相关论文: A Geometric Approach to Visualization of Variabili…
We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Mobile health studies often collect multiple within-day self-reported assessments of participants' behavior and well-being on different scales such as physical activity (continuous), pain levels (truncated), mood states (ordinal), and life…
Astronomical researchers often think of analysis and visualization as separate tasks. In the case of high-dimensional data sets, though, interactive exploratory data visualization can give far more insight than an approach where data…
This work proposes and study the concept of Functional Data Analysis transform, applying it to the performance improving of volumetric Bouligand-Minkowski fractal descriptors. The proposed transform consists essentially in changing the…
We propose a framework to analyze how multivariate representations disentangle ground-truth generative factors. A quantitative analysis of disentanglement has been based on metrics designed to compare how one variable explains each…
Change-plane analysis is a pivotal tool for identifying subgroups within a heterogeneous population, yet it presents challenges when applied to functional data. In this paper, we consider a change-plane model within the framework of…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
This paper presents an approach to analyzing two-dimensional temporal datasets focusing on identifying observations that are significant in calculating the outliers of a scatterplot. We also propose a prototype, called Outliagnostics, to…
Due to large variations in shape, appearance, and viewing conditions, object recognition is a key precursory challenge in the fields of object manipulation and robotic/AI visual reasoning in general. Recognizing object categories,…
Dimensionality reduction is used as an important tool for unraveling the complexities of high-dimensional datasets in many fields of science, such as cell biology, chemical informatics, and physics. Visualizations of the dimensionally…
Manifold-valued functional data analysis (FDA) recently becomes an active area of research motivated by the raising availability of trajectories or longitudinal data observed on non-linear manifolds. The challenges of analyzing such data…
The detection of outliers is of critical importance in the assurance of data quality. Outliers may exist in observed data or in data derived from these observed data, such as estimates and forecasts. An outlier may indicate a problem with…
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a…
Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data…
A range of charts with different strengths and weaknesses exists to support the visual analysis of univariate distributions, with a limited understanding of which charts best support which tasks and users, and how practitioners use charts.…
Considering the context of functional data analysis, we developed and applied a new Bayesian approach via Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…