Related papers: Permutation Entropy for Graph Signals
Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighboring values in a time series. This makes it possible to…
When inspecting information visualizations under time critical settings, such as emergency response or monitoring the heart rate in a surgery room, the user only has a small amount of time to view the visualization "at a glance". In these…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…
Symbolic transfer entropy is a powerful non-parametric tool to detect lead-lag between time series. Because a closed expression of the distribution of Transfer Entropy is not known for finite-size samples, statistical testing is often…
Evaluating robustness under temporal distribution shift remains an open challenge. Existing metrics quantify the average decline in performance, but fail to capture how models adapt to evolving data. As a result, temporal degradation is…
The goal of animal movement analysis is to understand how organisms explore and exploit the complex and varying environment. Animals usually exhibit varied and complicated movements, from apparently deterministic behaviors to highly random…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…
Permutation patterns-based approaches, such as permutation entropy (PerEn), have been widely and successfully used to analyze data. However, these methods have two main shortcomings. First, when a series is symbolized based on permutation…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
Centrality metrics aim to identify the most relevant nodes in a network. In literature, a broad set of metrics exists, either measuring local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the…
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J.…
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…
This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph…
Many multivariate time series anomaly detection frameworks have been proposed and widely applied. However, most of these frameworks do not consider intrinsic relationships between variables in multivariate time series data, thus ignoring…
Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend…
In this work we prove sufficient conditions for the Glauber dynamics corresponding to a sequence of (non-product) measures on finite product spaces to be rapidly mixing, i.e. that the mixing time with respect to the total variation distance…