# VSFCM: A Novel Viewpoint-Driven Subspace Fuzzy C-Means Algorithm
## 1 Introduction
In other words, different characteristic features should have different importance in clustering. [PERSON] and [PERSON] [29] proposed a feature-reduction FCM (FRFCM) algorithm, which automatically calculated the weight of a single feature while reducing the influence of these unrelated features. [PERSON] et al. [30] proposed a new kernel fuzzy clustering method called viewpoint-based kernel fuzzy clustering with weight information granules (VWKFC). Because its new initialization algorithm is more efficient in selecting cluster centers, namely the kernel-based hypersphere density initialization algorithm, combined with weight information particles and viewpoint induction mechanisms, VWKFC is significantly superior to the other eight existing related algorithms in processing high-dimensional data. In the early stage, the clustering process was entirely data-driven. In fact, domain knowledge could be used to assist the development of clustering. [PERSON] et al. [31] introduced knowledge into a data-driven process, where knowledge was embodied through viewpoints, thus giving a viewpoint-based fuzzy clustering algorithm V-FCM. [PERSON] et al. [32] proposed a new knowledge and data-driven fuzzy clustering algorithm, which was called the density viewpoint-induced possibilistic fuzzy clustering algorithm (DVPFCM). Therefore, a new calculation method of density radius was proposed. Based upon this, the hypersphere density-based cluster center initialization (HDCCI) algorithm was established to obtain the initial cluster centers in densely sampled areas. Then, the high-density points obtained by the HDCCI method were used as new viewpoints, and they would be integrated into the DVPFCM algorithm. The current problems of fuzzy clustering algorithms are mainly as follows:  
* Sensitive to cluster initialization Most fuzzy clustering algorithms are sensitive to the initial results of clustering. For example, FCM, V-FCM, SCAD, ESSC, and FRFCM all rely on the result of the initializationmethod. Compared with them, the initialization processing mechanism in the DVPFCM algorithm is better; that is, the initialization method HDCCI is based on the DPC algorithm. However, the HDCCI algorithm still has a shortcoming existing in the calculation method of cut-off distance. It uses a fixed and strict formula, which lacks a solid foundation and proof process and can not adapt to various data sets. * Weak adaptability to high-dimensional data With the arrival of the big data era, the volume of information is constantly increasing, and the dimensions are getting higher simultaneously, which forces clustering algorithms to have the ability to deal with high-dimensional data properly. However, most clustering algorithms are still weak in this aspect. When faced with high-dimensional data, FCM, V-FCM, and DVPFCM have no corresponding measures. Obviously, none of them can do this. SCAD, ESSC, and FRFCM all use subspace processing methods with different weights, which are relatively, better. However, the algorithms mentioned above are purely data-driven algorithms, and the clustering efficiency and accuracy of high-dimensional data cannot reach the ideal level. In this study, we put forward the VSFCM algorithm and the following is a brief introduction. On the one hand, we put forward a new optimized cut-off distance calculation method based on the DPC algorithm, which can select the point with the highest density as the viewpoint to induce the algorithm to find the cluster center more accurately. That is, the cut-off distance-induced clustering initialization method CDCI provides a new initialization strategy and perspective in this field. Under the guidance of this initialization method, the number of iterations of the algorithm is reduced, and the accuracy of the algorithm is also improved. On the other hand, we introduce viewpoints into subspace clustering to improve the convergence speed of each subspace.