An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them

Relational Algebra for In-Database Process Mining

The execution logs that are used for process mining in practice are often obtained by querying an operational database and storing the result in a flat file. Consequently, the data processing power of the database system cannot be used anymore for this information, leading to constrained flexibility in the definition of mining patterns and limited execution performance in mining large logs. Enabling process mining directly on a database - instead of via intermediate storage in a flat file - therefore provides additional flexibility and efficiency. To help facilitate this ideal of in-database process mining, this paper formally defines a database operator that extracts the 'directly follows' relation from an operational database. This operator can both be used to do in-database process mining and to flexibly evaluate process mining related queries, such as: "which employee most frequently changes the 'amount' attribute of a case from one task to the next". We define the operator using the well-known relational algebra that forms the formal underpinning of relational databases. We formally prove equivalence properties of the operator that are useful for query optimization and present time-complexity properties of the operator. By doing so this paper formally defines the necessary relational algebraic elements of a 'directly follows' operator, which are required for implementation of such an operator in a DBMS

Impliance: A Next Generation Information Management Appliance

ably successful in building a large market and adapting to the changes of the last three decades, its impact on the broader market of information management is surprisingly limited. If we were to design an information management system from scratch, based upon today's requirements and hardware capabilities, would it look anything like today's database systems?" In this paper, we introduce Impliance, a next-generation information management system consisting of hardware and software components integrated to form an easy-to-administer appliance that can store, retrieve, and analyze all types of structured, semi-structured, and unstructured information. We first summarize the trends that will shape information management for the foreseeable future. Those trends imply three major requirements for Impliance: (1) to be able to store, manage, and uniformly query all data, not just structured records; (2) to be able to scale out as the volume of this data grows; and (3) to be simple and robust in operation. We then describe four key ideas that are uniquely combined in Impliance to address these requirements, namely the ideas of: (a) integrating software and off-the-shelf hardware into a generic information appliance; (b) automatically discovering, organizing, and managing all data - unstructured as well as structured - in a uniform way; (c) achieving scale-out by exploiting simple, massive parallel processing, and (d) virtualizing compute and storage resources to unify, simplify, and streamline the management of Impliance. Impliance is an ambitious, long-term effort to define simpler, more robust, and more scalable information systems for tomorrow's enterprises.Comment: This article is published under a Creative Commons License Agreement (http://creativecommons.org/licenses/by/2.5/.) You may copy, distribute, display, and perform the work, make derivative works and make commercial use of the work, but, you must attribute the work to the author and CIDR 2007. 3rd Biennial Conference on Innovative Data Systems Research (CIDR) January 710, 2007, Asilomar, California, US

Conditional network embeddings

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that 'similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if 'similar' means being 'more likely to be connected') or classification (if 'similar' means 'being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create \emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization