Related papers: A tutorial on the dynamic Laplacian
We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to…
In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
Deep neural networks are a family of computational models that have led to a dramatical improvement of the state of the art in several domains such as image, voice or text analysis. These methods provide a framework to model complex,…
Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…
Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space.…
A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged…
We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial…
Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…
We propose a multi-dimensional persistent sheaf Laplacian (MPSL) framework on simplicial complexes for image analysis. The proposed method is motivated by the strong sensitivity of commonly used dimensionality reduction techniques, such as…
Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…
The work done in this paper, proposes a complex Laplacian-based distributed control scheme for convergence in the multi-agent network. The proposed scheme has been designated as cascade formulation. The proposed technique exploits the…
The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This…
In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time…
Eigenvectors and eigenvalues of discrete graph Laplacians are often used for manifold learning and nonlinear dimensionality reduction. It was previously proved by Belkin and Niyogi that the eigenvectors and eigenvalues of the graph…
This article proposes a novel methodology to learn a stable robot control law driven by dynamical systems. The methodology requires a single demonstration and can deduce a stable dynamics in arbitrary high dimensions. The method relies on…
Unsupervised multi-view clustering (MVC) aims to partition data into meaningful groups by leveraging complementary information from multiple views without labels, yet a central challenge is to obtain a reliable shared structural signal to…
Clustering aims to group unlabeled objects based on similarity inherent among them into clusters. It is important for many tasks such as anomaly detection, database sharding, record linkage, and others. Some clustering methods are taken as…
The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…
This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of…