Related papers: Comparing Euclidean and Hyperbolic K-Means for Gen…

K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of…

Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses.…

The issue of data sparsity poses a significant challenge to recommender systems. In response to this, algorithms that leverage side information such as review texts have been proposed. Furthermore, Cross-Domain Recommendation (CDR), which…

Developing deep learning models to analyze histology images has been computationally challenging, as the massive size of the images causes excessive strain on all parts of the computing pipeline. This paper proposes a novel deep…

Generalized Category Discovery (GCD) is a pragmatic and challenging open-world task, which endeavors to cluster unlabeled samples from both novel and old classes, leveraging some labeled data of old classes. Given that knowledge learned…

The idea of representations of the data in negatively curved manifolds recently attracted a lot of attention and gave a rise to the new research direction named {\it hyperbolic machine learning} (ML). In order to unveil the full potential…

Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…

Dimensionality reduction (DR) offers a useful representation of complex high-dimensional data. Recent DR methods focus on hyperbolic geometry to derive a faithful low-dimensional representation of hierarchical data. However, existing…

We revisit Pollard's classical result on consistency for $k$-means clustering in Euclidean space, with a focus on extensions in two directions: first, to problems where the data may come from interesting geometric settings (e.g., Riemannian…

Many real world categories are multimodal, with single classes occupying disjoint regions in feature space. Classical linear models (logistic regression, linear SVM) use a single global hyperplane and perform poorly on such data, while…

3D-aware visual pretraining has proven effective in improving the performance of downstream robotic manipulation tasks. However, existing methods are constrained to Euclidean embedding spaces, whose flat geometry limits their ability to…

Medical anomaly detection has emerged as a promising solution to challenges in data availability and labeling constraints. Traditional methods extract features from different layers of pre-trained networks in Euclidean space; however,…

Detecting events and their evolution through time is a crucial task in natural language understanding. Recent neural approaches to event temporal relation extraction typically map events to embeddings in the Euclidean space and train a…

Knowledge Graphs (KGs) are ubiquitous structures for information storagein several real-world applications such as web search, e-commerce, social networks, and biology. Querying KGs remains a foundational and challenging problem due to…

Publicly available collections of drug-like molecules have grown to comprise 10s of billions of possibilities in recent history due to advances in chemical synthesis. Traditional methods for identifying "hit" molecules from a large…

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

Hyperbolic ordinal embedding (HOE) represents entities as points in hyperbolic space so that they agree as well as possible with given constraints in the form of entity i is more similar to entity j than to entity k. It has been…

Generating graphs with hierarchical structures remains a fundamental challenge due to the limitations of Euclidean geometry in capturing exponential complexity. Here we introduce \textbf{GGBall}, a novel hyperbolic framework for graph…

Hyperbolic rotation is commonly used to effectively model knowledge graphs and their inherent hierarchies. However, existing hyperbolic rotation models rely on logarithmic and exponential mappings for feature transformation. These models…