Related papers: Parametric UMAP embeddings for representation and …

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…

-Background. Network neuroscience examines the brain as a complex system represented by a network (or connectome), providing deeper insights into the brain morphology and function, allowing the identification of atypical brain connectivity…

The Isomap is a well-known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its computational complexity mainly arises from two stages; a) embedding a full graph on the data in the ambient space,…

We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervised learning approach to more efficiently encode low-dimensional manifold geometry. Central to…

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path…

Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…

Nonlinear dimensionality reduction techniques, particularly UMAP, are widely used for visualizing high-dimensional data. However, UMAP's local Euclidean distance assumption often fails to capture intrinsic manifold geometry, leading to…

Real-world objects and environments are predominantly composed of edge features, including straight lines and curves. Such edges are crucial elements for various applications, such as CAD modeling, surface meshing, lane mapping, etc.…

In this work, we discuss low-parametric approaches for approximating SimRank matrices, which estimate the similarity between pairs of nodes in a graph. Although SimRank matrices and their computation require a significant amount of memory,…

An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…

TSNE and UMAP are two of the most popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings. However, while attempts have been made to improve on TSNE's computational complexity, no existing…

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

UMAP has supplanted t-SNE as state-of-the-art for visualizing high-dimensional datasets in many disciplines, but the reason for its success is not well understood. In this work, we investigate UMAP's sampling based optimization scheme in…

Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…

Effective feature representation is key to the predictive performance of any algorithm. This paper introduces a meta-procedure, called Non-Euclidean Upgrading (NEU), which learns feature maps that are expressive enough to embed the…

The Mapper algorithm is an essential tool for visualizing complex, high dimensional data in topology data analysis (TDA) and has been widely used in biomedical research. It outputs a combinatorial graph whose structure implies the shape of…

We propose Embedding Propagation (EP), an unsupervised learning framework for graph-structured data. EP learns vector representations of graphs by passing two types of messages between neighboring nodes. Forward messages consist of label…