Related papers: Curvature Regularization to Prevent Distortion in …
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…
One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
Steinerberger proposed a notion of curvature on graphs involving the graph distance matrix (J. Graph Theory, 2023). We show that nonnegative curvature is almost preserved under three graph operations. We characterize the distance matrix and…
Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality…
A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…
Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…
Contrastive learning has emerged as a premier method for learning representations with or without supervision. Recent studies have shown its utility in graph representation learning for pre-training. Despite successes, the understanding of…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…
Self-supervised learning (SSL) has recently advanced through non-contrastive methods that couple an invariance term with variance, covariance, or redundancy-reduction penalties. While such objectives shape first- and second-order statistics…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…
Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
Reconstructing high-quality 3D meshes and visuals from 3D Gaussian Splatting(3DGS) still remains a central challenge in computer graphics. Although existing models such as SuGaR offer effective solutions for rendering, there is is still…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
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-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
In this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular…