Graph BI & analytics: current state and future challenges

In an increasingly competitive market, making well-informed decisions requires the analysis of a wide range of heterogeneous, large and complex data. This paper focuses on the emerging field of graph warehousing. Graphs are widespread structures that yield a great expressive power. They are used for modeling highly complex and interconnected domains, and efficiently solving emerging big data application. This paper presents the current status and open challenges of graph BI and analytics, and motivates the need for new warehousing frameworks aware of the topological nature of graphs. We survey the topics of graph modeling, management, processing and analysis in graph warehouses. Then we conclude by discussing future research directions and positioning them within a unified architecture of a graph BI and analytics framework.Peer ReviewedPostprint (author's final draft

Assessing and Remedying Coverage for a Given Dataset

Data analysis impacts virtually every aspect of our society today. Often, this analysis is performed on an existing dataset, possibly collected through a process that the data scientists had limited control over. The existing data analyzed may not include the complete universe, but it is expected to cover the diversity of items in the universe. Lack of adequate coverage in the dataset can result in undesirable outcomes such as biased decisions and algorithmic racism, as well as creating vulnerabilities such as opening up room for adversarial attacks. In this paper, we assess the coverage of a given dataset over multiple categorical attributes. We first provide efficient techniques for traversing the combinatorial explosion of value combinations to identify any regions of attribute space not adequately covered by the data. Then, we determine the least amount of additional data that must be obtained to resolve this lack of adequate coverage. We confirm the value of our proposal through both theoretical analyses and comprehensive experiments on real data.Comment: in ICDE 201

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference

An Investigation into Three Dimensional Probabilistic Polyforms

Polyforms are created by taking squares, equilateral triangles, and regular hexagons and placing them side by side to generate larger shapes. This project addressed three-dimensional polyforms and focused on cubes. I investigated the probabilities of certain shape outcomes to discover what these probabilities could tell us about the polyforms’ characteristics and vice versa. From my findings, I was able to derive a formula for the probability of two different polyform patterns which add to a third formula found prior to my research. In addition, I found the probability that 8 cubes randomly attached together one by one would form a 2x2x2 cube. Finally, I discovered a strong correlation between the probability of a polyform and its number of exposed edges, and I noticed a possible relationship between a polyform’s probability and its graph representation

Automating the multidimensional design of data warehouses

Les experiències prèvies en l'àmbit dels magatzems de dades (o data warehouse), mostren que l'esquema multidimensional del data warehouse ha de ser fruit d'un enfocament híbrid; això és, una proposta que consideri tant els requeriments d'usuari com les fonts de dades durant el procés de disseny.Com a qualsevol altre sistema, els requeriments són necessaris per garantir que el sistema desenvolupat satisfà les necessitats de l'usuari. A més, essent aquest un procés de reenginyeria, les fonts de dades s'han de tenir en compte per: (i) garantir que el magatzem de dades resultant pot ésser poblat amb dades de l'organització, i, a més, (ii) descobrir capacitats d'anàlisis no evidents o no conegudes per l'usuari.Actualment, a la literatura s'han presentat diversos mètodes per donar suport al procés de modelatge del magatzem de dades. No obstant això, les propostes basades en un anàlisi dels requeriments assumeixen que aquestos són exhaustius, i no consideren que pot haver-hi informació rellevant amagada a les fonts de dades. Contràriament, les propostes basades en un anàlisi exhaustiu de les fonts de dades maximitzen aquest enfocament, i proposen tot el coneixement multidimensional que es pot derivar des de les fonts de dades i, conseqüentment, generen massa resultats. En aquest escenari, l'automatització del disseny del magatzem de dades és essencial per evitar que tot el pes de la tasca recaigui en el dissenyador (d'aquesta forma, no hem de confiar únicament en la seva habilitat i coneixement per aplicar el mètode de disseny elegit). A més, l'automatització de la tasca allibera al dissenyador del sempre complex i costós anàlisi de les fonts de dades (que pot arribar a ser inviable per grans fonts de dades).Avui dia, els mètodes automatitzables analitzen en detall les fonts de dades i passen per alt els requeriments. En canvi, els mètodes basats en l'anàlisi dels requeriments no consideren l'automatització del procés, ja que treballen amb requeriments expressats en llenguatges d'alt nivell que un ordenador no pot manegar. Aquesta mateixa situació es dona en els mètodes híbrids actual, que proposen un enfocament seqüencial, on l'anàlisi de les dades es complementa amb l'anàlisi dels requeriments, ja que totes dues tasques pateixen els mateixos problemes que els enfocament purs.En aquesta tesi proposem dos mètodes per donar suport a la tasca de modelatge del magatzem de dades: MDBE (Multidimensional Design Based on Examples) and AMDO (Automating the Multidimensional Design from Ontologies). Totes dues consideren els requeriments i les fonts de dades per portar a terme la tasca de modelatge i a més, van ser pensades per superar les limitacions dels enfocaments actuals.1. MDBE segueix un enfocament clàssic, en el que els requeriments d'usuari són coneguts d'avantmà. Aquest mètode es beneficia del coneixement capturat a les fonts de dades, però guia el procés des dels requeriments i, conseqüentment, és capaç de treballar sobre fonts de dades semànticament pobres. És a dir, explotant el fet que amb uns requeriments de qualitat, podem superar els inconvenients de disposar de fonts de dades que no capturen apropiadament el nostre domini de treball.2. A diferència d'MDBE, AMDO assumeix un escenari on es disposa de fonts de dades semànticament riques. Per aquest motiu, dirigeix el procés de modelatge des de les fonts de dades, i empra els requeriments per donar forma i adaptar els resultats generats a les necessitats de l'usuari. En aquest context, a diferència de l'anterior, unes fonts de dades semànticament riques esmorteeixen el fet de no tenir clars els requeriments d'usuari d'avantmà.Cal notar que els nostres mètodes estableixen un marc de treball combinat que es pot emprar per decidir, donat un escenari concret, quin enfocament és més adient. Per exemple, no es pot seguir el mateix enfocament en un escenari on els requeriments són ben coneguts d'avantmà i en un escenari on aquestos encara no estan clars (un cas recorrent d'aquesta situació és quan l'usuari no té clares les capacitats d'anàlisi del seu propi sistema). De fet, disposar d'uns bons requeriments d'avantmà esmorteeix la necessitat de disposar de fonts de dades semànticament riques, mentre que a l'inversa, si disposem de fonts de dades que capturen adequadament el nostre domini de treball, els requeriments no són necessaris d'avantmà. Per aquests motius, en aquesta tesi aportem un marc de treball combinat que cobreix tots els possibles escenaris que podem trobar durant la tasca de modelatge del magatzem de dades.Previous experiences in the data warehouse field have shown that the data warehouse multidimensional conceptual schema must be derived from a hybrid approach: i.e., by considering both the end-user requirements and the data sources, as first-class citizens. Like in any other system, requirements guarantee that the system devised meets the end-user necessities. In addition, since the data warehouse design task is a reengineering process, it must consider the underlying data sources of the organization: (i) to guarantee that the data warehouse must be populated from data available within the organization, and (ii) to allow the end-user discover unknown additional analysis capabilities.Currently, several methods for supporting the data warehouse modeling task have been provided. However, they suffer from some significant drawbacks. In short, requirement-driven approaches assume that requirements are exhaustive (and therefore, do not consider the data sources to contain alternative interesting evidences of analysis), whereas data-driven approaches (i.e., those leading the design task from a thorough analysis of the data sources) rely on discovering as much multidimensional knowledge as possible from the data sources. As a consequence, data-driven approaches generate too many results, which mislead the user. Furthermore, the design task automation is essential in this scenario, as it removes the dependency on an expert's ability to properly apply the method chosen, and the need to analyze the data sources, which is a tedious and timeconsuming task (which can be unfeasible when working with large databases). In this sense, current automatable methods follow a data-driven approach, whereas current requirement-driven approaches overlook the process automation, since they tend to work with requirements at a high level of abstraction. Indeed, this scenario is repeated regarding data-driven and requirement-driven stages within current hybrid approaches, which suffer from the same drawbacks than pure data-driven or requirement-driven approaches.In this thesis we introduce two different approaches for automating the multidimensional design of the data warehouse: MDBE (Multidimensional Design Based on Examples) and AMDO (Automating the Multidimensional Design from Ontologies). Both approaches were devised to overcome the limitations from which current approaches suffer. Importantly, our approaches consider opposite initial assumptions, but both consider the end-user requirements and the data sources as first-class citizens.1. MDBE follows a classical approach, in which the end-user requirements are well-known beforehand. This approach benefits from the knowledge captured in the data sources, but guides the design task according to requirements and consequently, it is able to work and handle semantically poorer data sources. In other words, providing high-quality end-user requirements, we can guide the process from the knowledge they contain, and overcome the fact of disposing of bad quality (from a semantical point of view) data sources.2. AMDO, as counterpart, assumes a scenario in which the data sources available are semantically richer. Thus, the approach proposed is guided by a thorough analysis of the data sources, which is properly adapted to shape the output result according to the end-user requirements. In this context, disposing of high-quality data sources, we can overcome the fact of lacking of expressive end-user requirements.Importantly, our methods establish a combined and comprehensive framework that can be used to decide, according to the inputs provided in each scenario, which is the best approach to follow. For example, we cannot follow the same approach in a scenario where the end-user requirements are clear and well-known, and in a scenario in which the end-user requirements are not evident or cannot be easily elicited (e.g., this may happen when the users are not aware of the analysis capabilities of their own sources). Interestingly, the need to dispose of requirements beforehand is smoothed by the fact of having semantically rich data sources. In lack of that, requirements gain relevance to extract the multidimensional knowledge from the sources.So that, we claim to provide two approaches whose combination turns up to be exhaustive with regard to the scenarios discussed in the literaturePostprint (published version

Interactive multidimensional modeling of linked data for exploratory OLAP

Exploratory OLAP aims at coupling the precision and detail of corporate data with the information wealth of LOD. While some techniques to create, publish, and query RDF cubes are already available, little has been said about how to contextualize these cubes with situational data in an on-demand fashion. In this paper we describe an approach, called iMOLD, that enables non-technical users to enrich an RDF cube with multidimensional knowledge by discovering aggregation hierarchies in LOD. This is done through a user-guided process that recognizes in the LOD the recurring modeling patterns that express roll-up relationships between RDF concepts, then translates these patterns into aggregation hierarchies to enrich the RDF cube. Two families of aggregation patterns are identified, based on associations and generalization respectively, and the algorithms for recognizing them are described. To evaluate iMOLD in terms of efficiency and effectiveness we compare it with a related approach in the literature, we propose a case study based on DBpedia, and we discuss the results of a test made with real users.Peer ReviewedPostprint (author's final draft