Related papers: Large-Margin Classification in Hyperbolic Space

Temporal knowledge graph (TKG) reasoning predicts future events based on historical data, but it's challenging due to the complex semantic and hierarchical information involved. Existing Euclidean models excel at capturing semantics but…

Data across modalities such as images, text, and graphs often contains hierarchical and relational structures, which are challenging to model within Euclidean geometry. Hyperbolic geometry provides a natural framework for representing such…

Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…

We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…

The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be…

We define finite-time hyperbolic coordinates, describe their geometry, and prove various results on both their convergence as the time scale increases, and on their variation in the state space. Hyperbolic coordinates reframe the classical…

Recent research in representation learning has shown that hierarchical data lends itself to low-dimensional and highly informative representations in hyperbolic space. However, even if hyperbolic embeddings have gathered attention in image…

Deep learning in hyperbolic space is quickly gaining traction in the fields of machine learning, multimedia, and computer vision. Deep networks commonly operate in Euclidean space, implicitly assuming that data lies on regular grids. Recent…

Taxonomies are valuable resources for many applications, but the limited coverage due to the expensive manual curation process hinders their general applicability. Prior works attempt to automatically expand existing taxonomies to improve…

This survey reviews hyperbolic graph embedding models, and evaluate them on anomaly detection, highlighting their advantages over Euclidean methods in capturing complex structures. Evaluating models like \textit{HGCAE},…

In recent years, the task of weakly supervised audio-visual violence detection has gained considerable attention. The goal of this task is to identify violent segments within multimodal data based on video-level labels. Despite advances in…

Most previous heterogeneous graph embedding models represent elements in a heterogeneous graph as vector representations in a low-dimensional Euclidean space. However, because heterogeneous graphs inherently possess complex structures, such…

Hyperbolic geometry have shown significant potential in modeling complex structured data, particularly those with underlying tree-like and hierarchical structures. Despite the impressive performance of various hyperbolic neural networks…

Clustering is a fundamental unsupervised learning task for uncovering patterns in data. While Gaussian Blurring Mean Shift (GBMS) has proven effective for identifying arbitrarily shaped clusters in Euclidean space, it struggles with…

Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…

The success of models operating on tokenized data has heightened the need for effective tokenization methods, particularly in vision and auditory tasks where inputs are naturally continuous. A common solution is to employ Vector…

Hyperbolic Neural Networks (HNNs), operating in hyperbolic space, have been widely applied in recent years, motivated by the existence of an optimal embedding in hyperbolic space that can preserve data hierarchical relationships (termed…

A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…

This paper presents a review on methods for class-imbalanced learning with the Support Vector Machine (SVM) and its variants. We first explain the structure of SVM and its variants and discuss their inefficiency in learning with…

Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…