On the discovery of relevant structures in dynamic and heterogeneous data

We are witnessing an explosion of available data coming from a huge amount of sources and domains, which is leading to the creation of datasets larger and larger, as well as richer and richer. Understanding, processing, and extracting useful information from those datasets requires specialized algorithms that take into consideration both the dynamism and the heterogeneity of the data they contain. Although several pattern mining techniques have been proposed in the literature, most of them fall short in providing interesting structures when the data can be interpreted differently from user to user, when it can change from time to time, and when it has different representations. In this thesis, we propose novel approaches that go beyond the traditional pattern mining algorithms, and can effectively and efficiently discover relevant structures in dynamic and heterogeneous settings. In particular, we address the task of pattern mining in multi-weighted graphs, pattern mining in dynamic graphs, and pattern mining in heterogeneous temporal databases. In pattern mining in multi-weighted graphs, we consider the problem of mining patterns for a new category of graphs called emph{multi-weighted graphs}. In these graphs, nodes and edges can carry multiple weights that represent, for example, the preferences of different users or applications, and that are used to assess the relevance of the patterns. We introduce a novel family of scoring functions that assign a score to each pattern based on both the weights of its appearances and their number, and that respect the anti-monotone property, pivotal for efficient implementations. We then propose a centralized and a distributed algorithm that solve the problem both exactly and approximately. The approximate solution has better scalability in terms of the number of edge weighting functions, while achieving good accuracy in the results found. An extensive experimental study shows the advantages and disadvantages of our strategies, and proves their effectiveness. Then, in pattern mining in dynamic graphs, we focus on the particular task of discovering structures that are both well-connected and correlated over time, in graphs where nodes and edges can change over time. These structures represent edges that are topologically close and exhibit a similar behavior of appearance and disappearance in the snapshots of the graph. To this aim, we introduce two measures for computing the density of a subgraph whose edges change in time, and a measure to compute their correlation. The density measures are able to detect subgraphs that are silent in some periods of time but highly connected in the others, and thus they can detect events or anomalies happened in the network. The correlation measure can identify groups of edges that tend to co-appear together, as well as edges that are characterized by similar levels of activity. For both variants of density measure, we provide an effective solution that enumerates all the maximal subgraphs whose density and correlation exceed given minimum thresholds, but can also return a more compact subset of representative subgraphs that exhibit high levels of pairwise dissimilarity. Furthermore, we propose an approximate algorithm that scales well with the size of the network, while achieving a high accuracy. We evaluate our framework with an extensive set of experiments on both real and synthetic datasets, and compare its performance with the main competitor algorithm. The results confirm the correctness of the exact solution, the high accuracy of the approximate, and the superiority of our framework over the existing solutions. In addition, they demonstrate the scalability of the framework and its applicability to networks of different nature. Finally, we address the problem of entity resolution in heterogeneous temporal data-ba-se-s, which are datasets that contain records that give different descriptions of the status of real-world entities at different periods of time, and thus are characterized by different sets of attributes that can change over time. Detecting records that refer to the same entity in such scenario requires a record similarity measure that takes into account the temporal information and that is aware of the absence of a common fixed schema between the records. However, existing record matching approaches either ignore the dynamism in the attribute values of the records, or assume that all the records share the same set of attributes throughout time. In this thesis, we propose a novel time-aware schema-agnostic similarity measure for temporal records to find pairs of matching records, and integrate it into an exact and an approximate algorithm. The exact algorithm can find all the maximal groups of pairwise similar records in the database. The approximate algorithm, on the other hand, can achieve higher scalability with the size of the dataset and the number of attributes, by relying on a technique called meta-blocking. This algorithm can find a good-quality approximation of the actual groups of similar records, by adopting an effective and efficient clustering algorithm.