Related papers: Tangent functional canonical correlation analysis …
Imaging genetics is a growing field that employs structural or functional neuroimaging techniques to study individuals with genetic risk variants potentially linked to specific illnesses. This area presents considerable challenges to…
Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or…
We propose an estimation approach to analyse correlated functional data which are observed on unequal grids or even sparsely. The model we use is a functional linear mixed model, a functional analogue of the linear mixed model. Estimation…
This paper studies high-dimensional canonical correlation analysis (CCA) with an emphasis on the vectors that define canonical variables. The paper shows that when two dimensions of data grow to infinity jointly and proportionally, the…
Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at…
In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…
Canonical Correlation Analysis (CCA) is a method for feature extraction of two views by finding maximally correlated linear projections of them. Several variants of CCA have been introduced in the literature, in particular, variants based…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
All neuroimaging modalities have their own strengths and limitations. A current trend is toward interdisciplinary approaches that use multiple imaging methods to overcome limitations of each method in isolation. At the same time…
We introduce a statistical method for modeling and forecasting functional panel data represented by multiple densities. Density functions are nonnegative and have a constrained integral and thus do not constitute a linear vector space. We…
We introduce continuous indexed points for improved multivariate volume visualization. Indexed points represent linear structures in parallel coordinates and can be used to encode local correlation of multivariate (including multifield,…
Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…
Canonical correlation analysis (CCA) is a standard tool for studying associations between two data sources; however, it is not designed for data with count or proportion measurement types. In addition, while CCA uncovers common signals, it…
Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a…
This work is motivated by multimodality breast cancer imaging data, which is quite challenging in that the signals of discrete tumor-associated microvesicles (TMVs) are randomly distributed with heterogeneous patterns. This imposes a…
A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are…
Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood…
We develop an extension of the Monte Carlo wave function approach that unambiguously identifies dynamical entanglement in general composite, open systems. Our algorithm performs tangential projections onto the set of separable states,…