Related papers: Beyond Spatio-Temporal Representations: Evolving F…
Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation,…
Representation learning on static graph-structured data has shown a significant impact on many real-world applications. However, less attention has been paid to the evolving nature of temporal networks, in which the edges are often changing…
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…
Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the…
Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural networks (MPNNs) face well-documented theoretical and…
Recent progress in graph signal processing (GSP) has addressed a number of problems, including sampling and filtering. Proposed methods have focused on generic graphs and defined signals with certain characteristics, e.g., bandlimited…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
We introduce the Latent Fourier Transform (LatentFT), a framework that provides novel frequency-domain controls for generative music models. LatentFT combines a diffusion autoencoder with a latent-space Fourier transform to separate musical…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
In this paper, we propose a differentiable version of the short-time Fourier transform (STFT) that allows for gradient-based optimization of the hop length or the frame temporal position by making these parameters continuous. Our approach…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…
We propose a graph spectral representation of time series data that 1) is parsimoniously encoded to user-demanded resolution; 2) is unsupervised and performant in data-constrained scenarios; 3) captures event and event-transition structure…
This paper develops fast graph Fourier transform (GFT) algorithms with O(n log n) runtime complexity for rank-one updates of the path graph. We first show that several commonly-used audio and video coding transforms belong to this class of…
In this work, we introduce a filtration on temporal graphs based on $\delta$-temporal motifs (recurrent subgraphs), yielding a multi-scale representation of temporal structure. Our temporal filtration allows tools developed for filtered…
Recently, many graph matching methods that incorporate pairwise constraint and that can be formulated as a quadratic assignment problem (QAP) have been proposed. Although these methods demonstrate promising results for the graph matching…
The conservation of the long wavelength fluctuations of the metric plays a vital role in cosmology as the link between quantum fluctuations during inflation and late time observations. This is a well-known property of the classical…
The Euler Characteristic Transform (ECT) is an efficiently-computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the Local Euler Characteristic Transform ($\ell$-ECT), a novel…