Graph Neural Networks (GNNs) have drawn great research attention for graph machine learning. However, graph learning techniques are extremely difficult for practical deployments in the industry applications owing to the scalability challenges incurred by data dependency. Although some works attempt to establish the known efficient MLPs with GNNs based on knowledge distillation (KD), they are primarily designed for graphs in Euclidean spaces, which can not provide the most powerful geometry for graph representation as numerous real- world graphs display a combination of Euclidean and Hyperbolic geometry. To achieve comprehensive expression for complex graph data with high efficiency, in this paper, we proposed a novel Advanced Graph-MLPs Distillation Framework (AGMDF) based on global and local hyperbolic geometry learning. The key point of our method is to fully exploit the complex graph with additional hyperbolic properties based on knowledge distillation. Specifically, the global cross-geometric knowledge fusion can exploit the compensation information learned from Euclidean view and Hyperbolic domain. Then, the local hyperbolic knowledge enhancement can employ prominent tree-likeness components among graph data to improve the graph representation ability. Thus, the distilled MLP model enjoys the high expressive ability of graph context-awareness based on global and local hyperbolic geometry learning. Extensive experiments show that AGMDF achieves competitive accuracy with GNNs and improves over stand-alone MLPs by 21.84% on average while inferring faster than GNNs across five benchmark datasets.

In real applications, several unpredictable or uncertain factors could result in unpaired multiview data, i.e., the observed samples between views cannot be matched. Since joint clustering among views is more effective than individual clustering in each view, we investigate unpaired multiview clustering (UMC), which is a valuable but insufficiently studied problem. Due to lack of matched samples between views, we could fail to build the connection between views. Therefore, we aim to learn the latent subspace shared by views. However, existing multiview subspace learning methods usually rely on the matched samples between views. To address this issue, we propose an iterative multiview subspace learning strategy [iterative unpaired multiview clustering (IUMC)], aiming to learn a complete and consistent subspace representation among views for UMC. Moreover, based on IUMC, we design two effective UMC methods: 1) Iterative unpaired multiview clustering via covariance matrix alignment (IUMC-CA) that further aligns the covariance matrix of subspace representations and then performs clustering on the subspace and 2) iterative unpaired multiview clustering via one-stage clustering assignments (IUMC-CY) that performs one-stage multiview clustering (MVC) by replacing the subspace representations with clustering assignments. Extensive experiments show the excellent performance of our methods for UMC, compared with the state-of-the-art methods. Also, the clustering performance of observed samples in each view can be considerably improved by those observed samples from the other views. In addition, our methods have good applicability in incomplete MVC.

In the fields of pattern recognition and data mining, two problems need to be addressed. First, the curse of dimensionality degrades the performance of many practical data processing techniques. Second, due to the existence of noise and outliers, feature extraction on corrupted data cannot be effectively achieved. Recently, some representation based methods have produced promising results. However, these methods cannot handle the case in which nonlinear similarity exists and have failed to provide the quantized interpretability for the importance of features. In this paper, we propose a novel low rank and sparse representation method to realize dimensionality reduction and robustly extract latent low dimensional discriminative features. Specifically, we first adopt multiple kernel learning to map the original data into an embedded reproducing kernel Hilbert space (RKHS) and then kernel based similarity discriminative projection is learned to explore the within-class and between-class variability. Notably, this low dimensional feature learning strategy is definitely integrated into the low rank matrix recovery of the kernel matrix. Next, we introduce the regularization of$l_{2,1}$norm on error matrix to eliminate noise and on projection matrix to lead the selected features to be more compact and interpretable. The non-convex optimization problem is effectively solved by the alternating direction method of multipliers (ADMM) methods. Extensive experiments on seven benchmark datasets are conducted to demonstrate the effectiveness of our method.

To defy the curse of dimensionality, the inputs are always projected from the original high-dimensional space into the target low-dimension space for feature extraction. However, due to the existence of noise and outliers, the feature extraction task for corrupted data is still a challenging problem. Recently, a robust method called low rank embedding (LRE) was proposed. Despite the success of LRE in experimental studies, it also has many disadvantages: 1) The learned projection cannot quantitatively interpret the importance of features. 2) LRE does not perform data reconstruction so that the features may not be capable of holding the main energy of the original “clean” data. 3) LRE explicitly transforms error into the target space. 4) LRE is an unsupervised method, which is only suitable for unsupervised scenarios. To address these problems, in this paper, we propose a novel method to exploit the latent discriminative features. In particular, we first utilize an orthogonal matrix to hold the main energy of the original data. Next, we introduce an 12,1-norm term to encourage the features to be more compact, discriminative and interpretable. Then, we enforce a columnwise 12,1-norm constraint on an error component to resist noise. Finally, we integrate a classification loss term into the objective function to fit supervised scenarios. Our method performs better than several state-of-the-art methods in terms of effectiveness and robustness, as demonstrated on six publicly available datasets.