# A Survey on the Recent Advances of Deep Community Detection
## 3 Deep Community Detection Strategies
### AE-Based Community Detection Strategies
The formation of \(k\) communities with \(n^{\prime}\) nodes is \(O(n+z)\) and the modularity optimization \(O(k\log(n^{\prime}))\) for modularity optimization. Different from other AE schemes, [PERSON] et al. [32] proposed ComE, a Community Embedding framework that jointly solves community embedding, community detection, and node embedding and suggests that community embedding is not only useful for community-level applications such as graph visualization, but it can support community detection and node classification. The community embedding problem is treated as a multivariate Gaussian distribution, and it is employed to reinforce the community detection. The Gaussian mixture formulation can not only detect the communities, but it can also determine their embedding distributions. For a community with its embedding expressed as a multivariate distribution in the low dimensional space, the member nodes can be forced to scatter near the embeddings mean vector. Such nodes have similar node embedding vectors without necessarily being directly linked. Thus, node embedding produces better inputs for the community detection that follows. The community detection time complexity for ComE is \(O(|V|+|E|)\), where \(V,E\) are the node and edge numbers. The NetRA model [33] is another network embedding strategy. Here, a generative adversarial training process is employed as a complementary regularizer. The advantages of this process are as follows: (1) The regularizer is helpful in detecting useful information about the data, and (2) the selected training implementation achieves a robust discrete space learning that overcomes the possible over-fitting on walks with sparse samples. The NetRa approach includes a random walk generator and the network embedding model with adversarially regularized auto-encoders. The random walks are sequences of nodes, and they are sampled in random by using the neighboring nodes of the last visited vertex. For training, after the random walks are executed, they pass through encoding layers to get the vector representations of vertices. These vector representations are then transformed back into \(n\) dimensions. The generator output and the encoder latent representation are used as inputs to the discriminator to obtain the adversarial loss. Moreover, the generator, through a training phase, transforms the Gaussian noise into the latent space, with a good approximation to the true data. After training, the network vertex representations are obtained by inputing the random walks to the encoder function. On a network with \(n\) nodes and \(m\) edges, the NetRa time complexity for learning is \(O(n)\) and a computational cost of \(O(n^{2})\) is added for embedding. To the best of our knowledge, a few recent works integrate community embedding in deep learning. Node embedding methods alone may preserve the directly connected nodes or nodes with similar embedding vectors, but, in order to have knowledge of the community structure, a community detection scheme is also required. This combination produces larger costs, so more work needs to be done in this area. [PERSON] et al. [34] presented the Community Detection Method via Ensemble Clustering (CDMEC). This framework combines transfer learning and a stacked auto-encoder to produce a feature representation of complex networks in low dimension. In addition, it aggregated multiple inputs via an ensemble clustering framework. This framework initially uses the results produced in the basic clustering in order to construct a consistent matrix, and then it uses the non-negative matrix factorization clustering to detect clusters resulting from the constructed consistent matrix. The time complexity is \(O(k\times L)\), where \(k\) and \(L\) are the number of iterations and layers of the autoencoder, respectively. The main advantage of the CDMEC is that the combination of the deep stacked autoencoder and transfer learning can result in obtaining a low-dimensional feature representation.