相关论文: Dimensionality reduction for homological stability…

Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces to extract hidden and useful information or facilitate visual understanding and interpretation of the data. However, few of them take…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Deep learning is mainly based on utilizing gradient-based optimization for training Deep Neural Network (DNN) models. Although robust and widely used, gradient-based optimization algorithms are prone to getting stuck in local minima. In…

Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…

Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…

t-distributed stochastic neighbor embedding (t-SNE) is a well-established visualization method for complex high-dimensional data. However, the original t-SNE method is nonparametric, stochastic, and often cannot well prevserve the global…

An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…

Non-linear dimensionality reduction can be performed by \textit{manifold learning} approaches, such as Stochastic Neighbour Embedding (SNE), Locally Linear Embedding (LLE) and Isometric Feature Mapping (ISOMAP). These methods aim to produce…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

Dimensionality reduction (DR) techniques are often characterized by whether they preserve global, high-level structures in the data or local, neighborhood structures. This distinction matters in visualization: global methods can obscure…

Nonlinear dimensionality reduction lacks interpretability due to the absence of source features in low-dimensional embedding space. We propose an interpretable method featMAP to preserve source features by tangent space embedding. The core…

We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we…

Searching for the $k$-nearest neighbors (KNN) in multimodal data retrieval is computationally expensive, particularly due to the inherent difficulty in comparing similarity measures across different modalities. Recent advances in multimodal…

Dimension reduction (DR) is commonly utilized to capture the intrinsic structure and transform high-dimensional data into low-dimensional space while retaining meaningful properties of the original data. It is used in various applications,…

One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

Correct risk estimation of policyholders is of great significance to auto insurance companies. While the current tools used in this field have been proven in practice to be quite efficient and beneficial, we argue that there is still a lot…

Quadrotor stability under complex dynamic disturbances and model uncertainties poses significant challenges. One of them remains the underfitting problem in high-dimensional features, which limits the identification capability of current…

In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and could accelerate optimization algorithms for solving large scale convex optimization problems with…