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Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…

Dynamical Systems · Mathematics 2022-06-23 Marina Vegué , Vincent Thibeault , Patrick Desrosiers , Antoine Allard

The interactions between parameters, model structure, and outputs can determine what inferences, predictions, and control strategies are possible for a given system. Parameter space reduction and parameter estimation---and, more generally,…

Dynamical Systems · Mathematics 2018-02-16 Andrew F. Brouwer , Marisa C. Eisenberg

Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…

Computational Geometry · Computer Science 2018-05-22 Jesse Anderton , Virgil Pavlu , Javed Aslam

Implicit neural rendering, which uses signed distance function (SDF) representation with geometric priors (such as depth or surface normal), has led to impressive progress in the surface reconstruction of large-scale scenes. However,…

Computer Vision and Pattern Recognition · Computer Science 2023-03-17 Xiaoyang Lyu , Peng Dai , Zizhang Li , Dongyu Yan , Yi Lin , Yifan Peng , Xiaojuan Qi

Dimensional data reduction methods are fundamental to explore and visualize large data sets. Basic requirements for unsupervised data exploration are simplicity, flexibility and scalability. However, current methods show complex…

Machine Learning · Computer Science 2021-12-03 Joan Garriga , Frederic Bartumeus

We present a novel approach enabling interactive visualization of volumetric Locally Refined B-splines (LR-splines). To this end we propose a highly efficient algorithm for direct visualization of scalar and vector fields given by an…

Graphics · Computer Science 2018-03-15 Franz G. Fuchs , Oliver J. D. Barrowclough , Jon M. Hjelmervik , Heidi E. I. Dahl

Neural implicit representations are drawing a lot of attention from the robotics community recently, as they are expressive, continuous and compact. However, city-scale continual implicit dense mapping based on sparse LiDAR input is still…

Computer Vision and Pattern Recognition · Computer Science 2023-04-13 Yongliang Shi , Runyi Yang , Pengfei Li , Zirui Wu , Hao Zhao , Guyue Zhou

With the aim to improve the performance of feature matching, we present an unsupervised approach to fuse various local descriptors in the space of homographies. Inspired by the observation that the homographies of correct feature…

Computer Vision and Pattern Recognition · Computer Science 2014-12-16 Yuan-Ting Hu , Yen-Yu Lin , Hsin-Yi Chen , Kuang-Jui Hsu , Bing-Yu Chen

Visual reasoning, particularly spatial reasoning, is a challenging cognitive task that requires understanding object relationships and their interactions within complex environments, especially in robotics domain. Existing vision_language…

Robotics · Computer Science 2025-11-03 Simindokht Jahangard , Mehrzad Mohammadi , Abhinav Dhall , Hamid Rezatofighi

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Methodology · Statistics 2025-05-27 Si Cheng , Magali N. Blanco , Timothy V. Larson , Lianne Sheppard , Adam Szpiro , Ali Shojaie

Collaborative data consist of ratings relating two distinct sets of objects: users and items. Much of the work with such data focuses on filtering: predicting unknown ratings for pairs of users and items. In this paper we focus on the…

Graphics · Computer Science 2012-07-02 Guobiao Mei , Christian R. Shelton

Dimensionality Reduction (DR) methods are widely used to visualize high-dimensional data. One key task in DR-based analysis is discovering neighborhoods, which relies on analyzing the fine-grained local structure of a projection. However,…

Machine Learning · Computer Science 2026-05-25 Diede P. M. van der Hoorn , Alessio Arleo , Fernando V. Paulovich

The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we…

Methodology · Statistics 2015-08-10 Luca Scrucca

Embedding learning transforms discrete data entities into continuous numerical representations, encoding features/properties of the entities. Despite the outstanding performance reported from different embedding learning algorithms, few…

Machine Learning · Computer Science 2023-08-04 Yan Zheng , Junpeng Wang , Chin-Chia Michael Yeh , Yujie Fan , Huiyuan Chen , Liang Wang , Wei Zhang

Dense indoor scene modeling from 2D images has been bottlenecked due to the absence of depth information and cluttered occlusions. We present an automatic indoor scene modeling approach using deep features from neural networks. Given a…

Computer Vision and Pattern Recognition · Computer Science 2020-02-25 Yinyu Nie , Shihui Guo , Jian Chang , Xiaoguang Han , Jiahui Huang , Shi-Min Hu , Jian Jun Zhang

This paper presents a simple yet very effective data-driven approach to fuse both low-level and high-level local geometric features for 3D rigid data matching. It is a common practice to generate distinctive geometric descriptors by fusing…

Computer Vision and Pattern Recognition · Computer Science 2019-04-30 Jiaqi Yang , Chen Zhao , Ke Xian , Angfan Zhu , Zhiguo Cao

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…

Numerical Analysis · Mathematics 2017-07-21 Kelum Gajamannage , Sachit Butail , Maurizio Porfiri , Erik M. Bollt

Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…

Computer Vision and Pattern Recognition · Computer Science 2013-04-10 Yao Nan , Qian Feng , Sun Zuolei

Effective data visualization is a key part of the discovery process in the era of big data. It is the bridge between the quantitative content of the data and human intuition, and thus an essential component of the scientific path from data…

We propose an efficient algorithm to visualise symmetries in neural networks. Typically, models are defined with respect to a parameter space, where non-equal parameters can produce the same input-output map. Our proposed method, GENNI,…