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High-dimensional vector similarity search (HVSS) is critical for many data processing and AI applications. However, traditional HVSS methods often require extensive data access for distance calculations, leading to inefficiencies.…

Hierarchical clustering is a fundamental task often used to discover meaningful structures in data, such as phylogenetic trees, taxonomies of concepts, subtypes of cancer, and cascades of particle decays in particle physics. Typically…

Keyword Spotting (KWS) provides the start signal of ASR problem, and thus it is essential to ensure a high recall rate. However, its real-time property requires low computation complexity. This contradiction inspires people to find a…

Both astronomy and biology are experiencing explosive growth of data, resulting in a "big data" problem that stands in the way of a "big data" opportunity for discovery. One common question asked of such data is that of approximate search…

Inspired by the human ability to learn and organize knowledge into hierarchical taxonomies with prototypes, this paper addresses key limitations in current deep hierarchical clustering methods. Existing methods often tie the structure to…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap…

The humanities, like many other areas of society, are currently undergoing major changes in the wake of digital transformation. However, in order to make collection of digitised material in this area easily accessible, we often still lack…

This paper studies the statistical and computational limits of high-order clustering with planted structures. We focus on two clustering models, constant high-order clustering (CHC) and rank-one higher-order clustering (ROHC), and study the…

The Volterra Tensor Network lifts the curse of dimensionality for truncated, discrete times Volterra models, enabling scalable representation of highly nonlinear system. This scalability comes at the cost of introducing randomness through…

Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…

Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspond to sum-product neural networks with a sparse connectivity…

In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Large biological datasets are being produced at a rapid pace and create substantial storage challenges, particularly in the domain of high-throughput sequencing (HTS). Most approaches currently used to store HTS data are either unable to…

For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data.…

Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

Simulated annealing (SA) attracts more attention among classical heuristic algorithms because the solution of the combinatorial optimization problem can be naturally mapped to the ground state of the Ising Hamiltonian. However, in practical…