Relational data factorization

Motivated by an analogy with matrix factorization, we introduce the problem of factorizing relational data. In matrix factorization, one is given a matrix and has to factorize it as a product of other matrices. In relational data factorization, the task is to factorize a given relation as a conjunctive query over other relations, i.e., as a combination of natural join operations. Given a conjunctive query and the input relation, the problem is to compute the extensions of the relations used in the query. Thus, relational data factorization is a relational analog of matrix factorization; it is also a form of inverse querying as one has to compute the relations in the query from the result of the query. The result of relational data factorization is neither necessarily unique nor required to be a lossless decomposition of the original relation. Therefore, constraints can be imposed on the desired factorization and a scoring function is used to determine its quality (often similarity to the original data). Relational data factorization is thus a constraint satisfaction and optimization problem. We show how answer set programming can be used for solving relational data factorization problems.Algorithms and the Foundations of Software technolog

Analyzing, Mining, and Predicting Networked Behaviors

Network structure exists in various types of data in the real world, such as online and offline social networks, traffic networks, computer networks, brain networks, and countless other cases where there are relationships between different entities in the data. What are the roles of network structures in these data? First, the network captures inherent characteristics of the data themselves. This is clear from the definition of the network, which represents the relationship between entities: e.g., the social links among people in a social network describe how they interact with each other; a road network summarizes how the roads are laid out geographically; a brain network obtained from fMRI images represents pairs of brain regions that are active at the same time; a computer network constrains the paths via which internet packages and thus information or viruses can spread. Second, the network structures affect the evolution of the data over time. For example, new friendship links in an online social network are frequently created between friends of friends. Similarly, the current road network structure is without a doubt taken into consideration when roads are added or temporarily closed. As we grow, our brains also grow, including the additions of useful links or the clean up of unnecessary links between brain regions. Third, the network structures act as guidance for many different processes happening in the data. For instance, the links between users on social network dictate how gossips can spread; the roads influence how traffic flows in a city; the links between brain regions affects the way we think and how effectively we do things; the connections between computers route the transfer of any information on the internet.In this thesis, I studied the network effect in various networked behaviors, including analyzing such effect, finding its patterns, and predicting future networked behaviors. First, I gained insights into the data by analyzing the accompanied network structures as well as its evolution. Second, I proposed algorithms for mining different network patterns that help summarize the effect of the network structures on different networked behaviors. Finally, I proposed models to predict the evolution of networked behaviors over time. Toward these tasks, I explored a wide variety of network data, including protein-protein interaction networks, online social networks, collaboration networks, chemical compounds, and traffic networks. Overall, I tackled these network data in different aspects and developed a number of methods for effectively mining and forecasting networked behaviors in data

Dynamic Boolean Matrix Factorizations

Abstract—Boolean matrix factorization is a method to decompose a binary matrix into two binary factor matrices. Akin to other matrix factorizations, the factor matrices can be used for various data analysis tasks. Many (if not most) real-world data sets are dynamic, though, meaning that new information is recorded over time. Incorporating this new information into the factorization can require a re-computation of the factorization – something we cannot do if we want to keep our factorization up-to-date after each update. This paper proposes a method to dynamically update the Boolean matrix factorization when new data is added to the data base. This method is extended with a mechanism to improve the factorization with a trade-off in speed of computation. The method is tested with a number of real-world and synthetic data sets including studying its efficiency against off-line methods. The results show that with good initialization the proposed online and dynamic methods can beat the stateof-the-art offline Boolean matrix factorization algorithms. Keywords-Boolean matrix factorization; On-line algorithms; Dynamic algorithms I