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The idea that complex systems have a hierarchical modular organization originates in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical…
The number of linear regions is one of the distinct properties of the neural networks using piecewise linear activation functions such as ReLU, comparing with those conventional ones using other activation functions. Previous studies showed…
We present a new layout algorithm for complex networks that combines a multi-scale approach for community detection with a standard force-directed design. Since community detection is computationally cheap, we can exploit the multi-scale…
Deep Brain Stimulation (DBS) has gained increasing attention as an effective method to mitigate Parkinsons disease (PD) disorders. Existing DBS systems are open-loop such that the system parameters are not adjusted automatically based on…
Local community detection, the problem of identifying a set of relevant nodes nearby a small set of input seed nodes, is an important graph primitive with a wealth of applications and research activity. Recent approaches include using local…
A multiplex network models different modes of interaction among same-type entities. In this article we provide a taxonomy of community detection algorithms in multiplex networks. We characterize the different algorithms based on various…
Community structure is a typical property of many real-world networks, and has become a key to understand the dynamics of the networked systems. In these networks most nodes apparently lie in a community while there often exists a few nodes…
How neural networks in the human brain represent commonsense knowledge, and complete related reasoning tasks is an important research topic in neuroscience, cognitive science, psychology, and artificial intelligence. Although the…
Artificial Neural Networks, the building blocks of AI, were inspired by the human brain's network of neurons. Over the years, these networks have evolved to replicate the complex capabilities of the brain, allowing them to handle tasks such…
Beyond the traditional neural network training methods based on gradient descent and its variants, state estimation techniques have been proposed to determine a set of ideal weights from a control-theoretic perspective. Hence, the concept…
We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However,…
Inspired by biology's most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles. Remarkably, analogous high-dimensional, highly-interconnected computational architectures also…
In this study, we propose a neural network approach to capture the functional connectivities among anatomic brain regions. The suggested approach estimates a set of brain networks, each of which represents the connectivity patterns of a…
It is common in the study of networks to investigate meso-scale features to try to gain an understanding of network structure and function. For example, numerous algorithms have been developed to try to identify "communities," which are…
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…
Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social…
Texture is a visual attribute largely used in many problems of image analysis. Currently, many methods that use learning techniques have been proposed for texture discrimination, achieving improved performance over previous handcrafted…
Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated features. A…
Communities are subsets of a network that are densely connected inside and share only few connections to the rest of the network. The aim of this research is the development and evaluation of an efficient algorithm for detection of…
In this paper, we propose a method that extends the persistence-based topological data analysis (TDA) that is typically used for characterizing shapes to general networks. We introduce the concept of the community tree, a tree structure…