# Improved Selective Deep-Learning-Based Clustering Ensemble
## 1 Introduction  
With the explosive growth of 5G, big data have penetrated into every aspect of daily life [1]. These data typically present large scales, high dimensions, and complex structures [2]. How to mine valuable information from these complex data has become an urgent challenge at present [3]. Clustering analysis [4] is an essential technique in many fields of research that involves processing multidimensional data, such as pattern recognition, data retrieval, and bioinformatics. It is normally considered an unsupervised method for grouping data based on similarity [5]. Traditional clustering methods, such as k-means [6], spectral clustering [7], and Gaussian mixture clustering [8], have achieved good performance in various fields. However, most traditional clustering algorithms are only able to exploit shallow features of the data and cannot excavate the interdependence of complex data features in latent space [9]. On the other hand, there is no single clustering algorithm capable of suitably applying to all datasets, so various clustering algorithms are proposed and improved. To address this problem, the concept of clustering ensemble (consensus clustering) [10] is introduced, which is inspired by the success of the supervised classifiers ensemble. Clustering ensemble has been applied in many fields [11] and combines a set of clusterings into a final consensus clustering [12]. Generally, the clustering ensemble method refers to two steps: generation and consensus function. Generation is the first step in generating the set of base clusterings. In clustering ensemble, an appropriate generation process is very important because thefinal consensus result will be affected by the initial clusterings obtained in this step. The consensus function is the second step, and plays a major role in the clustering ensemble. It is a great challenge to define an appropriate consensus function to improve the results of single clustering algorithms. However, most of the existing base clustering algorithms used in the generation step of clustering ensemble methods are traditional shallow clustering algorithms. It is difficult for these traditional clustering algorithms to exploit deep features of the data and excavate the interdependence of complex data features in latent space [5]. Therefore, the performance of these shallow clusterings after aggregation will also be limited. In recent years, the emergence and development of deep clustering methods [13] have provided the idea to address complex data clustering, which simultaneously learns cluster assignments and feature representations using deep neural networks. Deep clustering typically learns a mapping from the original data space to a lower-dimensional feature space and iteratively optimizes the clustering objective in that feature space. Existing deep clustering algorithms can be roughly divided into three categories based on different deep representation layers [14]: autoencoder-based (AE-based) deep clustering, variational-autoencoder-based (VAE-based) deep clustering, and generative-adversarial-network-based (GAN-based) deep clustering. We elaborate these deep clustering methods in detail in related work. Compared to traditional shallow clustering methods, existing deep clustering algorithms have achieved excellent performance in clustering complex high-dimensional data [15; 16]. However, the existing deep clustering is very sensitive to network parameters and hyperparameters, so the clustering results fluctuate greatly and are not robust enough [17]. To address the aforementioned problem in clustering ensemble and deep clustering, we propose a clustering ensemble method called improved selective deep clustering ensemble (ISDCE). It combines the idea of clustering ensemble with deep clustering and incorporates a selective strategy. ISDCE can be divided into two phases: the deep clustering generation phase and the selective clustering ensemble phase.