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Hierarchical clustering over graphs is a fundamental task in data mining and machine learning with applications in domains such as phylogenetics, social network analysis, and information retrieval. Specifically, we consider the recently…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
High-dimensional datasets are increasingly common across scientific and industrial domains, yet they remain difficult to cluster effectively due to the diminishing usefulness of distance metrics and the tendency of clusters to collapse or…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
The purpose of data warehouses is to enable business analysts to make better decisions. Over the years the technology has matured and data warehouses have become extremely successful. As a consequence, more and more data has been added to…
A data matrix may be seen simply as a means of organizing observations into rows ( e.g., by measured object) and into columns ( e.g., by measured variable) so that the observations can be analyzed with mathematical tools. As a mathematical…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
Cubic blocks are studied assembled from linear operators $\mathcal R$ acting in the tensor product of $d$ linear "spin" spaces. Such operator is associated with a linear transformation $A$ in a vector space over a field $F$ of a finite…
Deep clustering (DC), a fusion of deep representation learning and clustering, has recently demonstrated positive results in data science, particularly text processing and computer vision. However, joint optimization of feature learning and…
We introduce a new framework for distributed computing that extends and refines the standard master-worker approach of scheduling multi-threaded computations. In this framework, there are different roles: a supervisor, a source, a target,…
Big data refers to large and complex data sets that, under existing approaches, exceed the capacity and capability of current compute platforms, systems software, analytical tools and human understanding. Numerous lessons on the scalability…
A data model specifies how real-world entities and their relationships are represented and operated. In the NoSQL world data modeling usually begins from identifying application queries and designing the data model to efficiently answer…
Data fusion, the process of combining observational and experimental data, can enable the identification of causal effects that would otherwise remain non-identifiable. Although identification algorithms have been developed for specific…
Hyperdimensional (HD) computing is built upon its unique data type referred to as hypervectors. The dimension of these hypervectors is typically in the range of tens of thousands. Proposed to solve cognitive tasks, HD computing aims at…
A d-contraction is a d-tuple $(T_1,...,T_d)$ of mutually commuting operators acting on a common Hilbert space H such that $ \|T_1\xi_1+T_2\xi_2+... +T_d\xi_d\|^2\leq \|\xi_1\|^2+\|\xi_2\|^2+...+\|\xi_d\|^2 $ for all…
Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces, with each subspace defining a cluster with dimension lower than the ambient space. Many existing…
Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style…
We present a framework for creating small, informative sub-tables of large data tables to facilitate the first step of data science: data exploration. Given a large data table table T, the goal is to create a sub-table of small, fixed…
This tutorial overviews the state of the art in learning models over relational databases and makes the case for a first-principles approach that exploits recent developments in database research. The input to learning classification and…
Cluster analysis plays an indispensable role in machine learning and data mining. Learning a good data representation is crucial for clustering algorithms. Recently, deep clustering, which can learn clustering-friendly representations using…