Related papers: Quantum algorithms for topological and geometric a…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
Persistent homology is a tool of topological data analysis that has been used in a variety of settings to characterize different dimensional holes in data. However, persistent homology computations can be memory intensive with a…
Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss…
High-quality training data is the foundation of machine learning and artificial intelligence, shaping how models learn and perform. Although much is known about what types of data are effective for training, the impact of the data's…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…
Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
We develop here an algorithmic framework for constructing consistent multiscale Laplacian eigenfunctions (vectors) on data. Consequently, we address the unsupervised machine learning task of finding scalar functions capturing consistent…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as…
Using a set of $\Lambda$CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We…
A multicomplex structure is defined from an ordered lattice of multigraphs. This structure will help us to observe the features of Persistent Homology in this context, its interaction with the ordering and the repercussions of the process…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…