Related papers: Higher order co-occurrence tensors for hypergraphs…

Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing…

Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining…

In this paper, we tackle the challenge of predicting stock movements in financial markets by introducing Higher Order Transformers, a novel architecture designed for processing multivariate time-series data. We extend the self-attention…

We define a ternary product and more generally a (2k+1)-ary product on the vector space T^p_q(E) of tensors of type (p, q) that is contravariant of order p, covariant of order q and total order (p+q). This product is totally associative up…

In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may…

Multi-label Recognition (MLR) involves the identification of multiple objects within an image. To address the additional complexity of this problem, recent works have leveraged information from vision-language models (VLMs) trained on large…

Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected…

Spectral hypergraph theory mainly concerns using hypergraph spectra to obtain structural information about the given hypergraphs. The study of cospectral hypergraphs is important since it reveals which hypergraph properties cannot be…

In this paper, we propose a new model that is capable of recognizing overlapping mentions. We introduce a novel notion of mention separators that can be effectively used to capture how mentions overlap with one another. On top of a novel…

While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…

To achieve greater accuracy, hypergraph matching algorithms require exponential increases in computational resources. Recent kd-tree-based approximate nearest neighbor (ANN) methods, despite the sparsity of their compatibility tensor, still…

An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion of different matrix expressions is revealed. The various contracted products of…

Let T be a general complex tensor of format $(n_1,...,n_d)$. When the fraction $\prod_in_i/[1+\sum_i(n_i-1)]$ is an integer, and a natural inequality (called balancedness) is satisfied, it is expected that T has finitely many minimal…

A long-standing challenge in coreference resolution has been the incorporation of entity-level information - features defined over clusters of mentions instead of mention pairs. We present a neural network based coreference system that…

Tensor Kronecker products, the natural generalization of the matrix Kronecker product, are independently emerging in multiple research communities. Like their matrix counterpart, the tensor generalization gives structure for implicit…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction…

A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…

The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…

Neural networks are widely adopted, yet the integration of domain knowledge is still underutilized. We propose to integrate domain knowledge about co-occurring facial movements as a constraint in the loss function to enhance the training of…