Related papers: Hypergraph $p$-Laplacian equations for data interp…

Recent semi-supervised learning methods have shown to achieve comparable results to their supervised counterparts while using only a small portion of labels in image classification tasks thanks to their regularization strategies. In this…

Transformers update token representations through multi-head attention and residual connections as $X \leftarrow X + \sum_{i} P^{(i)}XW_{V_i}W_{o_i}$, where $P^{(i)}$ is the softmax attention matrix in head $i$. We propose replacing a…

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

We present a novel cost function for semi-supervised learning of neural networks that encourages compact clustering of the latent space to facilitate separation. The key idea is to dynamically create a graph over embeddings of labeled and…

Tensor-oriented multi-view subspace clustering has achieved significant strides in assessing high-order correlations and improving clustering analysis of multi-view data. Nevertheless, most of existing investigations are typically hampered…

In this work, we improve the accuracy of several known algorithms to address the classification of large datasets when few labels are available. Our framework lies in the realm of graph-based semi-supervised learning. With novel…

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…

This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference…

Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…

This paper is concerned with the numerical solution of a class of variational inequalities of the second kind, involving the $p$-Laplacian operator. This kind of problems arise, for instance, in the mathematical modelling of non-Newtonian…

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such…

In this paper, we consider an optimal control problem of an ordinary differential inclusion governed by the hypergraph Laplacian, which is defined as a subdifferential of a convex function and then is a set-valued operator. We can assure…

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…

Based on the computation of a superset of the implicit support, implicitization of a parametrically given hyper-surface is reduced to computing the nullspace of a numeric matrix. Our approach exploits the sparseness of the given parametric…

Recently, a number of variants of the notion of cut-preserving hypergraph sparsification have been studied in the literature. These variants include directed hypergraph sparsification, submodular hypergraph sparsification, general notions…

Semi-supervised learning, i.e. jointly learning from labeled and unlabeled samples, is an active research topic due to its key role on relaxing human supervision. In the context of image classification, recent advances to learn from…

Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is…

Video representation learning is a vital problem for classification task. Recently, a promising unsupervised paradigm termed self-supervised learning has emerged, which explores inherent supervisory signals implied in massive data for…

Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to…

Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works…