Generalized Matrix Factorizations as a Unifying Framework for Pattern Set Mining: Complexity Beyond Blocks

Abstract. Matrix factorizations are a popular tool to mine regularities from data. There are many ways to interpret the factorizations, but one particularly suited for data mining utilizes the fact that a matrix product can be interpreted as a sum of rank-1 matrices. Then the factorization of a matrix becomes the task of finding a small number of rank-1 matrices, sum of which is a good representation of the original matrix. Seen this way, it becomes obvious that many problems in data mining can be expressed as matrix factorizations with correct definitions of what a rank-1 matrix and a sum of rank-1 matrices mean. This paper develops a unified theory, based on generalized outer product operators, that encompasses many pattern set mining tasks. The focus is on the computational aspects of the theory and studying the computational complexity and approximability of many problems related to generalized matrix factorizations. The results immediately apply to a large number of data mining problems, and hopefully allow generalizing future results and algorithms, as well.

Social Data Mining for Crime Intelligence

With the advancement of the Internet and related technologies, many traditional crimes have made the leap to digital environments. The successes of data mining in a wide variety of disciplines have given birth to crime analysis. Traditional crime analysis is mainly focused on understanding crime patterns, however, it is unsuitable for identifying and monitoring emerging crimes. The true nature of crime remains buried in unstructured content that represents the hidden story behind the data. User feedback leaves valuable traces that can be utilised to measure the quality of various aspects of products or services and can also be used to detect, infer, or predict crimes. Like any application of data mining, the data must be of a high quality standard in order to avoid erroneous conclusions. This thesis presents a methodology and practical experiments towards discovering whether (i) user feedback can be harnessed and processed for crime intelligence, (ii) criminal associations, structures, and roles can be inferred among entities involved in a crime, and (iii) methods and standards can be developed for measuring, predicting, and comparing the quality level of social data instances and samples. It contributes to the theory, design and development of a novel framework for crime intelligence and algorithm for the estimation of social data quality by innovatively adapting the methods of monitoring water contaminants. Several experiments were conducted and the results obtained revealed the significance of this study in mining social data for crime intelligence and in developing social data quality filters and decision support systems

Extracting Taxonomies from Bipartite Graphs

Given a large bipartite graph that represents objects and their properties, how can we automatically extract semantic information that provides an overview of the data and -- at the same time -- enables us to drill down to specific parts for an in-depth analysis? In this work in-progress paper, we propose extracting a taxonomy that models the relation between the properties via an is-a hierarchy. The extracted taxonomy arranges the properties from general to specific providing different levels of abstraction.publishe