A new algorithm BE converts dendrograms to 2D scatter plots.
problem Preserving hierarchical structures in high-dimensional data.
method Converts a dendrogram to a 2D scatter plot.
result Moderately preserves the original hierarchical structures.
Automatically extracts data from scatter plots.
problem Challenges in extracting numerical data from scatter plots.
method Uses deep learning for component identification and optical character recognition for pixel-to-coordinate mapping.
result Achieves 89% successful data extraction on test set.
New method makes quality metrics scale-invariant for high-dimensional data.
problem Scale sensitivity in quality metrics affects the accuracy of data projections.
method Analytical and empirical investigation of stress and KL divergence; introduction of a scale-invariant technique.
result The proposed technique accurately captures expected behavior and makes metrics scale-invariant.
Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results…
A new hypersurface of Tzitzeica type is obtained in all three forms: parametric, implicit and explicit. Its two-dimensional version, although well-known from a theoretical point of view, is plotted with Matlab.
Visualizes deep neural network decisions in 2D for better understanding.
problem Difficulty in comprehending complex deep learning models.
method Discriminative dimensionality reduction for 2D visualization of model decisions.
result Insight into how different data properties are treated by the model.
Analyzes regional wealth inequalities in Italy using various statistical methods.
problem Examining regional wealth disparities in Italy over 2007-2011.
method Used frequency-size plots, cumulative distribution function plots, scatter plots, rank-size plots, and transformed aggregated tax income data into Gini, Theil, and Herfindahl-Hirschman indices.
result Confirmed significant regional wealth differences in Italy, with Molise being a notable case.
New methods implement manifold scattering transform for high-dimensional point cloud data.
problem Classifying data on complex, non-linear manifolds.
method Adapting diffusion maps theory for numerical implementation.
result Effective for signal and manifold classification tasks.
We show, that higher analogs of the Willmore functional, defined on the space of immersions M^2\rightarrow R^3, where M^2 is a two-dimensional torus, R^3 is the 3-dimensional Euclidean space are invariant under conformal transformations of R^3. This hypothesis was formulated recently by I.A.Taimanov (dg-ga/9610013). Hi…
In this paper, we consider a compact Riemannian manifold with boundary, endowed with a magnetic potential α and a potential U. For brevity, this type of systems are called $\MP$-systems. On simple $\MP$-systems, we consider both the boundary rigidity problem and scattering rigidity problem, see the introduction for…
Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis. A problem that has received much attention is how deal with sets of persistence diagrams. How do we summarize them, average them or cluster them? One approach -- th…
The paper presents an O(N log N)-implementation of t-SNE -- an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots and that normally runs in O(N^2). The new implementation uses vantage-point trees to compute sparse pairwise similarities between the input data object…
Paper reviews and synthesizes methods for evaluating dimensionality reduction techniques.
problem Evaluating and comparing dimensionality reduction techniques.
method Framework and toolkit in R for exploring and evaluating dimensionality reduction quality through visual insights.
result Helps researchers compare and select dimensionality reduction techniques using visual insights.
Neural networks' global minimum found using ridgelet transform.
problem Finding the global minimum of neural network training problems.
method Reduction to convex optimization via ridgelet transform.
result Global optimizer of shallow neural networks is given by ridgelet transform.
The paper supports task classification from eye movements, achieving 95.4% accuracy.
problem Decoding the observer's task from eye movements.
method Exploratory analysis, feature projection, feature elimination, SVM and Ada Boosting classifier training.
result Achieved 95.4% accuracy in task classification.
Automate residual plot assessment with R package and Shiny application
problem Diagnosing linear models
method Computer vision model for residual plot assessment
result Predicts visual signal strength and supports model fit assessment
Billiard trajectories in curved spaces have predictable travel times.
problem Understanding travel times in billiard trajectories on curved surfaces.
method Analyzing geodesic flows and sectional curvature to prove time-preserving conjugacy.
result Billiard trajectories with almost identical obstacles have identical shapes.
Proposes G2DLDA framework for robust 2DLDA with regularization.
problem Singularity issue and sensitivity to outliers in 2DLDA.
method Generalized Lp-norm 2DLDA with regularization for arbitrary p.
result Effective in solving singularity and improving generalization.
This research optimizes Andrews plots for better visual clarity in high-dimensional data.
problem Visualizing high-dimensional datasets with clarity and aesthetics.
method Developed a method to add spectral smoothing to Andrews plots to reduce visual clutter.
result Optimal spatial-spectral smoothing leads to more aesthetically pleasing and clutter-free visualizations.
FigureNet learns to answer questions about scientific plots.
problem Addressing reasoning tasks in question-answering on scientific plots.
method Introduces FigureNet, a deep learning model that identifies plot elements, quantifies values, and determines relative ordering.
result FigureNet outperforms state-of-the-art models by 7% on the FigureQA dataset.
This study revisits UQ validation methods based on consistency and adaptivity concepts.
problem Lack of comprehensive validation methods for UQ metrics across input feature ranges.
method Revisit and extend common validation methods for UQ metrics based on consistency and adaptivity concepts.
result Improved understanding and capabilities of UQ metrics validation methods.
Automates selection and visualization of model responses in various directions.
problem Manual selection and limited visualization of PDPs.
method Formalizes method for automating PDP selection and extends to arbitrary directions.
result Demonstrates usefulness across model selection, bias detection, and latent space exploration.
3D filament plots visualize curves in datasets, avoiding visual clutter.
problem Visualizing high-dimensional data relationships in scatterplots of points.
method Construct 3D filament plots using linear isometries and Frenet-Serret systems.
result 3D filament plots preserve Euclidean distances and avoid visual clutter.
A new visualization tool MD plot discovers interesting structures in continuous features.
problem Identifying interesting structures in data distributions, especially with skewed, clipped, or multimodal distributions.
method Proposes a new visualization tool called the mirrored density plot (MD plot) that does not require adjusting density estimation parameters.
result The MD plot outperforms conventional methods in identifying structures in complex distributions.
Used to investigate the presence of distinctive recurrent behaviours in natural processes, the recurrence plots can be applied to the analysis of economic data, and, in particular, to the characterization of exchange rates of currencies too. In this paper, we will show that these plots are able to characterize the peri…
Oil economy modeled using phase plots and Benard convection analogy.
problem Understanding the dynamics of world oil production, price, and EROEI.
method Phase plot of oil economy data, analogy with Benard convection, interpretation and forecast methods.
result Proposed methods for interpreting and forecasting oil economy behavior.
Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers and models justifying the presence of power laws in economic data. Most of the ti…
Paper exposes vulnerabilities in interpreting machine learning models using adversarial attacks on PD plots.
problem Vulnerability of permutation-based interpretation methods, particularly PD plots, to adversarial attacks.
method Adversarial framework to manipulate black-box models and produce deceptive PD plots.
result It is possible to hide discriminatory behaviors in machine learning models through interpretation tools like PD plots.
Proves two non-trapping obstacles coincide if scattering rays have similar travelling times or scattering length spectra.
problem Identifying non-trapping obstacles based on scattering properties.
method Proves two obstacles coincide if their scattering rays have similar travelling times or scattering length spectra under weak non-degeneracy conditions.
result Two non-trapping obstacles coincide if their scattering rays have similar travelling times or scattering length spectra.
Introduces PIT-plot for prioritizing projects based on their impact.
problem Optimizing R&D investments in project portfolios.
method Develops a new tool (PIT-plot) focusing on project impact rather than project properties.
result Identifies projects with the largest impact for risk mitigation or value-adding.
Unified framework for interpreting complex regression models with many predictors.
problem Interpreting nonparametric regression models with many predictors.
method Derivative-based approach for existing tools like partial-dependence plots.
result New technique called accumulated total derivative effects plot for complex models.
PLOT uses optimal transport to find neural site handles for causal abstraction.
problem Finding the relevant neural site for causal analysis is computationally challenging.
method PLOT employs optimal transport to localize causal variables from neural network outputs.
result PLOT efficiently finds intervention handles for causal abstraction in neural networks.
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines …
The paper explores transformations between power law problems and geodesics on cones.
problem Solving power law problems and understanding their geometric properties.
method Geometric transformations and cone metrics.
result Derivation of Maclaurin duality and Jacobi-Maupertuis metric reformulation.
The paper introduces scattering-symplectic manifolds and explores their properties.
problem Understanding minimally degenerate Poisson structures on manifolds.
method Constructing scattering-symplectic spheres and gluings, computing Poisson cohomology explicitly.
result Explicit computation of Poisson cohomology and new method introduced.
Develops Austen plots for assessing bias from unobserved confounding in observational studies.
problem Bias in causal estimates due to unobserved confounding.
method Formalizes confounding strength, uses Austen plots to visualize and quantify bias.
result Allows domain experts to assess the plausibility of strong confounders.
A new classification method using potential functions and pot-pot plots.
problem Supervised classification of data points.
method Transform data to a pot-pot plot, classify using α-procedure or k-NN. result Strongly Bayes-consistent for continuous distributions.
A method to simplify complex high-dimensional data visualization.
problem Difficult interpretation of linear projections in high-dimensional data.
method Decomposition of linear projections into axis-aligned projections using Dempster-Shafer theory.
result Linear projections can be effectively represented by a sparse set of axis-aligned projections, revealing more intuitive insights.
Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and volume interact, particularly when the levels of both are high. We find that the…
Plots show miscalibration directly as slopes of secant lines.
problem Detecting discrepancies between probabilistic predictions and actual outcomes.
method Cumulative differences between observed and expected values displayed as slopes of secant lines.
result Directly shows miscalibration without binning or kernel density estimation.
Geometric scattering on manifolds improves neural network performance.
problem Improving neural network performance on manifold data.
method Generalized Euclidean scattering transform to compact manifolds.
result Geometric scattering provides localized isometry invariant descriptions of manifold signals.
Automates identifying interesting plots in production yield data.
problem Identifying plots deemed interesting by analysts in production yield data.
method Uses Generative Adversarial Networks (GANs) to learn analyst's intent.
result Demonstrates improved identification of interesting plots in production yield data.
Two new plots confirm trend following and risk premia findings.
problem Confirming trend following and risk premia strategies over new data.
method Presenting two additional plots to corroborate findings.
result New data fully corroborates trend following and risk premia findings.
Computer vision model automates residual plot assessment for diagnosing model assumptions.
problem Automating residual plot assessment for model diagnostics.
method Trains a computer vision model to predict disparity between residual distributions and reference distributions using Kullback-Leibler divergence.
result Computer vision model is less sensitive to non-linearity but more sensitive than human judgment and conventional tests.
Geometric wavelet scattering on manifolds improves neural network understanding.
problem Improving neural network understanding on manifold and graph domains.
method Defining a geometric scattering transform based on wavelet filters and nonlinearities.
result Generalizes deformation stability and local translation invariance to manifolds.
We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probabil…
Study predicts synchronization state of financial time series using cross-recurrence plots.
problem Predicting the state of synchronization of financial time series.
method Cross-correlation analysis and deep learning framework for predicting synchronization state based on cross-recurrence plots.
result Satisfactory performance in predicting synchronization state for certain pairs of stocks.
Paper explains scattering diagrams' role in mirror symmetry.
problem Reconstruction problem in mirror symmetry.
method Introduction of scattering diagrams and their role in SYZ and HMS conjectures.
result Scattering diagrams help in understanding mirror symmetry.