# Improved Selective Deep-Learning-Based Clustering Ensemble
## 2 Related Work
### Clustering Ensemble  
Existing clustering ensemble methods can be divided into three main categories [12], including pair-wise-similarity-based approaches, median-partitioning-based approaches, and graph- and hypergraph-partitioning-based approaches. We elaborate on some of the popular and classical clustering ensemble algorithms in recent years. PTA [19] considers clustering ensemble based on sparse graph representation and probabilistic trajectory analysis. The problem of link uncertainty is solved using the elite neighbor selection strategy, and a similarity measure based on probabilistic trajectories is constructed using the K-elite neighbor sparse graph. PTA constructs a K-elite neighbor sparse graph to refine the local links using the random walk information, and derives the similarity based on the probabilistic trajectories by capturing global structural information through the random walk trajectories. Finally, two consensus functions, namely probabilistic trajectory accumulation and probabilistic-trajectory-based graph partitioning, are further proposed. ECFG [20] was proposed as a new ensemble clustering approach, termed ensemble clustering using a factor graph. It introduces super-object representation to facilitate the computation of ensemble processes and solves the optimization problem using an efficient solver based on the factor graph technique. WSCE [21] was developed as a new clustering ensemble framework, utilizing some concepts from the community detection domain and graph-based clustering that address the combination of different evaluated individual clustering results in the absence of a thresholding process. It introduces two-kernel spectral clustering to generate graph-based individual clustering results and normalized modularity measures to provide diversity estimates. SECWK [22] was proposed as spectral ensemble clustering to utilize the advantages of co-association matrices in information integration, but with higher operational efficiency. The time and space complexity of spectral ensemble clustering are significantly reduced by identifying the equivalence between spectral ensemble clustering and weighted k-means. It is a promising candidate for big data clustering. LWEA [23] is considered to be the most popular algorithm among the weighted clustering ensemble methods proposed in recent years. It considers the local diversity of clusters and utilizes uncertainty estimation and local weighted strategies. The uncertainty of each cluster is estimated by considering the cluster labels in the whole set through an entropy criterion. The ensemble-driven clustering validity measure was introduced and a locally weighted co-correlation matrix was proposed as a summary of the ensemble of different clusters. Two new consensus functions are proposed by exploiting the local diversity in the ensembles. The authors in [24] studied that the co-association matrix may be dominated by poor base clusterings in clustering ensemble, resulting in inferior performance. Then, they introduced low-rank tensor approximation (LRTA) to clustering ensemble and exploited the low-rankness of a three-dimensional tensor formed by the coherent-link matrix and the co-association matrix. LRTA formulates the algorithm as a convex constrained optimization problem and solves it efficiently. ECCMS [25] was introduced as a novel effective co-association matrix self-enhancement model for ensemble clustering that improved the traditional co-association matrix. It exploits the high-confidence information to form a sparse high-confidence matrix and denoising error connections simultaneously. Technically, ECCMS is formulated as a symmetric constrained convex optimization problem, which is efficiently solved by an alternating iterative algorithm. The authors in [26] considered that conventional clustering ensemble methods may usually be misguided by unreliable samples due to the lack of labels. Therefore, they integrated the active clustering ensemble method and proposed a self-paced learning framework (SPACE).