Discriminative Distance-Based Network Indices with Application to Link Prediction

In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a huge number of vertices may have exactly the same score. The third shortcoming is that in many applications, the distance between two vertices not only depends on the length of shortest paths, but also on the number of shortest paths. In this paper, first we develop a new distance measure between vertices of a graph that yields discriminative distance-based centrality indices. This measure is proportional to the length of shortest paths and inversely proportional to the number of shortest paths. We present algorithms for exact computation of the proposed discriminative indices. Second, we develop randomized algorithms that precisely estimate average discriminative path length and average discriminative eccentricity and show that they give $(\epsilon,\delta)$-approximations of these indices. Third, we perform extensive experiments over several real-world networks from different domains. In our experiments, we first show that compared to the traditional indices, discriminative indices have usually much more discriminability. Then, we show that our randomized algorithms can very precisely estimate average discriminative path length and average discriminative eccentricity, using only few samples. Then, we show that real-world networks have usually a tiny average discriminative path length, bounded by a constant (e.g., 2). Fourth, in order to better motivate the usefulness of our proposed distance measure, we present a novel link prediction method, that uses discriminative distance to decide which vertices are more likely to form a link in future, and show its superior performance compared to the well-known existing measures

Regression and Singular Value Decomposition in Dynamic Graphs

Most of real-world graphs are {\em dynamic}, i.e., they change over time. However, while problems such as regression and Singular Value Decomposition (SVD) have been studied for {\em static} graphs, they have not been investigated for {\em dynamic} graphs, yet. In this paper, we introduce, motivate and study regression and SVD over dynamic graphs. First, we present the notion of {\em update-efficient matrix embedding} that defines the conditions sufficient for a matrix embedding to be used for the dynamic graph regression problem (under $l_2$ norm). We prove that given an $n \times m$ update-efficient matrix embedding (e.g., adjacency matrix), after an update operation in the graph, the optimal solution of the graph regression problem for the revised graph can be computed in $O(nm)$ time. We also study dynamic graph regression under least absolute deviation. Then, we characterize a class of matrix embeddings that can be used to efficiently update SVD of a dynamic graph. For adjacency matrix and Laplacian matrix, we study those graph update operations for which SVD (and low rank approximation) can be updated efficiently

On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

Detection of Composite Communities in Multiplex Biological Networks

The detection of community structure is a widely accepted means of investigating the principles governing biological systems. Recent efforts are exploring ways in which multiple data sources can be integrated to generate a more comprehensive model of cellular interactions, leading to the detection of more biologically relevant communities. In this work, we propose a mathematical programming model to cluster multiplex biological networks, i.e. multiple network slices, each with a different interaction type, to determine a single representative partition of composite communities. Our method, known as SimMod, is evaluated through its application to yeast networks of physical, genetic and co-expression interactions. A comparative analysis involving partitions of the individual networks, partitions of aggregated networks and partitions generated by similar methods from the literature highlights the ability of SimMod to identify functionally enriched modules. It is further shown that SimMod offers enhanced results when compared to existing approaches without the need to train on known cellular interactions

Vocabulary Evolution on the Semantic Web: From Changes to Evolution of Vocabularies and its Impact on the Data

The main objective of the Semantic Web is to provide data on the web well-defined meaning. Vocabularies are used for modeling data in the web, provide a shared understanding of a domain and consist of a collection of types and properties. These types and properties are so-called terms. A vocabulary can import terms from other vocabularies, and data publishers use vocabulary terms for modeling data. Importing terms via vocabularies results in a Network of Linked vOcabularies (NeLO). Vocabularies are subject to change during their lifetime. When vocabularies change, the published data become a problem if they are not updated based on these changes. So far, there has been no study that analyzes vocabulary changes over time. Furthermore, it is unknown how data publishers reflect on such vocabulary changes. Ontology engineers and data publishers may not be aware of the changes in the vocabulary terms that have already happened since they occur rather rarely. This work addresses the problem of vocabulary changes and their impact on other vocabularies and the published data. We analyzed the changes of vocabularies and their reuse. We selected the most dominant vocabularies, based on their use by data publishers. Additionally, we analyzed the changes of 994 vocabularies. Furthermore, we analyzed various vocabularies to better understand by whom and how they are used in the modeled data, and how these changes are adopted in the Linked Open Data cloud. We computed the state of the NeLO from the available versions of vocabularies for over 17 years. We analyzed the static parameters of the NeLO such as its size, density, average degree, and the most important vocabularies at certain points in time. We further investigated how NeLO changes over time, specifically measuring the impact of a change in one vocabulary on others, how the reuse of terms changes, and the importance of vocabulary changes. Our results show that the vocabularies are highly static, and many of the changes occurred in annotation properties. Additionally, 16% of the existing terms are reused by other vocabularies, and some of the deprecated and deleted terms are still reused. Furthermore, most of the newly coined terms are adopted immediately. Our results show that even if the change frequency of terms is rather low, it can have a high impact on the data due to a large amount of data on the web. Moreover, due to a large number of vocabularies in the NeLO, and therefore the increase of available terms, the percentage of imported terms compared with the available ones has decreased over time. Additionally, based on the scores of the average number of exports for the vocabularies in the NeLO, some vocabularies have become more popular over time. Overall, understanding the evolution of vocabulary terms is important for ontology engineers and data publishers to avoid wrong assumptions about the data published on the web. Furthermore, it may foster a better understanding of the impact of the changes in vocabularies and how they are adopted to possibly learn from previous experience. Our results provide for the first time in-depth insights into the structure and evolution of the NeLO. Supported by proper tools exploiting the analysis of this thesis, it may help ontology engineers to identify data modeling shortcomings and assess the dependencies implied by the reusing of a specific vocabulary.Das Hauptziel des Semantic Web ist es, den Daten im Web eine klar definierte Bedeutung zu geben. Vokabulare werden zum Modellieren von Daten im Web verwendet. Vokabulare vermitteln ein gemeinsames Verständnis einer Domäne und bestehen aus einer Sammlung von Typen und Eigenschaften. Diese Typen und Eigenschaften sind sogenannte Begriffe. Ein Vokabular kann Begriffe aus anderen Vokabularen importieren, und Datenverleger verwenden die Begriffe der Vokabulare zum Modellieren von Daten. Durch das Importieren von Begriffen entsteht ein Netzwerk verknüpfter Vokabulare (NeLO). Vokabulare können sich im Laufe der Zeit ändern. Wenn sich Vokabulare ändern, kann dies zu Problemen mit bereits veröffentlichten Daten führen, falls diese nicht entsprechend angepasst werden. Bisher gibt es keine Studie, die die Veränderung der Vokabulare im Laufe der Zeit analysiert. Darüber hinaus ist nicht bekannt, inwiefern bereits veröffentlichte Daten an diese Veränderungen angepasst werden. Verantwortliche für Ontologien und Daten sind sich möglicherweise der Änderungen in den Vokabularen nicht bewusst, da solche Änderungen eher selten vorkommen. Diese Arbeit befasst sich mit dem Problem der Änderung von Vokabularen und deren Auswirkung auf andere Vokabulare sowie die Daten. Wir analysieren die Änderung von Vokabularen und deren Wiederverwendung. Für unsere Analyse haben wir diejenigen Vokabulare ausgewählt, die am häufigsten verwendet werden. Zusätzlich analysieren wir die Änderungen von 994 Vokabularen aus dem Verzeichnis "Linked Open Vocabulary". Wir analysieren die Vokabulare, um zu verstehen, von wem und wie sie in den modellierten Daten verwendet werden und inwiefern Änderungen in die Linked Open Data Cloud übernommen werden. Wir beobachten den Status von NeLO aus den verfügbaren Versionen der Vokabulare über einen Zeitraum von 17 Jahren. Wir analysieren statische Parameter von NeLO wie Größe, Dichte, Durchschnittsgrad und die wichtigsten Vokabulare zu bestimmten Zeitpunkten. Wir untersuchen weiter, wie sich NeLO mit der Zeit ändert. Insbesondere messen wir die Auswirkung einer Änderung in einem Vokabular auf andere, wie sich die Wiederverwendung von Begriffen ändert und wie wichtig Änderungen im Vokabular sind. Unsere Ergebnisse zeigen, dass die Vokabulare sehr statisch sind und viele Änderungen an sogenannten Annotations-Properties vorgenommen wurden. Darüber hinaus werden 16% der vorhandenen Begriffen von anderen Vokabularen wiederverwendet, und einige der veralteten und gelöschten Begriffe werden weiterhin wiederverwendet. Darüber hinaus werden die meisten neu erstellten Begriffe unmittelbar verwendet. Unsere Ergebnisse zeigen, dass selbst wenn die Häufigkeit von Änderungen an Vokabularen eher gering ist, so kann dies aufgrund der großen Datenmenge im Web erhebliche Auswirkungen haben. Darüber hinaus hat sich aufgrund einer großen Anzahl von Vokabularen in NeLO und damit der Zunahme der verfügbaren Begriffe der Prozentsatz der importierten Begriffe im Vergleich zu den verfügbaren Begriffen im Laufe der Zeit verringert. Basierend auf den Ergebnissen der durchschnittlichen Anzahl von Exporten für die Vokabulare in NeLO sind einige Vokabulare im Laufe der Zeit immer beliebter geworden. Insgesamt ist es für Verantwortliche für Ontologien und Daten wichtig, die Entwicklung der Vokabulare zu verstehen, um falsche Annahmen über die im Web veröffentlichten Daten zu vermeiden. Darüber hinaus ermöglichen unsere Ergebnisse ein besseres Verständnis der Auswirkungen von Änderungen in Vokabularen, sowie deren Nachnutzung, um möglicherweise aus früheren Erfahrungen zu lernen. Unsere Ergebnisse bieten erstmals detaillierte Einblicke in die Struktur und Entwicklung des Netzwerks der verknüpften Vokabularen. Unterstützt von geeigneten Tools für die Analyse in dieser Arbeit, kann es Verantwortlichen für Ontologien helfen, Mängel in der Datenmodellierung zu identifizieren und Abhängigkeiten zu bewerten, die durch die Wiederverwendung eines bestimmten Vokabulars entstehenden

Probabilistic Graphical Models for Credibility Analysis in Evolving Online Communities

One of the major hurdles preventing the full exploitation of information from online communities is the widespread concern regarding the quality and credibility of user-contributed content. Prior works in this domain operate on a static snapshot of the community, making strong assumptions about the structure of the data (e.g., relational tables), or consider only shallow features for text classification. To address the above limitations, we propose probabilistic graphical models that can leverage the joint interplay between multiple factors in online communities --- like user interactions, community dynamics, and textual content --- to automatically assess the credibility of user-contributed online content, and the expertise of users and their evolution with user-interpretable explanation. To this end, we devise new models based on Conditional Random Fields for different settings like incorporating partial expert knowledge for semi-supervised learning, and handling discrete labels as well as numeric ratings for fine-grained analysis. This enables applications such as extracting reliable side-effects of drugs from user-contributed posts in healthforums, and identifying credible content in news communities. Online communities are dynamic, as users join and leave, adapt to evolving trends, and mature over time. To capture this dynamics, we propose generative models based on Hidden Markov Model, Latent Dirichlet Allocation, and Brownian Motion to trace the continuous evolution of user expertise and their language model over time. This allows us to identify expert users and credible content jointly over time, improving state-of-the-art recommender systems by explicitly considering the maturity of users. This also enables applications such as identifying helpful product reviews, and detecting fake and anomalous reviews with limited information.Comment: PhD thesis, Mar 201

Scalable Algorithms for the Analysis of Massive Networks

Die Netzwerkanalyse zielt darauf ab, nicht-triviale Erkenntnisse aus vernetzten Daten zu gewinnen. Beispiele für diese Erkenntnisse sind die Wichtigkeit einer Entität im Verhältnis zu anderen nach bestimmten Kriterien oder das Finden des am besten geeigneten Partners für jeden Teilnehmer eines Netzwerks - bekannt als Maximum Weighted Matching (MWM). Da der Begriff der Wichtigkeit an die zu betrachtende Anwendung gebunden ist, wurden zahlreiche Zentralitätsmaße eingeführt. Diese Maße stammen hierbei aus Jahrzehnten, in denen die Rechenleistung sehr begrenzt war und die Netzwerke im Vergleich zu heute viel kleiner waren. Heute sind massive Netzwerke mit Millionen von Kanten allgegenwärtig und eine triviale Berechnung von Zentralitätsmaßen ist oft zu zeitaufwändig. Darüber hinaus ist die Suche nach der Gruppe von k Knoten mit hoher Zentralität eine noch kostspieligere Aufgabe. Skalierbare Algorithmen zur Identifizierung hochzentraler (Gruppen von) Knoten in großen Graphen sind von großer Bedeutung für eine umfassende Netzwerkanalyse. Heutigen Netzwerke verändern sich zusätzlich im zeitlichen Verlauf und die effiziente Aktualisierung der Ergebnisse nach einer Änderung ist eine Herausforderung. Effiziente dynamische Algorithmen sind daher ein weiterer wesentlicher Bestandteil moderner Analyse-Pipelines. Hauptziel dieser Arbeit ist es, skalierbare algorithmische Lösungen für die zwei oben genannten Probleme zu finden. Die meisten unserer Algorithmen benötigen Sekunden bis einige Minuten, um diese Aufgaben in realen Netzwerken mit bis zu Hunderten Millionen von Kanten zu lösen, was eine deutliche Verbesserung gegenüber dem Stand der Technik darstellt. Außerdem erweitern wir einen modernen Algorithmus für MWM auf dynamische Graphen. Experimente zeigen, dass unser dynamischer MWM-Algorithmus Aktualisierungen in Graphen mit Milliarden von Kanten in Millisekunden bewältigt.Network analysis aims to unveil non-trivial insights from networked data by studying relationship patterns between the entities of a network. Among these insights, a popular one is to quantify the importance of an entity with respect to the others according to some criteria. Another one is to find the most suitable matching partner for each participant of a network knowing the pairwise preferences of the participants to be matched with each other - known as Maximum Weighted Matching (MWM). Since the notion of importance is tied to the application under consideration, numerous centrality measures have been introduced. Many of these measures, however, were conceived in a time when computing power was very limited and networks were much smaller compared to today's, and thus scalability to large datasets was not considered. Today, massive networks with millions of edges are ubiquitous, and a complete exact computation for traditional centrality measures are often too time-consuming. This issue is amplified if our objective is to find the group of k vertices that is the most central as a group. Scalable algorithms to identify highly central (groups of) vertices on massive graphs are thus of pivotal importance for large-scale network analysis. In addition to their size, today's networks often evolve over time, which poses the challenge of efficiently updating results after a change occurs. Hence, efficient dynamic algorithms are essential for modern network analysis pipelines. In this work, we propose scalable algorithms for identifying important vertices in a network, and for efficiently updating them in evolving networks. In real-world graphs with hundreds of millions of edges, most of our algorithms require seconds to a few minutes to perform these tasks. Further, we extend a state-of-the-art algorithm for MWM to dynamic graphs. Experiments show that our dynamic MWM algorithm handles updates in graphs with billion edges in milliseconds

Faculty Publications and Creative Works 2004

Faculty Publications & Creative Works is an annual compendium of scholarly and creative activities of University of New Mexico faculty during the noted calendar year. Published by the Office of the Vice President for Research and Economic Development, it serves to illustrate the robust and active intellectual pursuits conducted by the faculty in support of teaching and research at UNM