Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications

Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem of extracting dense subgraphs has remained largely unexplored so far. In this work we study the problem of core decomposition of a multilayer network. The multilayer context is much challenging as no total order exists among multilayer cores; rather, they form a lattice whose size is exponential in the number of layers. In this setting we devise three algorithms which differ in the way they visit the core lattice and in their pruning techniques. We then move a step forward and study the problem of extracting the inner-most (also known as maximal) cores, i.e., the cores that are not dominated by any other core in terms of their core index in all the layers. Inner-most cores are typically orders of magnitude less than all the cores. Motivated by this, we devise an algorithm that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition. Finally, we showcase the multilayer core-decomposition tool in a variety of scenarios and problems. We start by considering the problem of densest-subgraph extraction in multilayer networks. We introduce a definition of multilayer densest subgraph that trades-off between high density and number of layers in which the high density holds, and exploit multilayer core decomposition to approximate this problem with quality guarantees. As further applications, we show how to utilize multilayer core decomposition to speed-up the extraction of frequent cross-graph quasi-cliques and to generalize the community-search problem to the multilayer setting

Flexible constrained sampling with guarantees for pattern mining

Pattern sampling has been proposed as a potential solution to the infamous pattern explosion. Instead of enumerating all patterns that satisfy the constraints, individual patterns are sampled proportional to a given quality measure. Several sampling algorithms have been proposed, but each of them has its limitations when it comes to 1) flexibility in terms of quality measures and constraints that can be used, and/or 2) guarantees with respect to sampling accuracy. We therefore present Flexics, the first flexible pattern sampler that supports a broad class of quality measures and constraints, while providing strong guarantees regarding sampling accuracy. To achieve this, we leverage the perspective on pattern mining as a constraint satisfaction problem and build upon the latest advances in sampling solutions in SAT as well as existing pattern mining algorithms. Furthermore, the proposed algorithm is applicable to a variety of pattern languages, which allows us to introduce and tackle the novel task of sampling sets of patterns. We introduce and empirically evaluate two variants of Flexics: 1) a generic variant that addresses the well-known itemset sampling task and the novel pattern set sampling task as well as a wide range of expressive constraints within these tasks, and 2) a specialized variant that exploits existing frequent itemset techniques to achieve substantial speed-ups. Experiments show that Flexics is both accurate and efficient, making it a useful tool for pattern-based data exploration.Comment: Accepted for publication in Data Mining & Knowledge Discovery journal (ECML/PKDD 2017 journal track

VISUAL SEMANTIC SEGMENTATION AND ITS APPLICATIONS

This dissertation addresses the difficulties of semantic segmentation when dealing with an extensive collection of images and 3D point clouds. Due to the ubiquity of digital cameras that help capture the world around us, as well as the advanced scanning techniques that are able to record 3D replicas of real cities, the sheer amount of visual data available presents many opportunities for both academic research and industrial applications. But the mere quantity of data also poses a tremendous challenge. In particular, the problem of distilling useful information from such a large repository of visual data has attracted ongoing interests in the fields of computer vision and data mining. Structural Semantics are fundamental to understanding both natural and man-made objects. Buildings, for example, are like languages in that they are made up of repeated structures or patterns that can be captured in images. In order to find these recurring patterns in images, I present an unsupervised frequent visual pattern mining approach that goes beyond co-location to identify spatially coherent visual patterns, regardless of their shape, size, locations and orientation. First, my approach categorizes visual items from scale-invariant image primitives with similar appearance using a suite of polynomial-time algorithms that have been designed to identify consistent structural associations among visual items, representing frequent visual patterns. After detecting repetitive image patterns, I use unsupervised and automatic segmentation of the identified patterns to generate more semantically meaningful representations. The underlying assumption is that pixels capturing the same portion of image patterns are visually consistent, while pixels that come from different backdrops are usually inconsistent. I further extend this approach to perform automatic segmentation of foreground objects from an Internet photo collection of landmark locations. New scanning technologies have successfully advanced the digital acquisition of large-scale urban landscapes. In addressing semantic segmentation and reconstruction of this data using LiDAR point clouds and geo-registered images of large-scale residential areas, I develop a complete system that simultaneously uses classification and segmentation methods to first identify different object categories and then apply category-specific reconstruction techniques to create visually pleasing and complete scene models