51,686 research outputs found
Filtering Random Graph Processes Over Random Time-Varying Graphs
Graph filters play a key role in processing the graph spectra of signals
supported on the vertices of a graph. However, despite their widespread use,
graph filters have been analyzed only in the deterministic setting, ignoring
the impact of stochastic- ity in both the graph topology as well as the signal
itself. To bridge this gap, we examine the statistical behavior of the two key
filter types, finite impulse response (FIR) and autoregressive moving average
(ARMA) graph filters, when operating on random time- varying graph signals (or
random graph processes) over random time-varying graphs. Our analysis shows
that (i) in expectation, the filters behave as the same deterministic filters
operating on a deterministic graph, being the expected graph, having as input
signal a deterministic signal, being the expected signal, and (ii) there are
meaningful upper bounds for the variance of the filter output. We conclude the
paper by proposing two novel ways of exploiting randomness to improve (joint
graph-time) noise cancellation, as well as to reduce the computational
complexity of graph filtering. As demonstrated by numerical results, these
methods outperform the disjoint average and denoise algorithm, and yield a (up
to) four times complexity redution, with very little difference from the
optimal solution
Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph Clustering
Recently there is a growing focus on graph data, and multi-view graph
clustering has become a popular area of research interest. Most of the existing
methods are only applicable to homophilous graphs, yet the extensive real-world
graph data can hardly fulfill the homophily assumption, where the connected
nodes tend to belong to the same class. Several studies have pointed out that
the poor performance on heterophilous graphs is actually due to the fact that
conventional graph neural networks (GNNs), which are essentially low-pass
filters, discard information other than the low-frequency information on the
graph. Nevertheless, on certain graphs, particularly heterophilous ones,
neglecting high-frequency information and focusing solely on low-frequency
information impedes the learning of node representations. To break this
limitation, our motivation is to perform graph filtering that is closely
related to the homophily degree of the given graph, with the aim of fully
leveraging both low-frequency and high-frequency signals to learn
distinguishable node embedding. In this work, we propose Adaptive Hybrid Graph
Filter for Multi-View Graph Clustering (AHGFC). Specifically, a graph joint
process and graph joint aggregation matrix are first designed by using the
intrinsic node features and adjacency relationship, which makes the low and
high-frequency signals on the graph more distinguishable. Then we design an
adaptive hybrid graph filter that is related to the homophily degree, which
learns the node embedding based on the graph joint aggregation matrix. After
that, the node embedding of each view is weighted and fused into a consensus
embedding for the downstream task. Experimental results show that our proposed
model performs well on six datasets containing homophilous and heterophilous
graphs.Comment: Accepted by AAAI202
Joint Multi-grained Popularity-aware Graph Convolution Collaborative Filtering for Recommendation
Graph Convolution Networks (GCNs), with their efficient ability to capture
high-order connectivity in graphs, have been widely applied in recommender
systems. Stacking multiple neighbor aggregation is the major operation in GCNs.
It implicitly captures popularity features because the number of neighbor nodes
reflects the popularity of a node. However, existing GCN-based methods ignore a
universal problem: users' sensitivity to item popularity is differentiated, but
the neighbor aggregations in GCNs actually fix this sensitivity through Graph
Laplacian Normalization, leading to suboptimal personalization.
In this work, we propose to model multi-grained popularity features and
jointly learn them together with high-order connectivity, to match the
differentiation of user preferences exhibited in popularity features.
Specifically, we develop a Joint Multi-grained Popularity-aware Graph
Convolution Collaborative Filtering model, short for JMP-GCF, which uses a
popularity-aware embedding generation to construct multi-grained popularity
features, and uses the idea of joint learning to capture the signals within and
between different granularities of popularity features that are relevant for
modeling user preferences. Additionally, we propose a multistage stacked
training strategy to speed up model convergence. We conduct extensive
experiments on three public datasets to show the state-of-the-art performance
of JMP-GCF
Forecasting Time Series with VARMA Recursions on Graphs
Graph-based techniques emerged as a choice to deal with the dimensionality
issues in modeling multivariate time series. However, there is yet no complete
understanding of how the underlying structure could be exploited to ease this
task. This work provides contributions in this direction by considering the
forecasting of a process evolving over a graph. We make use of the
(approximate) time-vertex stationarity assumption, i.e., timevarying graph
signals whose first and second order statistical moments are invariant over
time and correlated to a known graph topology. The latter is combined with VAR
and VARMA models to tackle the dimensionality issues present in predicting the
temporal evolution of multivariate time series. We find out that by projecting
the data to the graph spectral domain: (i) the multivariate model estimation
reduces to that of fitting a number of uncorrelated univariate ARMA models and
(ii) an optimal low-rank data representation can be exploited so as to further
reduce the estimation costs. In the case that the multivariate process can be
observed at a subset of nodes, the proposed models extend naturally to Kalman
filtering on graphs allowing for optimal tracking. Numerical experiments with
both synthetic and real data validate the proposed approach and highlight its
benefits over state-of-the-art alternatives.Comment: submitted to the IEEE Transactions on Signal Processin
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
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