相关论文: Density-based Isometric Mapping

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…

Manifold learning techniques for nonlinear dimension reduction assume that high-dimensional feature vectors lie on a low-dimensional manifold, then attempt to exploit manifold structure to obtain useful low-dimensional Euclidean…

Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…

New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented. By illuminating the way these metrics balance density and geometry in the underlying data, we clarify their key parameters and…

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…

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…

Dense Passage Retrieval (DPR) typically relies on Euclidean or cosine distance to measure query-passage relevance in embedding space, which is effective when embeddings lie on a linear manifold. However, our experiments across DPR…

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…

Acquiring plausible pathways on high-dimensional structural distributions is beneficial in several domains. For example, in the drug discovery field, a protein conformational pathway, i.e. a highly probable sequence of protein structural…

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…

The Densest Subgraph Problem (DSP) is widely used to identify community structures and patterns in networks such as bioinformatics and social networks. While solvable in polynomial time, traditional exact algorithms face computational and…

Intrinsic isometric shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency, i.e., the metric structure of the whole manifold…

Predicting human scanpaths when exploring panoramic videos is a challenging task due to the spherical geometry and the multimodality of the input, and the inherent uncertainty and diversity of the output. Most previous methods fail to give…

Cardiac parametric mapping is useful for evaluating cardiac fibrosis and edema. Parametric mapping relies on single-shot heartbeat-by-heartbeat imaging, which is susceptible to intra-shot motion during the imaging window. However, reducing…

In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance…

In order to process efficiently ever-higher dimensional data such as images, sentences, or audio recordings, one needs to find a proper way to reduce the dimensionality of such data. In this regard, SVD-based methods including PCA and…

When deciding where to place access points in a wireless network, it is useful to model the signal propagation loss between a proposed antenna location and the areas it may cover. The indoor dominant path (IDP) model, introduced by…

Sampling-based motion planners rely on incremental densification to discover progressively shorter paths. After computing feasible path $\xi$ between start $x_s$ and goal $x_t$, the Informed Set (IS) prunes the configuration space…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…