Graph autoencoders (GAEs) are powerful tools in representation learning for graph embedding. However, the performance of GAEs is very dependent on the quality of the graph structure, i.e., of the adjacency matrix. In other words, GAEs would perform poorly when the adjacency matrix is incomplete or be disturbed. In this paper, two novel unsupervised graph embedding methods, unsupervised graph embedding via adaptive graph learning (BAGE) and unsupervised graph embedding via variational adaptive graph learning (VBAGE) are proposed. The proposed methods expand the application range of GAEs on graph embedding, i.e, on the general datasets without graph structure. Meanwhile, the adaptive learning mechanism can initialize the adjacency matrix without being affected by the parameter. Besides that, the latent representations are embedded with the Laplacian graph structure to preserve the topology structure of the graph in the vector space. Moreover, the adjacency matrix can be self-learned for better embedding performance when the original graph structure is incomplete. With adaptive learning, the proposed method is much more robust to the graph structure. Experimental studies on several datasets validate our design and demonstrate that our methods outperform baselines by a wide margin in node clustering, node classification, link prediction, and graph visualization tasks.

As a hot topic in unsupervised learning, clustering methods have been greatly developed. However, the model becomes more and more complex, and the number of parameters becomes more and more with the continuous development of clustering methods. And parameter-tuning in most methods is a laborious work due to its complexity and unpredictability. How to propose a concise and beautiful model in which the parameters can be learned adaptively becomes a very meaningful problem. Aim at tackling this problem, we develop a novel self-weighted unsupervised linear discriminative analysis method, namely SWULDA. The proposed method not only avoids adjusting parameters but also explains the link between k -means and linear discriminant analysis (LDA). To obtain superior structural performance, the idea of minimizing the within-class scatter matrix and maximizing the between-class scatter matrix is embedded in the unsupervised model. Moreover, equipped with the proposed quadratic weighted optimization framework, the parameter can be adaptively learned. The extensive experiments on several datasets are conducted to validate the effectiveness of our method.

Ridge regression is frequently utilized by both supervised learning and semisupervised learning. However, the results cannot obtain the closed-form solution and perform manifold structure when ridge regression is directly applied to semisupervised learning. To address this issue, we propose a novel semisupervised feature selection method under generalized uncorrelated constraint, namely SFS. The generalized uncorrelated constraint equips the framework with the elegant closed-form solution and is introduced to the ridge regression with embedding the manifold structure. The manifold structure and closed-form solution can better save data's topology information compared to the deep network with gradient descent. Furthermore, the full rank constraint of the projection matrix also avoids the occurrence of excessive row sparsity. The scale factor of the constraint that can be adaptively obtained also provides the subspace constraint more flexibility. Experimental results on data sets validate the superiority of our method to the state-of-the-art semisupervised feature selection methods.

The performance of graph-based feature selection methods relies heavily on the quality of the construction of the similarity matrix. However, most of the graphs on these methods are initially fixed, where few of them are constrained. Once the graph is determined, it will remain constant in the whole optimization process. In other words, in case that the graph constructed on the raw data is not appropriate, it will drag down the entire algorithm. Aiming to tackle this defect, a novel unsupervised feature selection via adaptive graph learning and constraint (EGCFS) is proposed to select the uncorrelated yet discriminative features by exploiting the embedded graph learning and constraint. The adaptive graph learning method incorporates the structure of the similarity matrix into the optimization process, which not only learns the graph structure adaptively but also obtains the closed-form solution of the graph coefficient. Special graph constraint is embedded with the feature selection process to connect nearer data points with larger probability. The idea of maximizing between-class scatter matrix and the adaptive graph structure is integrated into a uniform framework to obtain excellent structural performance. Moreover, the proposed embedded graph constraint not only performs with manifold structure but also validates the link between graph-based approach and k -means from a unique perspective. Experiments on several benchmark data sets verify the effectiveness and superiority of the proposed method.

The diversity of recommendation has attracted a lot of attention in recommender systems due to its ability to improve user experience. Most of the diversified recommendation tasks usually exploit user-item interaction records for mining user explicit preferences, while rarely explore the user-item non-interaction records. For diversified recommendations, however, the neglected non-interaction records are especially important for capturing users’ potential interests to improve the diversity of recommendation. Moreover, the majority of diversified recommendation methods run in two stages: first optimizing the users and items embeddings by relevance, then generating the diversified items list by post-processing methods. These methods are not end-to-end thus can hardly reach global optimum. To solve above limitations, we propose an end-to-end Dynamic Diversified Graph framework (DDGraph) which constructs the user-item graph dynamically based on the users and items embeddings. Technically, we initialize a user-item interaction graph and dynamically update the graph by selecting a set of diverse items for each user and building links between the items and user. The selection of diverse items can be achieved by different candidate selection operators. Specifically, we design a Quantile Progressive Candidate Selection (QPCS) operator based on the latent space division. To the best of our knowledge, our method is the first to diversify recommendation results by dynamic end-to-end graph construction and the QPCS has a higher computational efficiency than other operators. Extensive experiments on the benchmark dataset illustrate the effectiveness and superiority of the DDGraph framework.