Related papers: Topological Signal Processing over Cell Complexes
Spectral clustering has gained importance in recent years due to its ability to cluster complex data as it requires only pairwise similarity among data points with its ease of implementation. The central point in spectral clustering is the…
Topology offers a means to formally generalize digital filtering methods based on digital linear translation-invariant (LTI) filters while also, in principle, incorporating translation-variant and nonlinear methods as well as studying large…
This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplicial complexes connected by simplicial maps, that captures…
Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that…
Neural networks have advanced combinatorial optimization, with Transformer-based solvers achieving near-optimal solutions on the Traveling Salesman Problem (TSP) in milliseconds. However, these models operate as black boxes, providing no…
A standard approach to reduce the complexity of very large networks is to group together sets of nodes into clusters according to some criterion which reflects certain structural properties of the network. Beyond the well-known modularity…
Time series classification(TSC) has always been an important and challenging research task. With the wide application of deep learning, more and more researchers use deep learning models to solve TSC problems. Since time series always…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
We present tensor and sequence parallelism (TSP), a parallel execution strategy that folds tensor parallelism and sequence parallelism onto a single device axis. In conventional multi-dimensional parallelism layouts, tensor parallelism (TP)…
This paper proposes a tensor-based parameter estimation algorithm for sensing in an intelligent reflecting surface-assisted system. We present a higher-order singular value decomposition-based solution that exploits the tensor structure of…
This paper introduces topological data analysis. Starting from notions of a metric space and some elementary graph theory, we take example sets of data and demonstrate some of their topological properties. We discuss simplicial complexes…
Transformer-based methods have achieved state-of-the-art performance in time series forecasting (TSF) by capturing positional and semantic topological relationships among input tokens. However, it remains unclear whether existing…
Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional…
Traditional fluorescence staining is phototoxic to live cells, slow, and expensive; thus, the subcellular structure prediction (SSP) from transmitted light (TL) images is emerging as a label-free, faster, low-cost alternative. However,…
Topological deep learning (TDL) is a rapidly growing field that seeks to leverage topological structure in data and facilitate learning from data supported on topological objects, ranging from molecules to 3D shapes. Most TDL architectures…
A method of {\it topological grammars} is proposed for multidimensional data approximation. For data with complex topology we define a {\it principal cubic complex} of low dimension and given complexity that gives the best approximation for…
Time-frequency packing (TFP) transmission provides the highest achievable spectral efficiency with a constrained symbol alphabet and detector complexity. In this work, the application of the TFP technique to fiber-optic systems is…
Simplicial homology is a tool that provides a mathematical way to compute the connectivity and the coverage of a cellular network without any node location information. In this article, we use simplicial homology in order to not only…
This paper proposes a concise coding of the cells of n-dimensional finite regular grids. It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms. Discrete subsets of…
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…