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In this paper, a Lie group-based neural network method is proposed for solving initial value problems of non linear dynamics. Due to its single-layer structure (MLP), the approach is substantially cheaper than the multilayer perceptron…
Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship…
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…
There is currently an unprecedented demand for large-scale temporal data analysis due to the explosive growth of data. Dynamic topic modeling has been widely used in social and data sciences with the goal of learning latent topics that…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better…
Seasonal time series exhibit intricate long-term dependencies, posing a significant challenge for accurate future prediction. This paper introduces the Multi-scale Seasonal Decomposition Model (MSSD) for seasonal time-series forecasting.…
This study introduces the Lower Ricci Curvature (LRC), a novel, scalable, and scale-free discrete curvature designed to enhance community detection in networks. Addressing the computational challenges posed by existing curvature-based…
Social communities extraction and their dynamics are one of the most important problems in today's social network analysis. During last few years, many researchers have proposed their own methods for group discovery in social networks.…
Network representations have been effectively employed to analyze complex systems across various areas and applications, leading to the development of network science as a core tool to study systems with multiple components and complex…
Dynamic multilayer networks are frequently used to describe the structure and temporal evolution of multiple relationships among common entities, with applications in fields such as sociology, economics, and neuroscience. However,…
Community detection for large networks poses challenges due to the high computational cost as well as heterogeneous community structures. In this paper, we consider widely existing real-world networks with ``grouped communities'' (or ``the…
Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…
A distinctive representation of image patches in form of features is a key component of many computer vision and robotics tasks, such as image matching, image retrieval, and visual localization. State-of-the-art descriptors, from…
Detecting communities in networks is essential for understanding the mesoscopic organization of complex systems. Interactions in most real-world networks evolve over time and exhibit diverse modalities: instantaneous events, continuous…
Membership diversity is a characteristic aspect of social networks in which a person may belong to more than one social group. For this reason, discovering overlapping structures is necessary for realistic social analysis. In this paper, we…
Dynamic community detection has been prospered as a powerful tool for quantifying changes in dynamic brain network connectivity patterns by identifying strongly connected sets of nodes. However, as the network science problems and network…
We present a principled approach for detecting overlapping temporal community structure in dynamic networks. Our method is based on the following framework: find the overlapping temporal community structure that maximizes a quality function…
Community detection is one of the fundamental problems in the study of network data. Most existing community detection approaches only consider edge information as inputs, and the output could be suboptimal when nodal information is…
This article considers the problem of community detection in sparse dynamical graphs in which the community structure evolves over time. A fast spectral algorithm based on an extension of the Bethe-Hessian matrix is proposed, which benefits…