 41; 42], but its effectiveness is not outstanding and can be further improved in the future. Moreover, there is room for improvement in the number of iterations and iteration time of our algorithm, which can be reduced by optimizing our algorithm structure and parameter settings.  
In addition, the work of this study can be extended to the clustering of granular information [30; 43; 44; 45], which will offer new directions for data analysis. Moreover, we can develop our fuzzy clustering algorithm in the field of fuzzy reasoning [46; 47] and carry on clustering for the fuzzy rules.  
Conceptualization, Y.T. and R.C.; methodology, Y.T. and B.X.; software, R.C. and B.X.; validation, Y.T., R.C. and B.X.; formal analysis, Y.T.; investigation, R.C.; resources, B.X.; data curation, R.C.; writing--original draft preparation, R.C. and B.X.; writing--review and editing, Y.T.; visualization, R.C.; supervision, Y.T.; project administration, R.C.; funding acquisition, Y.T. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Key Research and Development Program of China under Grant 2020 YFC1523100, the National Natural Science Foundation of China under Grants 62176083, 62176084, 61877016, and 61976078, the Key Research and Development Program of Anhui Province under Grant 202004d07020004, the Natural Science Foundation of Anhui Province under Grant 2108085 MF203.  
Not applicable.  
A preliminary version of this work was presented at the 2 nd International Conference on AI Logic and Applications (AILA 2022), and its title is \"Viewpoint-driven Subspace Fuzzy C-Means Algorithm\".  
The authors declare no conflict of interest.  
Following are two abbreviation lists corresponding to the algorithm and symbols presented in this manuscript, respectively.