Related papers: Quantum-inspired Benchmark for Estimating Intrinsi…
We present a comprehensive investigation into the learning capabilities of a simple d-level system (qudit). Our study is specialized for classification tasks using real-world databases, specifically the Iris, breast cancer, and MNIST…
The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in…
Accurate estimation of Intrinsic Dimensionality (ID) is of crucial importance in many data mining and machine learning tasks, including dimensionality reduction, outlier detection, similarity search and subspace clustering. However, since…
Electrical Impedance Tomography (EIT) is a non-invasive, low-cost bedside imaging modality with high temporal resolution, making it suitable for bedside monitoring. However, its inherently ill-posed inverse problem poses significant…
Intrusion Detection Systems (IDSs) must maintain high detection sensitivity while operating under strict false-positive constraints, a challenge intensified by class imbalance and heterogeneous IoT traffic. This work investigates whether…
The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…
It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…
Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of…
Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multi-dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine learning approach as well as to understand its behavior and…
Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…
This paper introduces a novel quantum embedding search algorithm (QES, pronounced as "quest"), enabling search for optimal quantum embedding design for a specific dataset of interest. First, we establish the connection between the…
One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…
When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…
Model quantization has emerged as an indispensable technique to accelerate deep learning inference. While researchers continue to push the frontier of quantization algorithms, existing quantization work is often unreproducible and…
This paper reconsiders common benchmarking approaches to nearest neighbor search. It is shown that the concept of local intrinsic dimensionality (LID) allows to choose query sets of a wide range of difficulty for real-world datasets.…
Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only…
Quantum classification and hypothesis testing are two tightly related subjects, the main difference being that the former is data driven: how to assign to quantum states $\rho(x)$ the corresponding class $c$ (or hypothesis) is learnt from…
Quantum computers have the potential to outperform classical computers in a range of computational tasks, such as prime factorisation and unstructured searching. However, real-world quantum computers are subject to noise. Quantifying noise…
Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e.g., forcing terms, boundary conditions,…
The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets…