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STEM XEDS spectrum images can be drastically denoised by application of the principal component analysis (PCA). This paper looks inside the PCA workflow step by step on an example of a complex semiconductor structure consisting of a number…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
Community detection, aiming to group the graph nodes into clusters with dense inner-connection, is a fundamental graph mining task. Recently, it has been studied on the heterogeneous graph, which contains multiple types of nodes and edges,…
The process of selecting points for training a machine learning model is often a challenging task. Many times, we will have a lot of data, but for training, we require the labels and labeling is often costly. So we need to select the points…
Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that…
Signal processing on graphs has received a lot of attention in the recent years. A lot of techniques have arised, inspired by classical signal processing ones, to allow studying signals on any kind of graph. A common aspect of these…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important…
Modeling functions that are sequentially observed as functional time series is becoming increasingly common. In such models, it is often crucial to ensure data homogeneity. We investigate the sensitivity of graph-based change point…
In this paper, we propose an interpretable feature selection method based on principal component analysis (PCA) and principal component regression (PCR), which can extract important features for underwater source localization by only…
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…
Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
Evaluating node importance is a critical aspect of analyzing complex systems, with broad applications in digital marketing, rumor suppression, and disease control. However, existing methods typically rely on conventional network structures…
The largest balanced element in signed graphs plays a vital role in helping researchers understand the fundamental structure of the graph, as it reveals valuable information about the complex relationships between vertices in the network.…
In active learning for graph-structured data, Graph Neural Networks (GNNs) have shown effectiveness. However, a common challenge in these applications is the underutilization of crucial structural information. To address this problem, we…
Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…
Learning the graph underlying a networked system from nodal signals is crucial to downstream tasks in graph signal processing and machine learning. The presence of hidden nodes whose signals are not observable might corrupt the estimated…