Related papers: Tensor Methods in High Dimensional Data Analysis: …
Imaging sites around the world generate growing amounts of medical scan data with ever more versatile and affordable technology. Large-scale studies acquire MRI for tens of thousands of participants, together with metadata ranging from…
In recent years, promising statistical modeling approaches to tensor data analysis have been rapidly developed. Traditional multivariate analysis tools, such as multivariate regression and discriminant analysis, are generalized from…
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…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
Music is an art, perceived in unique ways by every listener, coming from acoustic signals. In the meantime, standards as musical scores exist to describe it. Even if humans can make this transcription, it is costly in terms of time and…
As information becomes increasingly sizable for organizations to maintain the challenge of organizing data still remains. More importantly, the on-going process of analysing incoming data occurs on a continual basis and organizations should…
Multilayer networks have been widely used to represent and analyze systems of interconnected entities where both the entities and their connections can be of different types. However, real multilayer networks can be difficult to analyze…
We develop algebraic methods for computations with tensor data. We give 3 applications: extracting features that are invariant under the orthogonal symmetries in each of the modes, approximation of the tensor spectral norm, and…
Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of…
In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…
Time-series anomaly detection plays an important role in engineering processes, like development, manufacturing and other operations involving dynamic systems. These processes can greatly benefit from advances in the field, as…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this…
Tabular data, structured as rows and columns, is among the most prevalent data types in machine learning classification and regression applications. Models for learning from tabular data have continuously evolved, with Deep Neural Networks…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
This thesis presents a new methodology to analyze one-dimensional signals trough a new approach called Multi Layer Analysis, for short MLA. It also provides some new insights on the relationship between one-dimensional signals processed by…
Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication…
The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…