Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong potential in such tasks due to its capacity to embed hierarchical structures with minimal distortion. Previous evidence indicates that the hyperbolic representation capacity can be further enhanced through kernel methods. However, existing hyperbolic kernels still suffer from mild geometric distortion or lack adaptability. This paper addresses these issues by introducing a curvature-aware de Branges–Rovnyak space, a reproducing kernel Hilbert space (RKHS) that is isometric to a Poincaré ball. We design an adjustable multiplier to select the appropriate RKHS corresponding to the hyperbolic space with any curvature adaptively. Building on this foundation, we further construct a family of adaptive hyperbolic kernels, including the novel adaptive hyperbolic radial kernel, whose learnable parameters modulate hyperbolic features in a task-aware manner. Extensive experiments on visual and language benchmarks demonstrate that our proposed kernels outperform existing hyperbolic kernels in modeling hierarchical dependencies.

Multimodal neuroimages, such as diffusion tensor imaging (DTI) and resting-state functional MRI (fMRI), offer complementary perspectives on brain activities by capturing structural or functional interactions among brain regions. While existing studies suggest that fusing these multimodal data helps detect abnormal brain activity caused by neurocognitive decline, they are generally implemented in Euclidean space and can't effectively capture the intrinsic hierarchical organization of structural/functional brain networks. This paper presents a hyperbolic kernel graph fusion (HKGF) framework for neurocognitive decline analysis with multimodal neuroimages. It consists of a multimodal graph construction module, a graph representation learning module that encodes brain graphs in hyperbolic space through a family of hyperbolic kernel graph neural networks (HKGNNs), a cross-modality coupling module that enables effective multimodal data fusion, and a hyperbolic neural network for downstream predictions. Notably, HKGNNs represent graphs in hyperbolic space to capture both local and global dependencies among brain regions while preserving the hierarchical structure of brain networks. Extensive experiments involving over 4,000 subjects with DTI and/or fMRI data demonstrate the superiority of HKGF over state-of-the-art methods in two neurocognitive decline prediction tasks. The proposed HKGF is a general framework for multimodal data analysis, facilitating objective quantification of brain structural or functional connectivity changes associated with neurocognitive decline.

Modeling data relation as a hierarchical structure has proven beneficial for many learning scenarios, and the hyperbolic space, with negative curvature, can encode such data hierarchy without distortion. Several recent studies also show that the representation power of the hyperbolic space can be further improved by endowing the kernel methods. Unfortunately, the known kernel methods, developed in hyperbolic space, are limited by the adaptation capacity or distortion issues. This paper addresses the issues through a novel embedding function. To this end, we propose a curvature-aware isometric embedding, which establishes an isometry from the Poincar\'e model to a special reproducing kernel Hilbert space (RKHS). Then we can further define a series of kernels on this RKHS, including several positive definite kernels and an indefinite kernel. Thorough experiments are conducted to demonstrate the superiority of our proposals over existing-known hyperbolic and Euclidean kernels in various learning tasks, e.g., graph learning and zero-shot learning.

Abstract The visibility of outdoor images is usually significantly degraded by haze. Existing dehazing algorithms, such as dark channel prior (DCP) and colour attenuation prior (CAP), have made great progress and are highly effective. However, they all suffer from the problems of dark distortion and detailed information loss. This paper proposes an improved algorithm for single‐image haze removal based on dark channel prior with weighted guided coefficient and union self‐adaptive image enhancement. First, a weighted guided coefficient method with sampling based on guided image filtering is proposed to refine the transmission map efficiently. Second, the k ‐means clustering method is adopted to calibrate the original image into bright and non‐bright colour areas and form a transmission constraint matrix. The constraint matrix is then marked by connected‐component labelling, and small bright regions are eliminated to form an atmospheric light constraint matrix, which can suppress the halo effect and optimize the atmospheric light. Finally, an adaptive linear contrast enhancement algorithm with a union score is proposed to optimize restored images. Experimental results demonstrate that the proposed algorithm can overcome the problems of image distortion and detailed information loss and is more efficient than conventional dehazing algorithms.

Cataract is one of the most common diseases that might cause blindness. Previous research shows that cataract occupies almost 50% in severe visually impairments. Considering the fact that retinal image is one of the most important medical references that help to diagnose the cataract, this paper proposes to use a neural network classifier for automatic cataract detection based on the classification of retinal images. The classifier building procedure includes three parts: preprocessing, feature extraction, and classifier construction. In the pre-processing part, an improved Top-bottom hat transformation is proposed to enhance the contrast between the foreground and the object, and a trilateral filter is used to decrease the noise in the image. According to the analysis of pre-processed image, the luminance and texture message of the image are extracted as classification features. The classifier is constructed by back propagation (BP) neural network which has two layers. Based on the clearness degree of the retinal image, the patients' cataracts are classified into normal, mild, medium or severe ones. The initial evaluation results illustrate the effectiveness of our proposed approach, which has great potential to improve diagnosis efficiency of the ophthalmologist and reduce the physical and economic burden of the patients and society.