Related papers: Extending compositional data analysis from a graph…
In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity. We show that the method…
Archetypal analysis represents each individual member of a set of data vectors as a mixture (a constrained linear combination) of the pure types or archetypes of the data set. The archetypes are themselves required to be mixtures of the…
Classical approaches like process algebras or labelled transition systems deal with static composition to model non-trivial concurrent or distributed systems; this is not sufficient for systems with dynamic architecture and with variable…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
The paper revisits the $\alpha$--regression framework for compositional data. The model uses a flexible power transformation parameterized by $\alpha$ to interpolate between raw data analysis and log--ratio methods, naturally handling zeros…
Compositional generalization -- the ability to understand and generate novel combinations of learned concepts -- enables models to extend their capabilities beyond limited experiences. While effective, the data structures and principles…
We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
Understanding the structural and cognitive underpinnings of musical compositions remains a key challenge in music theory and computational musicology. While traditional methods focus on harmony and rhythm, cognitive models such as the…
Widespread use of the Internet and social networks invokes the generation of big data, which is proving to be useful in a number of applications. To deal with explosively growing amounts of data, data analytics has emerged as a critical…
Theoretical development and applications of graph signal processing (GSP) have attracted much attention. In classical GSP, the underlying structures are restricted in terms of dimensionality. A graph is a combinatorial object that models…
Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…
With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent…
Many modern datasets are large and carry complex structural relationships. Graph-based methods have traditionally been used to represent networked data, modeling individual elements as nodes and pairwise interactions as edges. Furthermore,…
Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical…
The restricted polynomially-tilted pairwise interaction (RPPI) distribution gives a flexible model for compositional data. It is particularly well-suited to situations where some of the marginal distributions of the components of a…
Since many physical laws -- from classical mechanics to electromagnetism -- are formulated as two-body interactions, the same perspective naturally extends to biological and social dynamics. Here we focus on rhythmic phenomena, where phase…
Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…
The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…