Related papers: A Relational Matrix Algebra and its Implementation…
We set up an algebraic theory of multivariable integration, based on a hierarchy of Rota-Baxter operators and an action of the matrix monoid as linear substitutions. Given a suitable coefficient domain with a bialgebra structure, this…
Neural networks excel in detecting regular patterns but are less successful in representing and manipulating complex data structures, possibly due to the lack of an external memory. This has led to the recent development of a new line of…
Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…
Relational databases excel at structured data analysis, but real-world queries increasingly require capabilities beyond standard SQL, such as semantically matching entities across inconsistent names, extracting information not explicitly…
Graph database query languages cannot express algorithms like PageRank, forcing costly data wrangling, while existing solutions such as algorithm libraries, vertex-centric APIs, and recursive CTEs lack the necessary combination of…
Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data…
On the set of mappings of the given set, we define the product of mappings. If A is associative algebra, then we consider the set of matrices, whose elements are linear mappings of algebra A. In algebra of matrices of linear mappings we…
Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process…
Considering relational databases having powerful capabilities in handling security, user authentication, query optimization, etc., several commercial and academic frameworks reuse relational databases to store and query semi-structured data…
We present a system called Dist-$\mu$-RA for the distributed evaluation of recursive graph queries. Dist-$\mu$-RA builds on the recursive relational algebra and extends it with evaluation plans suited for the distributed setting. The goal…
In natural language, often multiple entities appear in the same text. However, most previous works in Relation Extraction (RE) limit the scope to identifying the relation between two entities at a time. Such an approach induces a quadratic…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
Graph analytics is becoming increasingly popular, with a deluge of new systems for graph analytics having been proposed in the past few years. These systems often start from the assumption that a new storage or query processing system is…
The natural join and the inner union combine in different ways tables of a relational database. Tropashko [18] observed that these two operations are the meet and join in a class of lattices-called the relational lattices- and proposed…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
In order to efficiently learn with small amount of data on new tasks, meta-learning transfers knowledge learned from previous tasks to the new ones. However, a critical challenge in meta-learning is the task heterogeneity which cannot be…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated…
Over the past few years, table interpretation tasks have made significant progress due to their importance and the introduction of new technologies and benchmarks in the field. This work experiments with a hybrid approach for detecting…