In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on
higher-order networks. Drawing analogies from discrete and graph signal processing, we …

Using graphs to model pairwise relationships between entities is a ubiquitous framework for
studying complex systems and data. Simplicial complexes extend this dyadic model of …

Advances in wearable sensing and mobile computing have enabled the collection of health
and well-being data outside of traditional laboratory and hospital settings, paving the way for …

We consider the construction of neural network architectures for data on simplicial
complexes. In studying maps on the chain complex of a simplicial complex, we define three …

Network data has become widespread, larger, and more complex over the years. Traditional
network data is dyadic, capturing the relations among pairs of entities. With the need to …

We propose a simplicial complex convolutional neural network (SCCNN) to learn data
representations on simplicial complexes. It performs convolutions based on the multi-hop …

Obtaining sparse, interpretable representations of observable data is crucial in many
machine learning and signal processing tasks. For data representing flows along the edges …

Searching for similar GPS trajectories is a fundamental problem that faces challenges of
large data volume and intrinsic complexity of trajectory comparison. In this paper, we present …

We consider the construction of neural network architectures for data on simplicial
complexes. In studying maps on the chain complex of a simplicial complex, we define three …

We propose a method to detect outliers in empirically observed trajectories on a discrete or
discretized manifold modeled by a simplicial complex. Our approach is similar to spectral …