Related papers: Inductive Global and Local Manifold Approximation …

Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The…

Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

Topology based dimensionality reduction methods such as t-SNE and UMAP have seen increasing success and popularity in high-dimensional data. These methods have strong mathematical foundations and are based on the intuition that the topology…

Manifold Learning is a class of algorithms seeking a low-dimensional non-linear representation of high-dimensional data. Thus manifold learning algorithms are, at least in theory, most applicable to high-dimensional data and sample sizes to…

Dimension reduction and visualization of high-dimensional data have become very important research topics because of the rapid growth of large databases in data science. In this paper, we propose using a generalized sigmoid function to…

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

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…

An important task in image processing and neuroimaging is to extract quantitative information from the acquired images in order to make observations about the presence of disease or markers of development in populations. Having a…

Euclidean representation learning methods have achieved promising results in image fusion tasks, which can be attributed to their clear advantages in handling with linear space. However, data collected from a realistic scene usually has a…

In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we…

Neighbor embeddings are a family of methods for visualizing complex high-dimensional datasets using $k$NN graphs. To find the low-dimensional embedding, these algorithms combine an attractive force between neighboring pairs of points with a…

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…

It has become standard to use gradient-based dimensionality reduction (DR) methods like tSNE and UMAP when explaining what AI models have learned. This makes sense: these methods are fast, robust, and have an uncanny ability to find…

Large-scale incremental mapping is fundamental to the development of robust and reliable autonomous systems, as it underpins incremental environmental understanding with sequential inputs for navigation and decision-making. LiDAR is widely…

In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…

Modeling scene geometry using implicit neural representation has revealed its advantages in accuracy, flexibility, and low memory usage. Previous approaches have demonstrated impressive results using color or depth images but still have…

Manifold learning techniques seek to discover structure-preserving mappings of high-dimensional data into low-dimensional spaces. While the new sets of coordinates specified by these mappings can closely parameterize the data, they are…

Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited…