Related papers: Tree! I am no Tree! I am a Low Dimensional Hyperbo…

Electronic health records (EHR) contain narrative notes that provide extensive details on the medical condition and management of patients. Natural language processing (NLP) of clinical notes can use observed frequencies of clinical terms…

Learning embeddings of entities and relations existing in knowledge bases allows the discovery of hidden patterns in data. In this work, we examine the geometrical space's contribution to the task of knowledge base completion. We focus on…

We present a novel hierarchical triplet loss (HTL) capable of automatically collecting informative training samples (triplets) via a defined hierarchical tree that encodes global context information. This allows us to cope with the main…

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…

Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Information retrieval is a core component of many intelligent systems as it enables conditioning of outputs on new and large-scale datasets. While effective, the standard practice of encoding data into high-dimensional representations for…

Decision trees are an extremely popular machine learning technique. Unfortunately, overfitting in decision trees still remains an open issue that sometimes prevents achieving good performance. In this work, we present a novel approach for…

We prove an exponential separation in sample complexity between Euclidean and hyperbolic representations for learning on hierarchical data under standard Lipschitz regularization. For depth-$R$ hierarchies with branching factor $m$, we…

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…

Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…

Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

Metric learning aims at finding a suitable distance metric over the input space, to improve the performance of distance-based learning algorithms. In high-dimensional settings, it can also serve as dimensionality reduction by imposing a…

In this paper, we propose a simple and effective {geometric} model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking…

Protein-ligand binding prediction is central to virtual screening and affinity ranking, two fundamental tasks in drug discovery. While recent retrieval-based methods embed ligands and protein pockets into Euclidean space for…

We introduce a semiparametric approach to neighbor-based classification. We build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015) which enables fast neighbor-based classification, regression and retrieval in large…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…