Graph-based Semi-Supervised & Active Learning for Edge Flows

We present a graph-based semi-supervised learning (SSL) method for learning edge flows defined on a graph. Specifically, given flow measurements on a subset of edges, we want to predict the flows on the remaining edges. To this end, we develop a computational framework that imposes certain constraints on the overall flows, such as (approximate) flow conservation. These constraints render our approach different from classical graph-based SSL for vertex labels, which posits that tightly connected nodes share similar labels and leverages the graph structure accordingly to extrapolate from a few vertex labels to the unlabeled vertices. We derive bounds for our method's reconstruction error and demonstrate its strong performance on synthetic and real-world flow networks from transportation, physical infrastructure, and the Web. Furthermore, we provide two active learning algorithms for selecting informative edges on which to measure flow, which has applications for optimal sensor deployment. The first strategy selects edges to minimize the reconstruction error bound and works well on flows that are approximately divergence-free. The second approach clusters the graph and selects bottleneck edges that cross cluster-boundaries, which works well on flows with global trends

Weighted Spectral Embedding of Graphs

We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the Laplacian. We prove that these eigenvectors correspond to the configurations of lowest energy of an equivalent physical system, either mechanical or electrical, in which the weight of each node can be interpreted as its mass or its capacitance, respectively. Experiments on a real dataset illustrate the impact of weighting on the embedding

Improving analytics in urban water management: a spectral clustering-based approach for leakage localization

Worldwide growing water demand has been forcing utilities to successfully manage their costs. Contemporarily, within an era of tight budgets in most economic and social sectors, it affects also Water Distribution Networks (WDN). So, an efficient urban water management is needed to get a balance between consumer satisfaction and infrastructural assets inherent to WDN. Particular case is referred to pipe networks which suffer for frequent leaks, failures and service disruptions. The ensuing costs due to inspection, repair and replacement, are a significant part of operational expenses and give rise to difficult decision making. Recently, the goal regarding the improvement of the traditional leakage management process through the development of analytical leakage localization tools has been brought to the forefront leading to the proposal of several approaches. The basis of all methods relies on the fact that leaks can be detected correlating changes in flow to the output of a simulation model whose parameters are related to both location and severity of the leak. This paper, starting from a previous work of the authors, shows how the critical phases of leak localization can be accomplished through a combination of hydraulic simulation and clustering. The research deals with the benefits provided by Spectral Clustering which is usually adopted for network analysis tasks (e.g., community or sub-network discovery). A transformation from a data points dataset, consisting of leakage scenarios simulated through a hydraulic simulation model, to a similarity graph is presented. Spectral Clustering is then applied on the similarity graph and results are compared with those provided by traditional clustering techniques on the original data points dataset. The proposed spectral approach proved to be more effective with respect to traditional clustering, having a better performance to analytically localize leaks in a water distribution network and, consequently, reducing costs for intervention, inspection and rehabilitation.Peer ReviewedPostprint (published version

Optimal Sensor Placement in a Partitioned Water Distribution Network for the Water Protection from Contamination

Water network protection from accidental and intentional contamination is one of the most critical issues for preserving the citizen health. Recently, some techniques have been proposed in the literature to define the optimal sensor placement. On the other hand, through the definition of permanent DMAs (District Meter Areas), water network partitioning allows significant reduction in the number of exposed users through the full isolation of DMA. In this paper, the optimal sensor placement is coupled with water network partitioning in order to define the best location of isolation valves and control stations, to be closed and installed respectively. The proposed procedure is based on different procedures, and it was tested on a real water network, showing that it is possible both to mitigate the impact of a water contamination and simplify the sensor placement through the water network partitioning

Improving water network management by efficient division into supply clusters

El agua es un recurso escaso que, como tal, debe ser gestionado de manera eficiente. Así, uno de los propósitos de dicha gestión debiera ser la reducción de pérdidas de agua y la mejora del funcionamiento del abastecimiento. Para ello, es necesario crear un marco de trabajo basado en un conocimiento profundo de la redes de distribución. En los casos reales, llegar a este conocimiento es una tarea compleja debido a que estos sistemas pueden estar formados por miles de nodos de consumo, interconectados entre sí también por miles de tuberías y sus correspondientes elementos de alimentación. La mayoría de las veces, esas redes no son el producto de un solo proceso de diseño, sino la consecuencia de años de historia que han dado respuesta a demandas de agua continuamente crecientes con el tiempo. La división de la red en lo que denominaremos clusters de abastecimiento, permite la obtención del conocimiento hidráulico adecuado para planificar y operar las tareas de gestión oportunas, que garanticen el abastecimiento al consumidor final. Esta partición divide las redes de distribución en pequeñas sub-redes, que son virtualmente independientes y están alimentadas por un número prefijado de fuentes. Esta tesis propone un marco de trabajo adecuado en el establecimiento de vías eficientes tanto para dividir la red de abastecimiento en sectores, como para desarrollar nuevas actividades de gestión, aprovechando esta estructura dividida. La propuesta de desarrollo de cada una de estas tareas será mediante el uso de métodos kernel y sistemas multi-agente. El spectral clustering y el aprendizaje semi-supervisado se mostrarán como métodos con buen comportamiento en el paradigma de encontrar una red sectorizada que necesite usar el número mínimo de válvulas de corte. No obstante, sus algoritmos se vuelven lentos (a veces infactibles) dividiendo una red de abastecimiento grande.Herrera Fernández, AM. (2011). Improving water network management by efficient division into supply clusters [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/11233Palanci

The stability of a graph partition: A dynamics-based framework for community detection

Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the study of real-world systems leads to highly complex networks and a current challenge is to extract intelligible, simplified descriptions from the network in terms of relevant subgraphs, which can provide insight into the structure and function of the overall system. Sparked by seminal work by Newman and Girvan, an interesting line of research has been devoted to investigating modular community structure in networks, revitalising the classic problem of graph partitioning. However, modular or community structure in networks has notoriously evaded rigorous definition. The most accepted notion of community is perhaps that of a group of elements which exhibit a stronger level of interaction within themselves than with the elements outside the community. This concept has resulted in a plethora of computational methods and heuristics for community detection. Nevertheless a firm theoretical understanding of most of these methods, in terms of how they operate and what they are supposed to detect, is still lacking to date. Here, we will develop a dynamical perspective towards community detection enabling us to define a measure named the stability of a graph partition. It will be shown that a number of previously ad-hoc defined heuristics for community detection can be seen as particular cases of our method providing us with a dynamic reinterpretation of those measures. Our dynamics-based approach thus serves as a unifying framework to gain a deeper understanding of different aspects and problems associated with community detection and allows us to propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte