arXiv research

Explains visual metrics on hyperbolic space boundaries.

Suppose a finitely generated group $G$ is hyperbolic relative to $\mathcal P$ a set of proper finitely generated subgroups of $G$. Established results in the literature imply that a "visual" metric on $\partial (G,\mathcal P)$ is "linearly connected" if and only if the boundary $\partial (G,\mathcal P)$ has no cut poin…

Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to evaluate the quality of a visualization due to a variety of factors such as lack of…

Entangled bisimulation improves policy learning from visual input.

We present numerical visualizations of Ricci Flow of surfaces and 3-dimensional manifolds of revolution. Ricci_rot is an educational tool which visualizes surfaces of revolution moving under Ricci flow. That these surfaces tend to remain embedded in R3 is what makes direct visualization possible. The numerical lessons …

The paper explains knowledge distillation by analyzing visual concepts in DNNs.

New method makes quality metrics scale-invariant for high-dimensional data.

We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual stimulus and its associated percept. They take place in the visual areas V1/V2 whose functional architecture have been modelled in previous wo…

IsUMap improves data visualization of complex geometries.

Method generates visual explanations for similarity models without classification.

Croke and Kleiner constructed two homeomorphic locally CAT(0) complexes whose universal covers have visual boundaries that are not homeomorphic. We construct two homeomorphic locally CAT(0) complexes so that the visual boundary of one universal cover contains a nonplanar graph, while the visual boundary of the other do…

The horoboundary of Teichmüller space is path connected and has non-dense Busemann points.

Spatial and visual connectivity are important metrics when developing workplace layouts. Calculating those metrics in real-time can be difficult, depending on the size of the floor plan being analysed and the resolution of the analyses. This paper investigates the possibility of considerably speeding up the outcomes of…

A commonly used evaluation metric for text-to-image synthesis is the Inception score (IS) \cite{inceptionscore}, which has been shown to be a quality metric that correlates well with human judgment. However, IS does not reveal properties of the generated images indicating the ability of a text-to-image synthesis method…

This research converts visual information into audio for users to perceive.

ExMatrix visualizes RF models, aiding in decision understanding.

A visualization aids in comparing regression models by highlighting errors and correlations.

As machine learning becomes more pervasive, there is an urgent need for interpretable explanations of predictive models. Prior work has developed effective methods for visualizing global model behavior, as well as generating local (instance-specific) explanations. However, relatively little work has addressed regional …

Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to se…

We present GraphTSNE, a novel visualization technique for graph-structured data based on t-SNE. The growing interest in graph-structured data increases the importance of gaining human insight into such datasets by means of visualization. Among the most popular visualization techniques, classical t-SNE is not suitable o…

We prove that a PQ-symmetric homeomorphism between two complete metric spaces can be extended to a quasi-isometry between their hyperbolic approximations. This result is used to prove that two visual Gromov hyperbolic spaces are quasi-isometric if and only if there is a PQ-symmetric homeomorphism between their boundari…

We introduce simple cost and risk proxy metrics that can be attached to Treasury issuance strategy to complement analysis of the resulting portfolio weighted-average maturity (WAM). These metrics are based on mapping issuance fractions to their long-term, asymptotic portfolio implications for cost and risk under mechan…

Efficient auto-tuning for DR hyperparameters with BO.

Proposes a neural network method to improve consistencies in high dimensional data analysis.

Deep metric learning is often used to learn an embedding function that captures the semantic differences within a dataset. A key factor in many problem domains is how this embedding generalizes to new classes of data. In observing many triplet selection strategies for Metric Learning, we find that the best performance …

This paper proposes a new evaluation metric and boosting method for weight separability in neural network design. In contrast to general visual recognition methods designed to encourage both intra-class compactness and inter-class separability of latent features, we focus on estimating linear independence of column vec…

Modern datasets and models are notoriously difficult to explore and analyze due to their inherent high dimensionality and massive numbers of samples. Existing visualization methods which employ dimensionality reduction to two or three dimensions are often inefficient and/or ineffective for these datasets. This paper in…

The paper clusters group fairness metrics and visualizes them using PCA.

In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of …

The set of maximal non-integrable structures $(SU(2)\times SU(2),B,I)$, where $B$ is Killing-Cartan metric is described as subset of $\mathbb{CP}^3$. The visualization of complex projective space $\mathbb{CP}^3$ as tetrahedron which edges and faces are $\mathbb{CP}^1$ and $\mathbb{CP}^2$ is used.

This paper gives a review and synthesis of methods of evaluating dimensionality reduction techniques. Particular attention is paid to rank-order neighborhood evaluation metrics. A framework is created for exploring dimensionality reduction quality through visualization. An associated toolkit is implemented in R. The to…

Prior work in visual dialog has focused on training deep neural models on VisDial in isolation. Instead, we present an approach to leverage pretraining on related vision-language datasets before transferring to visual dialog. We adapt the recently proposed ViLBERT (Lu et al., 2019) model for multi-turn visually-grounde…

One of the primary challenges of visual storytelling is developing techniques that can maintain the context of the story over long event sequences to generate human-like stories. In this paper, we propose a hierarchical deep learning architecture based on encoder-decoder networks to address this problem. To better help…

Uncertainty Toolbox aids in assessing and improving uncertainty quantification in machine learning.

A Thurston map is a branched covering map from $§^2$ to $§^2$ with a finite postcritical set. We associate a natural Gromov hyperbolic graph $\G=\G(f,\mathcal C)$ with an expanding Thurston map $f$ and a Jordan curve $\mathcal C$ on $§^2$ containing $\post(f)$. The boundary at infinity of $\G$ with associated visual me…

Interactive tool helps choose and understand classification metrics.

The paper quantifies uncertainty in aggregated machine learning metrics.

Reassesses calibration metrics in machine learning models.

We consider properly discontinuous, isometric, convex cocompact actions of surface groups on a CAT(-1) space. We show that the limit set of such an action, equipped with the canonical visual metric, is a (weak) quasicircle in the sense of Falconer and Marsh. It follows that the visual metrics on such limit sets are cla…

Figures are an important channel for scientific communication, used to express complex ideas, models and data in ways that words cannot. However, this visual information is mostly ignored in analyses of the scientific literature. In this paper, we demonstrate the utility of using scientific figures as markers of knowle…

Selecting an optimal set of icons is a crucial step in the pipeline of visual design to structure and navigate through content. However, designing the icons sets is usually a difficult task for which expert knowledge is required. In this work, to ease the process of icon set selection to the users, we propose a similar…

Traditionally, the vision community has devised algorithms to estimate the distance between an original image and images that have been subject to perturbations. Inspiration was usually taken from the human visual perceptual system and how the system processes different perturbations in order to replicate to what exten…

CAMEL embeds data into a manifold using curvature-augmented forces.

Paper develops a framework for generating coherent image captions using visual features and hierarchical topics.

MetaStackVis aids in choosing better metamodels for stacking ensembles.

Metric-based meta-learning techniques have successfully been applied to few-shot classification problems. In this paper, we propose to leverage cross-modal information to enhance metric-based few-shot learning methods. Visual and semantic feature spaces have different structures by definition. For certain concepts, vis…

Proposes QQE for transforming and embedding data distributions.

iConViz helps banks manage default contagion risk in networked loans.