Autoencoders have become a hot researched topic in unsupervised learning due to their ability to learn data features and act as a dimensionality reduction method. With rapid evolution of autoencoder methods, there has yet to be a complete study that provides a full autoencoders roadmap for both stimulating technical improvements and orienting research newbies to autoencoders. In this paper, we present a comprehensive survey of autoencoders, starting with an explanation of the principle of conventional autoencoder and their primary development process. We then provide a taxonomy of autoencoders based on their structures and principles and thoroughly analyze and discuss the related models. Furthermore, we review the applications of autoencoders in various fields, including machine vision, natural language processing, complex network, recommender system, speech process, anomaly detection, and others. Lastly, we summarize the limitations of current autoencoder algorithms and discuss the future directions of the field.

Community detection has become an important research topic in machine learning due to the proliferation of network data. However, most existing methods have been developed based on only exploiting the topology structures of the network, which can result in missing the advantage of using the nodes' attribute information. As a result, it is expected that much valuable information that could be used to improve the quality of discovered communities will be ignored. To solve this limitation, we propose a novel Augment Graph Regularization Nonnegative Matrix Factorization for Attributed Networks (AGNMF-AN) method, which is simple yet effective. Firstly, Augment Attributed Graph (AAG) is applied to combine both the topological structure and attributed nodes of the network. Secondly, we introduced an effective framework to update the affinity matrix, in which the affinity matrix's weight in each iteration is modified adaptively instead of using a fixed affinity matrix in the classical graph regularization-based nonnegative matrix factorization methods. Thirdly, the $l_{2,1}$ -norm is utilized to reduce the effect of random noise and outliers in the quality of structure community. Experimental results show that our method performs unexpectedly well in comparison to existing state-of-the-art methods in attributed networks.

Attributed graph clustering aims to group nodes into disjoint categories using deep learning to represent node embeddings and has shown promising performance across various applications. However, two main challenges hinder further performance improvement. First, reliance on unsupervised methods impedes the learning of low-dimensional, clustering-specific features in the representation layer, thus impacting clustering performance. Second, the predominant use of separate approaches leads to suboptimal learned embeddings that are insufficient for subsequent clustering steps. To address these limitations, we propose a novel method called Semi-supervised Deep Attributed Clustering using Dual Autoencoder (SDAC-DA). This approach enables semi-supervised deep end-to-end clustering in attributed networks, promoting high structural cohesiveness and attribute homogeneity. SDAC-DA transforms the attribute network into a dual-view network, applies a semi-supervised autoencoder layering approach to each view, and integrates dimensionality reduction matrices by considering complementary views. The resulting representation layer contains high clustering-friendly embeddings, which are optimized through a unified end-to-end clustering process for effectively identifying clusters. Extensive experiments on both synthetic and real networks demonstrate the superiority of our proposed method over seven state-of-the-art approaches.