Most deep clustering methods despite providing complex networks to learn better from data, use a shallow clustering method. These methods have difficulty in finding good clusters due to the lack of ability to handle between local search and global search to prevent premature convergence. In other words, they do not consider different aspects of the search and it causes them to get stuck in the local optimum. In addition, the majority of existing deep clustering approaches perform clustering with the knowledge of the number of clusters, which is not practical in most real scenarios where such information is not available. To address these problems, this paper presents a novel automatic deep sparse clustering approach based on an evolutionary algorithm called Multi-Trial Vectorbased Differential Evolution (MTDE). Sparse auto-encoder is first applied to extract embedded features. Manifold learning is then adopted to obtain representation and extract the spatial structure of features. Afterward, MTDE clustering is performed without prior information on the number of clusters to find the optimal clustering solution. The proposed approach was evaluated on various datasets, including images and time-series. The results demonstrate that the proposed method improved MTDE by 18.94% on average and compared to the most recent deep clustering algorithms, is consistently among the top three in the majority of datasets. Source code is available on Github: https://github.com/parhamhadikhani/ADSMTDE_Clustering.

Many algorithms have been proposed to solve the clustering problem. However, most of them lack a proper strategy to maintain a good balance between exploration and exploitation to prevent premature convergence. Multi-Trial Vector-based Differential Evolution (MTDE) is an improved differential evolution (DE) algorithm that is done by combining three strategies and distributing the population between these strategies to avoid getting stuck at a local optimum. In addition, it records inferior solutions to share information about visited regions with solutions of the next generations. In this paper, an Improved version of the Multi-Trial Vector-based Differential Evolution (IMTDE) algorithm is proposed and adapted for clustering data. The purpose here is to enhance the balance between the exploration and exploitation mechanisms in MTDE by employing Gaussian crossover and modifying the sub-population distribution between the strategies. To evaluate the performance of the proposed clustering, 19 datasets with different dimensions, shapes, and sizes were employed. The obtained results of IMTDE demonstrate improvement in MTDE performance by an average of 12%. Our comparative study with state-of-the-art algorithms demonstrates the superiority of IMTDE in most of these datasets because of the effective search strategies and the sharing of previous experiences in generating more promising solutions. Source code is available on Github: https://github.com/parhamhadikhani/IMTDE-Clustering.