Related papers: Embedding Functional Data: Multidimensional Scalin…
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…
Autoencoders, which consist of an encoder and a decoder, are widely used in machine learning for dimension reduction of high-dimensional data. The encoder embeds the input data manifold into a lower-dimensional latent space, while the…
Classification using variational quantum circuits is a promising frontier in quantum machine learning. Quantum supervised learning (QSL) applied to classical data using variational quantum circuits involves embedding the data into a quantum…
Embedding of large but redundant data, such as images or text, in a hierarchy of lower-dimensional spaces is one of the key features of representation learning approaches, which nowadays provide state-of-the-art solutions to problems once…
Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret…
The assignment flow is a smooth dynamical system that evolves on an elementary statistical manifold and performs contextual data labeling on a graph. We derive and introduce the linear assignment flow that evolves nonlinearly on the…
Modeling data using manifold values is a powerful concept with numerous advantages, particularly in addressing nonlinear phenomena. This approach captures the intrinsic geometric structure of the data, leading to more accurate descriptors…
Standard multidimensional scaling takes as input a dissimilarity matrix of general term $\delta _{ij}$ which is a numerical value. In this paper we input $\delta _{ij}=[\underline{\delta _{ij}},\overline{\delta _{ij}}]$ where…
Functional data analysis is a growing research field as more and more practical applications involve functional data. In this paper, we focus on the problem of regression and classification with functional predictors: the model suggested…
The rapid advancement of autonomous systems, including self-driving vehicles and drones, has intensified the need to forge true Spatial Intelligence from multi-modal onboard sensor data. While foundation models excel in single-modal…
Text embeddings have become central to computational social science and psychology, enabling scalable measurement of meaning and mixed-method inference. Yet most representation learning is optimized and evaluated for prediction and…
Self Organizing Map (SOM) has been applied into several classical modeling tasks including clustering, classification, function approximation and visualization of high dimensional spaces. The final products of a trained SOM are a set of…
The joint alignment of multivariate functional data plays an important role in various fields such as signal processing, neuroscience and medicine, including the statistical analysis of data from wearable devices. Traditional methods often…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
As a measure for the centrality of a point in a set of multivariate data, statistical depth functions play important roles in multivariate analysis, because one may conveniently construct descriptive as well as inferential procedures…
Score matching is a vital tool for learning the distribution of data with applications across many areas including diffusion processes, energy based modelling, and graphical model estimation. Despite all these applications, little work…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
The classical Mat\'ern model has been a staple in spatial statistics. Novel data-rich applications in environmental and physical sciences, however, call for new, flexible vector-valued spatial and space-time models. Therefore, the extension…
Multimodal deep learning has been used to predict clinical endpoints and diagnoses from clinical routine data. However, these models suffer from scaling issues: they have to learn pairwise interactions between each piece of information in…
Decoding brain states from functional magnetic resonance imaging (fMRI) data is vital for advancing neuroscience and clinical applications. While traditional machine learning and deep learning approaches have made strides in leveraging the…