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 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.

Subspace clustering plays an important role in the tasks such as data processing and pattern recognition. Since the high-dimensional data may contain complex noise, as well as non-linear structure, learning low-dimensional subspace structures is a challenging task. However, the existing methods to deal with both problems relax the original problem convexly. The results of solving by these methods deviate from the solution of the original problem. In this paper, to overcome this deficiency, we propose a robust low-rank kernel subspace clustering model, which coalesces the non-convex Schatten p-norm (0 <; p ≤ 1) regularizer with “kernel trick” and correntropy. Our “kernel trick” extends linear subspace clustering to non-linear counterparts, the Schatten p-norm regularizer can approximate the rank of the data in feature space effectively, and the correntropy is a robust measure to large corruptions. Furthermore, an efficient iterative algorithm (HQ-ADMM) is designed to solve the formulated problem, which coalesces the half-quadratic technique and Alternating Direction Method of Multipliers. This algorithm can ensure the closed form solutions at each iteration, which improves the computation speed of the algorithm. Extensive experiments on face/object clustering and motion segmentation clearly attest the ascendancy of the proposed method over several state-of-the-art methods.

DLRC is an extension of LRC that extends LRC from conventional still image based method to the image set based method. DLRC has a demonstrated better performance on image set classification. However, when the image sets of different objects are not linear separable, or when the linear regression axes of class-specific samples of different classes have an intersection, DLRC may be failed for well classifying the image sets. In this paper, a new classification method, kernel dual linear regression classification (KDLRC), is proposed. KDLRC is a nonlinear version of DLRC and can overcome the drawback of DLRC. KDLRC first embeds the input data into a high-dimensional Hilbert space, then in the kernel space, the data become easier to classify. Extensive experiments on four well-known databases prove that the performance of KDLRC is better than that of DLRC and several state-of-the-art classifiers.