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Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or…

A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…

The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…

Dynamic graphs arise in a plethora of practical scenarios such as social networks, communication networks, and financial transaction networks. Given a dynamic graph, it is fundamental and essential to learn a graph representation that is…

Over-parameterization and adaptive methods have played a crucial role in the success of deep learning in the last decade. The widespread use of over-parameterization has forced us to rethink generalization by bringing forth new phenomena,…

Graph Neural Networks (GNNs) have become the state-of-the-art method for many applications on graph structured data. GNNs are a model for graph representation learning, which aims at learning to generate low dimensional node embeddings that…

Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…

Deep neural networks often generalize well despite heavy over-parameterization, challenging classical parameter-based analyses. We study generalization from a representation-centric perspective and analyze how the geometry of learned…

Graph Neural Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data and are deployed in various fields, from social network analysis to drug discovery. However, there is limited…

Graphs can model real-world, complex systems by representing entities and their interactions in terms of nodes and edges. To better exploit the graph structure, graph neural networks have been developed, which learn entity and edge…

In this paper, we study the factors that contribute to the effect of oversmoothing in deep Graph Neural Networks (GNNs). Specifically, our analysis is based on a new metric (Mean Average Squared Distance - $MASED$) to quantify the extent of…

Recent advances in machine learning research have produced powerful neural graph embedding methods, which learn useful, low-dimensional vector representations of network data. These neural methods for graph embedding excel in graph machine…

Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…

Deep metric learning is often used to learn an embedding function that captures the semantic differences within a dataset. A key factor in many problem domains is how this embedding generalizes to new classes of data. In observing many…

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…

Graphs are ubiquitous due to their flexibility in representing social and technological systems as networks of interacting elements. Graph representation learning methods, such as node embeddings, are powerful approaches to map nodes into a…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

In the last two decades we are witnessing a huge increase of valuable big data structured in the form of graphs or networks. To apply traditional machine learning and data analytic techniques to such data it is necessary to transform graphs…

The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning…

Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still…