Related papers: A tutorial on the dynamic Laplacian
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
The spectral structure of the Laplacian-Beltrami operator (LBO) on manifolds has been widely used in many applications, include spectral clustering, dimensionality reduction, mesh smoothing, compression and editing, shape segmentation,…
Spectral clustering is a powerful technique for clustering high-dimensional data, utilizing graph-based representations to detect complex, non-linear structures and non-convex clusters. The construction of a similarity graph is essential…
Multi-view data clustering attracts more attention than their single view counterparts due to the fact that leveraging multiple independent and complementary information from multi-view feature spaces outperforms the single one. Multi-view…
In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that…
We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the…
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a…
We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived…
Manifold Learning is a class of algorithms seeking a low-dimensional non-linear representation of high-dimensional data. Thus manifold learning algorithms are, at least in theory, most applicable to high-dimensional data and sample sizes to…
Spectral Clustering (SC) is widely used for clustering data on a nonlinear manifold. SC aims to cluster data by considering the preservation of the local neighborhood structure on the manifold data. This paper extends Spectral Clustering to…
To cluster data is to separate samples into distinctive groups that should ideally have some cohesive properties. Today, numerous clustering algorithms exist, and their differences lie essentially in what can be perceived as ``cohesive…
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…
Many real-analytic flows, e.g. in chemical kinetics, share a multiple time scale spectral structure. The trajectories of the corresponding dynamical systems are observed to bundle near so-called slow invariant manifolds (SIMs), which are…
Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…
The stability of topological persistence is one of the fundamental issues in topological data analysis. Numerous methods have been proposed to address the stability of persistent modules or persistence diagrams. Recently, the concept of…
One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gomez et al. [Phys. Rev. Lett. 101, 028701…
The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The…
TimeCluster is a visual analytics technique for discovering structure in long multivariate time series by projecting overlapping windows of data into a low-dimensional space. We show that, when Principal Component Analysis (PCA) is chosen…
Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs…
It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or…