arXiv research

A novel 3D shape registration method using spectral graph embedding and probabilistic matching.

We propose a novel method to embed a functional magnetic resonance imaging (fMRI) dataset in a low-dimensional space. The embedding optimally preserves the local functional coupling between fMRI time series and provides a low-dimensional coordinate system for detecting activated voxels. To compute the embedding, we bui…

In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time series have led to state-of-the art techniques for classification, denoising, and the study of nonlinear dynamics. The mai…

The Schlesinger equations $S_{(n,m)}$ describe monodromy preserving deformations of order $m$ Fuchsian systems with $n+1$ poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of $n$ copies of $m\times m$ matrix algebras equipped with the standard linear Poisson…

The Schlesinger equations $S_{(n,m)}$ describe monodromy preserving deformations of order $m$ Fuchsian systems with $n+1$ poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of $n$ copies of $m\times m$ matrix algebras equipped with the standard linear Poisson…

There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…

In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand the structural evolution of the financial networks with time. For a set of time-v…

Graph curvature measured by inverse resistance distance.

Transportation modes prediction is a fundamental task for decision making in smart cities and traffic management systems. Traffic policies designed based on trajectory mining can save money and time for authorities and the public. It may reduce the fuel consumption and commute time and moreover, may provide more pleasa…

Graph neural networks improve with affinity measures from random walks.

New analysis shows over-squashing limits GNNs' power.

We study the ever more integrated and ever more unbalanced trade relationships between European countries. To better capture the complexity of economic networks, we propose two global measures that assess the trade integration and the trade imbalances of the European countries. These measures are the network (or indire…

A new metric based on hitting probabilities for directed graphs and Markov chains.

Embeddings are ubiquitous in machine learning, appearing in recommender systems, NLP, and many other applications. Researchers and developers often need to explore the properties of a specific embedding, and one way to analyze embeddings is to visualize them. We present the Embedding Projector, a tool for interactive v…

Proposes QQE for transforming and embedding data distributions.

Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.

New embeddings for manifolds using heat kernels.

Introduces PELP for graph-enhanced word embeddings.

Curvature regularization prevents distortion in graph embeddings.

Word embeddings are a powerful approach for unsupervised analysis of language. Recently, Rudolph et al. (2016) developed exponential family embeddings, which cast word embeddings in a probabilistic framework. Here, we develop dynamic embeddings, building on exponential family embeddings to capture how the meanings of w…

Proposes cone embedding for better graph hierarchical structure representation.

Classifies linear embeddings of grassmannians and ind-grassmannians.

BC-Aligner maintains backward compatibility of embeddings after frequent updates.

Embedding calculus proves convergence for surfaces.

Unified framework for word embedding models using noise examples.

Models use embeddings and attention for better claim severity prediction.

A fast graph embedding method for large graphs.

Paper proves impossibility of three desirable properties in node embedding.

The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.

Proves uniqueness of embedding complex manifold into infinite-dimensional space.

The paper defines invariants for almost graph embeddings and explores their properties.

Recently, click-through rate (CTR) prediction models have evolved from shallow methods to deep neural networks. Most deep CTR models follow an Embedding\&MLP paradigm, that is, first mapping discrete id features, e.g. user visited items, into low dimensional vectors with an embedding module, then learn a multi-layer pe…

This work analyzes PPR-based node embeddings and their topological information.

Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph embedding methods are designed for static networks and they cannot capture evol…

For leveled spatial graphs, we find a surface embedding that allows cellular embedding.

Long spacelike embeddings can be approximated by isometric ones.

A {\it wrinkled embedding} $f:V^n\to W^m$ is a topological embedding which is a smooth embedding everywhere on $V$ except a set of $(n-1)$-dimensional spheres, where $f$ has cuspidal corners. In this paper we prove that any rotation of the tangent plane field $TV\subset TW$ of a {\it smoothly embedded} submanifold $V\s…

Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques aim to automatically create a low-dimensional representation of a given graph, whi…

Graphs embeddable on torus and linklessly in 3D can be embedded linklessly in standard torus.

Geometrically transforms word embeddings into a common space for better comparison.

Obtaining continuous representations of structural data such as directed acyclic graphs (DAGs) has gained attention in machine learning and artificial intelligence. However, embedding complex DAGs in which both ancestors and descendants of nodes are exponentially increasing is difficult. Tackling in this problem, we de…

The paper proves nonexistence and existence results for minimal surfaces in R^4.

Recent works reveal that network embedding techniques enable many machine learning models to handle diverse downstream tasks on graph structured data. However, as previous methods usually focus on learning embeddings for a single network, they can not learn representations transferable on multiple networks. Hence, it i…

MCE reduces embedding instability in nonlinear dimensionality reduction.

Natural language processing has improved tremendously after the success of word embedding techniques such as word2vec. Recently, the same idea has been applied on source code with encouraging results. In this survey, we aim to collect and discuss the usage of word embedding techniques on programs and source code. The a…

A new method for fast graph embedding using diffusion graphs.

Paper uses JIVE to decompose word embeddings, improving sentiment analysis performance.

Well-quasi-orders proved on embedded planar graphs.