Deep graph embedding is an important approach for community discovery. Deep graph neural network with self-supervised mechanism can obtain the low-dimensional embedding vectors of nodes from unlabeled and unstructured graph data. The high-order information of graph can provide more abundant structure information for the representation learning of nodes. However, most self-supervised graph neural networks only use adjacency matrix as the input topology information of graph and cannot obtain too high-order information since the number of layers of graph neural network is fairly limited. If there are too many layers, the phenomenon of over smoothing will appear. Therefore how to obtain and fuse high-order information of graph by a shallow graph neural network is an important problem. In this paper, a deep graph embedding algorithm with self-supervised mechanism for community discovery is proposed. The proposed algorithm uses self-supervised mechanism and different high-order information of graph to train multiple deep graph convolution neural networks. The outputs of multiple graph convolution neural networks are fused to extract the representations of nodes which include the attribute and structure information of a graph. In addition, data augmentation and negative sampling are introduced into the training process to facilitate the improvement of embedding result. The proposed algorithm and the comparison algorithms are conducted on the five experimental data sets. The experimental results show that the proposed algorithm outperforms the comparison algorithms on the most experimental data sets. The experimental results demonstrate that the proposed algorithm is an effective algorithm for community discovery.

As a widely used method in machine learning, principal component analysis (PCA) shows excellent properties for dimensionality reduction. It is a serious problem that PCA is sensitive to outliers, which has been improved by numerous Robust PCA (RPCA) versions. However, the existing state-of-the-art RPCA approaches cannot easily remove or tolerate outliers by a non-iterative manner. To tackle this issue, this paper proposes Angular Embedding (AE) to formulate a straightforward RPCA approach based on angular density, which is improved for large scale or high-dimensional data. Furthermore, a trimmed AE (TAE) is introduced to deal with data with large scale outliers. Extensive experiments on both synthetic and real-world datasets with vector-level or pixel-level outliers demonstrate that the proposed AE/TAE outperforms the state-of-the-art RPCA based methods.

Manifold Learning occupies a vital role in the field of nonlinear dimensionality reduction and its ideas also serve for other relevant methods. Graph-based methods such as Graph Convolutional Networks (GCN) show ideas in common with manifold learning, although they belong to different fields. Inspired by GCN, we introduce neighbor propagation into LLE and propose Local Neighbor Propagation Embedding (LNPE). With linear computational complexity increase compared with LLE, LNPE enhances the local connections and interactions between neighborhoods by extending $1$-hop neighbors into $n$-hop neighbors. The experimental results show that LNPE could obtain more faithful and robust embeddings with better topological and geometrical properties.

Manifold learning now plays a very important role in machine learning and many relevant applications. Although its superior performance in dealing with nonlinear data distribution, data sparsity is always a thorny knot. There are few researches to well handle it in manifold learning. In this paper, we propose Hierarchic Neighbors Embedding (HNE), which enhance local connection by the hierarchic combination of neighbors. After further analyzing topological connection and reconstruction performance, three different versions of HNE are given. The experimental results show that our methods work well on both synthetic data and high-dimensional real-world tasks. HNE develops the outstanding advantages in dealing with general data. Furthermore, comparing with other popular manifold learning methods, the performance on sparse samples and weak-connected manifolds is better for HNE.

Music genre recognition based on visual representation has been successfully explored over the last years. Recently, there has been increasing interest in attempting convolutional neural networks (CNNs) to achieve the task. However, most of existing methods employ the mature CNN structures proposed in image recognition without any modification, which results in the learning features that are not adequate for music genre classification. Faced with the challenge of this issue, we fully exploit the low-level information from spectrograms of audios and develop a novel CNN architecture in this paper. The proposed CNN architecture takes the long contextual information into considerations, which transfers more suitable information for the decision-making layer. Various experiments on several benchmark datasets, including GTZAN, Ballroom, and Extended Ballroom, have verified the excellent performances of the proposed neural network. Codes and model will be available at "ttps://github.com/CaifengLiu/music-genre-classification".

Extreme learning machine (ELM) is a new single hidden layer feedback neural network. The weights of the input layer and the biases of neurons in hidden layer are randomly generated, the weights of the output layer can be analytically determined. ELM has been achieved good results for a large number of classification tasks. In this paper, a new extreme learning machine called rough extreme learning machine (RELM) was proposed. RELM uses rough set to divide data into upper approximation set and lower approximation set, and the two approximation sets are utilized to train upper approximation neurons and lower approximation neurons. In addition, an attribute reduction is executed in this algorithm to remove redundant attributes. The experimental results showed, comparing with the comparison algorithms, RELM can get a better accuracy and repeatability in most cases, RELM can not only maintain the advantages of fast speed, but also effectively cope with the classification task for high-dimensional data.