Related papers: Tangent functional canonical correlation analysis …
Continuous variables systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as…
We present an approach to the coupling of mixed-dimensional continua by employing the mathematically enriched linear Cosserat micropolar model. The kinematical reduction of the model to lower dimensional domains leaves its fundamental…
A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised…
Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the differing associations between those predictors and responses. Here we…
We develop a new method to locally cluster curves and discover functional motifs, i.e.~typical ``shapes'' that may recur several times along and across the curves capturing important local characteristics. In order to identify these shared…
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
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…
Deep learning models in medical imaging are susceptible to shortcut learning, relying on confounding metadata (e.g., scanner model) that is often encoded in image embeddings. The crucial question is whether the model actively utilizes this…
Canonical Correlation Analysis (CCA) is a widespread technique for discovering linear relationships between two sets of variables $X \in \mathbb{R}^{n \times p}$ and $Y \in \mathbb{R}^{n \times q}$. In high dimensions however, standard…
Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited…
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
The infinite set of coupled integral nonlinear equations for correlation functions in the case of classical canonical ensemble is considered. Some kind of graph expansions of correlation functions in the density parameter are constructed.…
Canonical Correlation Analysis (CCA) is a classical tool for finding correlations among the components of two random vectors. In recent years, CCA has been widely applied to the analysis of genomic data, where it is common for researchers…
This paper provides robust estimators for the first canonical correlation and directions of random elements on Hilbert separable spaces by using robust association and scale measures combined with basis expansion and/or penalizations as a…
We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations…
Canonical correlation analysis (CCA) is a classical and important multivariate technique for exploring the relationship between two sets of continuous variables. CCA has applications in many fields, such as genomics and neuroimaging. It can…
We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis…
Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…