相关论文: Laplacian Canonization: A Minimalist Approach to S…

Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…

Unsupervised localization and segmentation are long-standing computer vision challenges that involve decomposing an image into semantically-meaningful segments without any labeled data. These tasks are particularly interesting in an…

A novel, fast and practical way of enhancing images is introduced in this paper. Our approach builds on Laplacian operators of well-known edge-aware kernels, such as bilateral and nonlocal means, and extends these filter's capabilities to…

Many machine learning models leverage group invariance which is enjoyed with a wide-range of applications. For exploiting an invariance structure, one common approach is known as \emph{frame averaging}. One popular example of frame…

This paper develops an invariant--geometric interpretation of the canonization problem for simple undirected weighted graphs based on the {discrete moving frame method} for finite groups. We consider the action of the {pair group}…

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…

Nearly all state of the art vision models are sensitive to image rotations. Existing methods often compensate for missing inductive biases by using augmented training data to learn pseudo-invariances. Alongside the resource demanding data…

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Laplacian of a balanced…

As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of semi-supervised learning. To benefit from the access to…

In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…

Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…

We propose a novel method to enhance the performance of coordinate-MLPs by learning instance-specific positional embeddings. End-to-end optimization of positional embedding parameters along with network weights leads to poor generalization…

Deriving meaningful representations from complex, high-dimensional data in unsupervised settings is crucial across diverse machine learning applications. This paper introduces a framework for multi-scale graph network embedding based on…

In this work, we theoretically demonstrate that current graph positional encodings (PEs) are not beneficial and could potentially hurt performance in tasks involving heterophilous graphs, where nodes that are close tend to have different…

This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…

In this paper, we study the entries of the principal eigenvector of the signless Laplacian matrix of a hypergraph. More precisely, we obtain bounds for this entries. These bounds are computed trough other important parameters, such as…

This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation…

With an increasing influx of classical signal processing methodologies into the field of graph signal processing, approaches grounded in discrete linear canonical transform have found application in graph signals. In this paper, we…

Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…

Batch effects arising from technical variations in histopathology staining protocols, scanners, and acquisition pipelines pose a persistent challenge for computational pathology, hindering cross-batch generalization and limiting reliable…