Related papers: Functional Data Analysis of Amplitude and Phase Va…
Functional variables are often used as predictors in regression problems. A commonly-used parametric approach, called {\it scalar-on-function regression}, uses the $\ltwo$ inner product to map functional predictors into scalar responses.…
Correlation functions in one-dimensional complex scalar field theory provide a toy model for phase fluctuations, sign problems, and signal-to-noise problems in lattice field theory. Phase unwrapping techniques from signal processing are…
Multivariate functional data are becoming ubiquitous with advances in modern technology and are substantially more complex than univariate functional data. We propose and study a novel model for multivariate functional data where the…
The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…
Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation…
Motivation: Alignment-free (AF) distance/similarity functions are a key tool for sequence analysis. Experimental studies on real datasets abound and, to some extent, there are also studies regarding their control of false positive rate…
In the framework of Symbolic Data Analysis (SDA), distribution-variables are a particular case of multi-valued variables: each unit is represented by a set of distributions (e.g. histograms, density functions or quantile functions), one for…
In one-dimensional case the search for presence of the anomalous phenomena in multiplicity distributions is usually performed in frame of the horizontal, vertical and mixed types of the analysis. We show that if the data involve a…
Phase aberration is one of the primary sources of image quality degradation in ultrasound, which is induced by spatial variations in sound speed across the heterogeneous medium. This effect disrupts transmitted waves and prevents coherent…
Assessment of voice signals has long been performed with the assumption of periodicity as this facilitates analysis. Near periodicity of normal voice signals makes short-time harmonic modeling an appealing choice to extract vocal feature…
Happ and Greven (2018) developed a methodology for principal components analysis of multivariate functional data observed on different dimensional domains. Their approach relies on an estimation of univariate functional principal components…
In the era of big data, an ever-growing volume of information is recorded, either continuously over time or sporadically, at distinct time intervals. Functional Data Analysis (FDA) stands at the cutting edge of this data revolution,…
The advent of big data has raised significant challenges in analysing high-dimensional datasets across various domains such as medicine, ecology, and economics. Functional Data Analysis (FDA) has proven to be a robust framework for…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
A common issue in exploiting simulated ultrasound data for training neural networks is the domain shift problem, where the trained models on synthetic data are not generalizable to clinical data. Recently, Fourier Domain Adaptation (FDA)…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
In many modern applications, discretely-observed data may be naturally understood as a set of functions. Functional data often exhibit two confounded sources of variability: amplitude (y-axis) and phase (x-axis). The extraction of amplitude…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
Consider a set of multiple, multimodal sensors capturing a complex system or a physical phenomenon of interest. Our primary goal is to distinguish the underlying sources of variability manifested in the measured data. The first step in our…
Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering…