Related papers: Wavelet analysis on symbolic sequences and two-fol…
We investigate the semiclassical mechanism of tunneling process in non-integrable systems. The significant role of complex-phase-space chaos in the description of the tunneling process is elucidated by studying a simple scattering map…
Modelling musical structure is vital yet challenging for artificial intelligence systems that generate symbolic music compositions. This literature review dissects the evolution of techniques for incorporating coherent structure, from…
Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is…
We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics. By lifting neural parameters to a measure space and modeling training as Wasserstein…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly…
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…
Symbolic Data Analysis is based on special descriptions of data - symbolic objects (SO). Such descriptions preserve more detailed information about units and their clusters than the usual representations with mean values. A special kind of…
Symbolic models or abstractions are known to be powerful tools for the control design of cyber-physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach to the construction of symbolic…
We present Clusterplot, a multi-class high-dimensional data visualization tool designed to visualize cluster-level information offering an intuitive understanding of the cluster inter-relations. Our unique plots leverage 2D blobs devised to…
A de Bruijn sequence of order n over a k-symbol alphabet is a circular sequence where each length-n sequence occurs exactly once. We present a way of extending de Bruijn sequences by adding a new symbol to the alphabet: the extension is…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Unsupervised learning has gained prominence in the big data era, offering a means to extract valuable insights from unlabeled datasets. Deep clustering has emerged as an important unsupervised category, aiming to exploit the non-linear…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
In this chapter we take a closer look at the distribution of symbolic regression models generated by genetic programming in the search space. The motivation for this work is to improve the search for well-fitting symbolic regression models…
We investigate statistical properties of Cluster-Weighted Modeling, which is a framework for supervised learning originally developed in order to recreate a digital violin with traditional inputs and realistic sound. The analysis is carried…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
Mode-based clustering methods define clusters to be the basins of attraction of the modes of a density estimate. The most common version is mean shift clus- tering which uses a gradient ascent algorithm to find the basins. Rodriguez and…