Related papers: Laplacian Matrix for Dimensionality Reduction and …

Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…

Real-world events exhibit a high degree of interdependence and connections, and hence data points generated also inherit the linkages. However, the majority of AI/ML techniques leave out the linkages among data points. The recent surge of…

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be…

We propose unsupervised representation learning and feature extraction from dendrograms. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level…

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.…

In real-world applications, perfect labels are rarely available, making it challenging to develop robust machine learning algorithms that can handle noisy labels. Recent methods have focused on filtering noise based on the discrepancy…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…

In this paper, we focus on learning product graphs from multi-domain data. We assume that the product graph is formed by the Cartesian product of two smaller graphs, which we refer to as graph factors. We pose the product graph learning…

In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…

We consider the problem of learning from a similarity matrix (such as spectral clustering and lowd imensional embedding), when computing pairwise similarities are costly, and only a limited number of entries can be observed. We provide a…

We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…

Graph neural networks have been widely used for learning representations of nodes for many downstream tasks on graph data. Existing models were designed for the nodes on a single graph, which would not be able to utilize information across…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…

NodeTrix representations are a popular way to visualize clustered graphs; they represent clusters as adjacency matrices and inter-cluster edges as curves connecting the matrix boundaries. We study the complexity of constructing NodeTrix…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

In this paper, the problem of decentralized eigenvalue decomposition of a general symmetric matrix that is important, e.g., in Principal Component Analysis, is studied, and a decentralized online learning algorithm is proposed. Instead of…

Graph model is emerging as a very effective tool for learning the complex structures and relationships hidden in data. Generally, the critical purpose of graph-oriented learning algorithms is to construct an informative graph for image…

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…

Deep Learning (DL) has attracted a lot of attention for its ability to reach state-of-the-art performance in many machine learning tasks. The core principle of DL methods consists in training composite architectures in an end-to-end…