Related papers: A Cube Algebra with Comparative Operations: Contai…
Decisional systems are based on multidimensional databases improving OLAP analyses. The paper describes a new OLAP operator named "BLEND" to perform multigradual analyses. The operation transforms multidimensional structures during querying…
In OLAP, analysts often select an interesting sample of the data. For example, an analyst might focus on products bringing revenues of at least 100 000 dollars, or on shops having sales greater than 400 000 dollars. However, current systems…
We introduce two notions of coarse embeddability between operator spaces: almost complete coarse embeddability of bounded subsets and spherically-complete coarse embeddability. We provide examples showing that these notions are strictly…
Data Warehouses are structures with large amount of data collected from heterogeneous sources to be used in a decision support system. Data Warehouses analysis identifies hidden patterns initially unexpected which analysis requires great…
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
Many data insight questions can be viewed as searching in a large space of tables and finding important ones, where the notion of importance is defined in some adhoc user defined manner. This paper presents Holistic Cube Analysis (HoCA), a…
This document is part of original research work by the authors in a bid to explore new fields for applying Data Mining Techniques. The sample data is part of a large data set from University of Maryland (UMD) and outlines how more…
Covering model provides a general framework for granular computing in that overlapping among granules are almost indispensable. For any given covering, both intersection and union of covering blocks containing an element are exploited as…
In this work we discuss the elements required for the construction of the operator algebra for the space of paths over a simply laced $SU(3)$ graph. These operators are an important step in the construction of the bialgebra required to find…
Recent strides in multimodal model development have ignited a paradigm shift in the realm of text-to-image generation. Among these advancements, CLIP stands out as a remarkable achievement which is a sophisticated autoencoder adept at…
Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional data warehouse is incomplete. Multidimensional give the able to analyze business measurement in many…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
Basic experimental findings about human working memory can be described by an algebra built on high-dimensional binary states, representing information items, and two operations: multiplication for binding and addition for bundling. In…
Retrieval-Augmented Generation (RAG) systems are increasingly deployed on large-scale document collections, often comprising millions of documents and tens of millions of text chunks. In industrial-scale retrieval platforms, scalability is…
The \emph{Order-Maintenance} (OM) data structure maintains a total order list of items for insertions, deletions, and comparisons. As a basic data structure, OM has many applications, such as maintaining the topological order, core numbers,…
We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear…
In spite of its fundamental importance, inference has not been an inherent function of multidimensional models and analytical applications. These models are mainly aimed at numeric (quantitative) analysis where the notions of inference and…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…