Related papers: Laplacian Matrix for Dimensionality Reduction and …

This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation…

Network data appears in very diverse applications, like biological, social, or sensor networks. Clustering of network nodes into categories or communities has thus become a very common task in machine learning and data mining. Network data…

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…

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…

Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…

We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…

Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering…

In this paper, we focus on graph learning from multi-view data of shared entities for spectral clustering. We can explain interactions between the entities in multi-view data using a multi-layer graph with a common vertex set, which…

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…

This paper addresses graph learning in Gaussian Graphical Models (GGMs). In this context, data matrices often come with auxiliary metadata (e.g., textual descriptions associated with each node) that is usually ignored in traditional graph…

The problem of fitting a union of subspaces to a collection of data points drawn from multiple subspaces is considered in this paper. In the traditional low rank representation model, the dictionary used to represent the data points is…

Node embedding is a central topic in graph representation learning. Computational efficiency and scalability can be challenging to any method that requires full-graph operations. We propose sampling approaches to node embedding, with or…

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…

We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm…

Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and…

Graphs possess exotic features like variable size and absence of natural ordering of the nodes that make them difficult to analyze and compare. To circumvent this problem and learn on graphs, graph feature representation is required. A good…

In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…

Probabilistic theory and differential equation are powerful tools for the interpretability and guidance of the design of machine learning models, especially for illuminating the mathematical motivation of learning latent variable from…