A Dual-Masked Deep Structural Clustering Network With Adaptive Bidirectional Information Delivery.

Structured clustering networks, which alleviate the oversmoothing issue by delivering hidden features from autoencoder (AE) to graph convolutional networks (GCNs), involve two shortcomings for the clustering task. For one thing, they used vanilla structure to learn clustering representations without considering feature and structure corruption; for another thing, they exhibit network degradation and vanishing gradient issues after stacking multilayer GCNs. In this article, we propose a clustering method called dual-masked deep structural clustering network (DMDSC) with adaptive bidirectional information delivery (ABID). Specifically, DMDSC enables generative self-supervised learning to mine deeper interstructure and interfeature correlations by simultaneously reconstructing corrupted structures and features. Furthermore, DMDSC develops an ABID module to establish an information transfer channel between each pairwise layer of AE and GCNs to alleviate the oversmoothing and vanishing gradient problems. Numerous experiments on six benchmark datasets have shown that the proposed DMDSC outperforms the most advanced deep clustering algorithms.

Multi-graph Fusion Graph Convolutional Networks with pseudo-label supervision.

Graph convolutional networks (GCNs) have become a popular tool for learning unstructured graph data due to their powerful learning ability. Many researchers have been interested in fusing topological structures and node features to extract the correlation information for classification tasks. However, it is inadequate to integrate the embedding from topology and feature spaces to gain the most correlated information. At the same time, most GCN-based methods assume that the topology graph or feature graph is compatible with the properties of GCNs, but this is usually not satisfied since meaningless, missing, or even unreal edges are very common in actual graphs. To obtain a more robust and accurate graph structure, we intend to construct an adaptive graph with topology and feature graphs. We propose Multi-graph Fusion Graph Convolutional Networks with pseudo-label supervision (MFGCN), which learn a connected embedding by fusing the multi-graphs and node features. We can obtain the final node embedding for semi-supervised node classification by propagating node features over multi-graphs. Furthermore, to alleviate the problem of labels missing in semi-supervised classification, a pseudo-label generation mechanism is proposed to generate more reliable pseudo-labels based on the similarity of node features. Extensive experiments on six benchmark datasets demonstrate the superiority of MFGCN over state-of-the-art classification methods.

Probabilistic Linear Discriminant Analysis Based on L1-Norm and Its Bayesian Variational Inference.

Probabilistic linear discriminant analysis (PLDA) is a very effective feature extraction approach and has obtained extensive and successful applications in supervised learning tasks. It employs the squared L2 -norm to measure the model errors, which assumes a Gaussian noise distribution implicitly. However, the noise in real-life applications may not follow a Gaussian distribution. Particularly, the squared L2 -norm could extremely exaggerate data outliers. To address this issue, this article proposes a robust PLDA model under the assumption of a Laplacian noise distribution, called L1-PLDA. The learning process employs the approach by expressing the Laplacian density function as a superposition of an infinite number of Gaussian distributions via introducing a new latent variable and then adopts the variational expectation-maximization (EM) algorithm to learn parameters. The most significant advantage of the new model is that the introduced latent variable can be used to detect data outliers. The experiments on several public databases show the superiority of the proposed L1-PLDA model in terms of classification and outlier detection.

Adaptive Fusion of Heterogeneous Manifolds for Subspace Clustering.

Multiview clustering (MVC) has recently received great interest due to its pleasing efficacy in combining the abundant and complementary information to improve clustering performance, which overcomes the drawbacks of view limitation existed in the standard single-view clustering. However, the existing MVC methods are mostly designed for vectorial data from linear spaces and, thus, are not suitable for multiple dimensional data with intrinsic nonlinear manifold structures, e.g., videos or image sets. Some works have introduced manifolds' representation methods of data into MVC and obtained considerable improvements, but how to fuse multiple manifolds efficiently for clustering is still a challenging problem. Particularly, for heterogeneous manifolds, it is an entirely new problem. In this article, we propose to represent the complicated multiviews' data as heterogeneous manifolds and a fusion framework of heterogeneous manifolds for clustering. Different from the empirical weighting methods, an adaptive fusion strategy is designed to weight the importance of different manifolds in a data-driven manner. In addition, the low-rank representation is generalized onto the fused heterogeneous manifolds to explore the low-dimensional subspace structures embedded in data for clustering. We assessed the proposed method on several public data sets, including human action video, facial image, and traffic scenario video. The experimental results show that our method obviously outperforms a number of state-of-the-art clustering methods.

Probabilistic Linear Discriminant Analysis With Vectorial Representation for Tensor Data.

Linear discriminant analysis (LDA) has been a widely used supervised feature extraction and dimension reduction method in pattern recognition and data analysis. However, facing high-order tensor data, the traditional LDA-based methods take two strategies. One is vectorizing original data as the first step. The process of vectorization will destroy the structure of high-order data and result in high dimensionality issue. Another is tensor LDA-based algorithms that extract features from each mode of high-order data and the obtained representations are also high-order tensor. This paper proposes a new probabilistic LDA (PLDA) model for tensorial data, namely, tensor PLDA. In this model, each tensorial data are decomposed into three parts: the shared subspace component, the individual subspace component, and the noise part. Furthermore, the first two parts are modeled by a linear combination of latent tensor bases, and the noise component is assumed to follow a multivariate Gaussian distribution. Model learning is conducted through a Bayesian inference process. To further reduce the total number of model parameters, the tensor bases are assumed to have tensor CandeComp/PARAFAC (CP) decomposition. Two types of experiments, data reconstruction and classification, are conducted to evaluate the performance of the proposed model with the convincing result, which is superior or comparable against the existing LDA-based methods.

Vectorial Dimension Reduction for Tensors Based on Bayesian Inference.

Dimension reduction for high-order tensors is a challenging problem. In conventional approaches, dimension reduction for higher order tensors is implemented via Tucker decomposition to obtain lower dimensional tensors. This paper introduces a probabilistic vectorial dimension reduction model for tensorial data. The model represents a tensor by using a linear combination of the same order basis tensors, thus it offers a learning approach to directly reduce a tensor to a vector. Under this expression, the projection base of the model is based on the tensor CandeComp/PARAFAC (CP) decomposition and the number of free parameters in the model only grows linearly with the number of modes rather than exponentially. A Bayesian inference has been established via the variational Expectation Maximization (EM) approach. A criterion to set the parameters (a factor number of CP decomposition and the number of extracted features) is empirically given. The model outperforms several existing principal component analysis-based methods and CP decomposition on several publicly available databases in terms of classification and clustering accuracy.

Image Outlier Detection and Feature Extraction via L1-Norm-Based 2D Probabilistic PCA.

This paper introduces an L1-norm-based probabilistic principal component analysis model on 2D data (L1-2DPPCA) based on the assumption of the Laplacian noise model. The Laplacian or L1 density function can be expressed as a superposition of an infinite number of Gaussian distributions. Under this expression, a Bayesian inference can be established based on the variational expectation maximization approach. All the key parameters in the probabilistic model can be learned by the proposed variational algorithm. It has experimentally been demonstrated that the newly introduced hidden variables in the superposition can serve as an effective indicator for data outliers. Experiments on some publicly available databases show that the performance of L1-2DPPCA has largely been improved after identifying and removing sample outliers, resulting in more accurate image reconstruction than the existing PCA-based methods. The performance of feature extraction of the proposed method generally outperforms other existing algorithms in terms of reconstruction errors and classification accuracy.