Many novel graph neural network models have reported an impressive performance on benchmark dataset, but the theory behind these networks is still being developed. In this thesis, we study the trajectory of Gradient descent (GD) and Stochastic gradient descent (SGD) in the loss landscape of Graph neural networks by replicating Xing et al. [1] study for feed-forward networks. Furthermore, we empirically examine if the training process could be accelerated by an optimization algorithm inspired from Stochastic gradient Langevin dynamics and what effect the topology of the graph has on the convergence of GD by perturbing its structure. We find that the loss landscape is relatively flat and that SGD does not encounter any significant obstacles during its propagation. The noise-induced gradient appears to aid SGD in finding a stationary point with desirable generalisation capabilities when the learning rate is poorly optimized. Additionally, we observe that the topological structure of the graph plays a part in the convergence of GD but further research is required to understand how. / Många nya grafneurala nätverk har visat imponerande resultat på existerande dataset, dock är teorin bakom dessa nätverk fortfarande under utveckling. I denna uppsats studerar vi banor av gradientmetoden (GD) och den stokastiska gradientmetoden (SGD) i lösningslandskapet till grafiska faltningsnätverk genom att replikera studien av feed-forward nätverk av Xing et al. [1]. Dessutom undersöker vi empiriskt om träningsprocessen kan accelereras genom en optimeringsalgoritm inspirerad av Stokastisk gradient Langevin dynamik, samt om grafens topologi har en inverkan på konvergensen av GD genom att ändra strukturen. Vi ser att lösningslandskapet är relativt plant och att bruset inducerat i gradienten verkar hjälpa SGD att finna stabila stationära punkter med önskvärda generaliseringsegenskaper när inlärningsparametern har blivit olämpligt optimerad. Dessutom observerar vi att den topologiska grafstrukturen påverkar konvergensen av GD, men det behövs mer forskning för att förstå hur.

<p dir="ltr">Since graphs are natural representations for encoding relational data, the problem of graph matching is an emerging task and has attracted increasing attention, which could potentially impact various domains such as social network de-anonymization and computer vision. Our main interest is designing polynomial-time algorithms for seeded graph matching problems where a subset of pre-matched vertex-pairs (seeds) is revealed. </p><p dir="ltr">However, the existing work does not fully investigate the pivotal role of seeds and falls short of making the most use of the seeds. Notably, the majority of existing hand-crafted algorithms only focus on using ``witnesses'' in the 1-hop neighborhood. Although some advanced algorithms are proposed to use multi-hop witnesses, their theoretical analysis applies only to \ER random graphs and requires seeds to be all correct, which often do not hold in real applications. Furthermore, a parallel line of research, Graph Neural Network (GNN) approaches, typically employs a semi-supervised approach, which requires a large number of seeds and lacks the capacity to distill knowledge transferable to unseen graphs.</p><p dir="ltr">In my dissertation, I have taken two approaches to address these limitations. In the first approach, we study to design hand-crafted algorithms that can properly use multi-hop witnesses to match graphs. We first study graph matching using multi-hop neighborhoods when partially-correct seeds are provided. Specifically, consider two correlated graphs whose edges are sampled independently from a parent \ER graph $\mathcal{G}(n,p)$. A mapping between the vertices of the two graphs is provided as seeds, of which an unknown fraction is correct. We first analyze a simple algorithm that matches vertices based on the number of common seeds in the $1$-hop neighborhoods, and then further propose a new algorithm that uses seeds in the $D$-hop neighborhoods. We establish non-asymptotic performance guarantees of perfect matching for both $1$-hop and $2$-hop algorithms, showing that our new $2$-hop algorithm requires substantially fewer correct seeds than the $1$-hop algorithm when graphs are sparse. Moreover, by combining our new performance guarantees for the $1$-hop and $2$-hop algorithms, we attain the best-known results (in terms of the required fraction of correct seeds) across the entire range of graph sparsity and significantly improve the previous results. We then study the role of multi-hop neighborhoods in matching power-law graphs. Assume that two edge-correlated graphs are independently edge-sampled from a common parent graph with a power-law degree distribution. A set of correctly matched vertex-pairs is chosen at random and revealed as initial seeds. Our goal is to use the seeds to recover the remaining latent vertex correspondence between the two graphs. Departing from the existing approaches that focus on the use of high-degree seeds in $1$-hop neighborhoods, we develop an efficient algorithm that exploits the low-degree seeds in suitably-defined $D$-hop neighborhoods. Our result achieves an exponential reduction in the seed size requirement compared to the best previously known results.</p><p dir="ltr">In the second approach, we study GNNs for seeded graph matching. We propose a new supervised approach that can learn from a training set how to match unseen graphs with only a few seeds. Our SeedGNN architecture incorporates several novel designs, inspired by our theoretical studies of seeded graph matching: 1) it can learn to compute and use witness-like information from different hops, in a way that can be generalized to graphs of different sizes; 2) it can use easily-matched node-pairs as new seeds to improve the matching in subsequent layers. We evaluate SeedGNN on synthetic and real-world graphs and demonstrate significant performance improvements over both non-learning and learning algorithms in the existing literature. Furthermore, our experiments confirm that the knowledge learned by SeedGNN from training graphs can be generalized to test graphs of different sizes and categories.</p>

<p dir="ltr">This research involves numerous network intrusion techniques through novel applications of graph representation learning and image representation learning. The methods are tested on multiple publicly available network flow datasets.</p>

Les relations entre la structure des composés chimiques et leurs propriétés sont complexes et à haute dimension. Dans le processus de développement de médicaments, plusieurs proprié- tés d’un composé doivent souvent être optimisées simultanément, ce qui complique encore la tâche. Ce travail explore deux représentations des composés chimiques pour les tâches de prédiction des propriétés. L’objectif de ces représentations proposées est d’améliorer l’explicabilité afin de faciliter le processus d’optimisation des propriétés des composés. Pre- mièrement, nous décomposons l’algorithme ECFP (Extended connectivity Fingerprint) et le rendons plus simple pour la compréhension humaine. Nous remplaçons une fonction de hachage sujet aux collisions par une relation univoque de sous structure à bit. Nous consta- tons que ce changement ne se traduit pas par une meilleure performance prédictive d’un perceptron multicouche par rapport à l’ECFP. Toutefois, si la capacité du prédicteur est ra- menée à celle d’un prédicteur linéaire, ses performances sont meilleures que celles de l’ECFP. Deuxièmement, nous appliquons l’apprentissage automatique à l’analyse des paires molécu- laires appariées (MMPA), un paradigme de conception du développement de médicaments. La MMPA compare des paires de composés très similaires, dont la structure diffère par une modification sur un site. Nous formons des modèles de prédiction sur des paires de com- posés afin de prédire les différences d’activité. Nous utilisons des contraintes de similarité par paires comme MMPA, mais nous utilisons également des paires échantillonnées de façon aléatoire pour entraîner les modèles. Nous constatons que les modèles sont plus performants sur des paires choisies au hasard que sur des paires avec des contraintes de similarité strictes. Cependant, les meilleurs modèles par paires ne sont pas capables de battre les performances de prédiction du modèle simple de base. Ces deux études, RCFP et comparaisons par paires, visent à aborder la prédiction des propriétés d’une manière plus compréhensible. En utili- sant l’intuition et l’expérience des chimistes médicinaux dans le cadre de la modélisation prédictive, nous espérons encourager l’explicabilité en tant que composante nécessaire des modèles cheminformatiques prédictifs. / The relationships between the structure of chemical compounds and their properties are complex and high dimensional. In the drug development process, multiple properties of a compound often need to be optimized simultaneously, further complicating the task. This work explores two representations of chemical compounds for property prediction tasks. The goal of these suggested representations is improved explainability to better understand the compound property optimization process. First, we decompose the Extended Connectivity Fingerprint (ECFP) algorithm and make it more straightforward for human understanding. We replace a collision-prone hash function with a one-to-one substructure-to-bit relationship. We find that this change which does not translate to higher predictive performance of a multi- layer perceptron compared to ECFP. However, if the capacity of the predictor is lowered to that of a linear predictor, it does perform better than ECFP. Second, we apply machine learning to Matched Molecular Pair Analysis (MMPA), a drug development design paradigm. MMPA compares pairs of highly similar compounds, differing in structure by modification at one site. We train prediction models on pairs of compounds to predict differences in activity. We use pairwise similarity constraints like MMPA, but also use randomly sampled pairs to train the models. We find that models perform better on randomly chosen pairs than on pairs with strict similarity constraints. However, the best pairwise models are not able to beat the prediction performance of the simpler baseline single model. Both of these investigations, RCFP and pairwise comparisons, aim to approach property prediction in a more explainable way. By using intuition and experience of medicinal chemists within predictive modelling, we hope to encourage explainability as a necessary component of predictive cheminformatic models.

In this masters thesis we focused on using machine learning methods for detecting money laundering in financial transaction networks, in order to demonstrate that it can be used as a complement or instead of the more commonly used rule based systems. The graph learning method graph convolutional networks (GCN) has been a hot topic in the field since they were shown to scale well with data size back in 2018. However the typical GCN models cannot use edge features, which is why this thesis combines the GCN model with a node and edge neural network (NENN) in order to solve this problem. This new method will be compared towards an already established machine learning method for financial transactions, namely the tree boosting method (XGBoost). Because of confidentiality concerns for financial transactions data, the machine learning algorithms will be tested on two carefully constructed synthetically generated data sets, which from agent based simulations resembles real financial data. The results showed the viability and superiority of the new implementation of the GCN model with it being a preferable method for connectivly structured data, meaning that a transaction or account is analyzed in the context of its financial environment. On the other hand the XGBoost method showed better results when examining transactions independently. Hence it was more accurately able to find fraudulent and non fraudulent patterns from the transactional features themselves. / I detta examensarbete fokuserar vi på användandet av maskininlärningsmetoder för att detektera penningtvätt i finansiella transaktionsnätverk, med målet att demonstrera att dess kan användas som ett komplement till eller i stället för de mer vanligt använda regelbaserade systemen. Grafinlärningsmetoden \textit{graph convolutional networks} (GCN) som har varit ett hett ämne inom området sedan metoden under 2018 visades fungera bra för stora datamängder. Däremot kan inte en vanlig GCN-modell använda kantinformation, vilket är varför denna avhandling kombinerar GCN-modellen med \textit{node and edge neural networks} (NENN) för att mer effektivt detektera penningtvätt. Denna nya metod kommer att jämföras med en redan etablerad maskininlärningsmetod för finansiella transaktioner, nämligen \textit{tree boosting} (XGBoost). På grund av sekretessanledningar för finansiella transaktionsdata var maskininlärningsalgoritmerna testade på två noggrant konstruerade syntetiskt genererade datamängder som från agentbaserade simuleringar liknar riktiga finansiella data. Resultaten visade på applikationsmöjligheter och överlägsenhet för den nya implementationen av GCN-modellen vilken är att föredra för relationsstrukturerade data, det vill säga när transaktioner och konton analyseras i kontexten av deras finansiella omgivning. Å andra sidan visar XGBoost bättre resultat på att examinera transaktioner individuellt eftersom denna metod mer precist kan identifiera bedrägliga och icke-bedrägliga mönster från de transnationella funktionerna.

<p>The most important networks from different domains—such as Computing, Organization, Economic, Social, Academic, and Biology—are networks that change over time. For example, in an organization there are email and collaboration networks (e.g., different people or teams working on a document). Apart from the connectivity of the networks changing over time, they can contain attributes such as the topic of an email or message, contents of a document, or the interests of a person in an academic citation or a social network. Analyzing these dynamic networks can be critical in decision-making processes. For instance, in an organization, getting insight into how people from different teams collaborate, provides important information that can be used to optimize workflows.</p> <p><br></p> <p>Network generative models provide a way to study and analyze networks. For example, benchmarking model performance and generalization in tasks like node classification, can be done by evaluating models on synthetic networks generated with varying structure and attribute correlation. In this work, we begin by presenting our systemic study of the impact that graph structure and attribute auto-correlation on the task of node classification using collective inference. This is the first time such an extensive study has been done. We take advantage of a recently developed method that samples attributed networks—although static—with varying network structure jointly with correlated attributes. We find that the graph connectivity that contributes to the network auto-correlation (i.e., the local relationships of nodes) and density have the highest impact on the performance of collective inference methods.</p> <p><br></p> <p>Most of the literature to date has focused on static representations of networks, partially due to the difficulty of finding readily-available datasets of dynamic networks. Dynamic network generative models can bridge this gap by generating synthetic graphs similar to observed real-world networks. Given that motifs have been established as building blocks for the structure of real-world networks, modeling them can help to generate the graph structure seen and capture correlations in node connections and activity. Therefore, we continue with a study of motif evolution in <em>dynamic</em> temporal graphs. Our key insight is that motifs rarely change configurations in fast-changing dynamic networks (e.g. wedges intotriangles, and vice-versa), but rather keep reappearing at different times while keeping the same configuration. This finding motivates the generative process of our proposed models, using temporal motifs as building blocks, that generates dynamic graphs with links that appear and disappear over time.</p> <p><br></p> <p>Our first proposed model generates dynamic networks based on motif-activity and the roles that nodes play in a motif. For example, a wedge is sampled based on the likelihood of one node having the role of hub with the two other nodes being the spokes. Our model learns all parameters from observed data, with the goal of producing synthetic graphs with similar graph structure and node behavior. We find that using motifs and node roles helps our model generate the more complex structures and the temporal node behavior seen in real-world dynamic networks.</p> <p><br></p> <p>After observing that using motif node-roles helps to capture the changing local structure and behavior of nodes, we extend our work to also consider the attributes generated by nodes’ activities. We propose a second generative model for attributed dynamic networks that (i) captures network structure dynamics through temporal motifs, and (ii) extends the structural roles of nodes in motifs to roles that generate content embeddings. Our new proposed model is the first to generate synthetic dynamic networks and sample content embeddings based on motif node roles. To the best of our knowledge, it is the only attributed dynamic network model that can generate <em>new</em> content embeddings—not observed in the input graph, but still similar to that of the input graph. Our results show that modeling the network attributes with higher-order structures (e.g., motifs) improves the quality of the networks generated.</p> <p><br></p> <p>The generative models proposed address the difficulty of finding readily-available datasets of dynamic networks—attributed or not. This work will also allow others to: (i) generate networks that they can share without divulging individual’s private data, (ii) benchmark model performance, and (iii) explore model generalization on a broader range of conditions, among other uses. Finally, the evaluation measures proposed will elucidate models, allowing fellow researchers to push forward in these domains.</p>

Proteins are considered the primary actors in living organisms. Proteins mainly perform their functions by interacting with other proteins. Protein-protein interactions underpin various biological activities such as metabolic cycles, signal transduction, and immune response. PPI identification has been addressed by various experimental methods such as the yeast two-hybrid, mass spectrometry, and protein microarrays, to mention a few. However, due to the sheer number of proteins, experimental methods for finding interacting and non-interacting protein pairs are time-consuming and costly. Therefore a sequence-based framework called ProtInteract is developed to predict protein-protein interaction. ProtInteract comprises two components: first, a novel autoencoder architecture that encodes each protein's primary structure to a lower-dimensional vector while preserving its underlying sequential pattern by extracting uncorrelated attributes and more expressive descriptors. This leads to faster training of the second network, a deep convolutional neural network (CNN) that receives encoded proteins and predicts their interaction. Three different scenarios formulate the prediction task. In each scenario, the deep CNN predicts the class of a given encoded protein pair. Each class indicates different ranges of confidence scores corresponding to the probability of whether a predicted interaction occurs or not. The proposed framework features significantly low computational complexity and relatively fast response. The present study makes two significant contributions to the field of protein-protein interaction (PPI) prediction. Firstly, it addresses the computational challenges posed by the high dimensionality of protein datasets through the use of dimensionality reduction techniques, which extract highly informative sequence attributes. Secondly, the proposed framework, ProtInteract, utilises this information to identify the interaction characteristics of a protein based on its amino acid configuration. ProtInteract encodes the protein's primary structure into a lower-dimensional vector space, thereby reducing the computational complexity of PPI prediction. Our results provide evidence of the proposed framework's accuracy and efficiency in predicting protein-protein interactions.

With the arrival of 5G networks, telecommunication systems are becoming more intelligent, integrated, and broadly used. This thesis focuses on predicting the upcoming traffic to efficiently promote resource allocation, guarantee stability and reliability of the network. Since networks modeled as graphs potentially capture more information than tabular data, the construction of the graph and choice of the model are key to achieve a good prediction. In this thesis traffic prediction is based on a time-evolving graph, whose node and edges encode the structure and activity of the system. Edges are created by dynamic time-warping (DTW), geographical distance, and $k$-nearest neighbors. The node features contain different temporal information together with spatial information computed by methods from topological data analysis (TDA). To capture the temporal and spatial dependency of the graph several dynamic graph methods are compared. Throughout experiments, we could observe that the most successful model GConvGRU performs best for edges created by DTW and node features that include temporal information across multiple time steps. / Med ankomsten av 5G nätverk blir telekommunikationssystemen alltmer intelligenta, integrerade, och bredare använda. Denna uppsats fokuserar på att förutse den kommande nättrafiken, för att effektivt hantera resursallokering, garantera stabilitet och pålitlighet av nätverken. Eftersom nätverk som modelleras som grafer har potential att innehålla mer information än tabulär data, är skapandet av grafen och valet av metod viktigt för att uppnå en bra förutsägelse. I denna uppsats är trafikförutsägelsen baserad på grafer som ändras över tid, vars noder och länkar fångar strukturen och aktiviteten av systemet. Länkarna skapas genom dynamisk time warping (DTW), geografisk distans, och $k$-närmaste grannarna. Egenskaperna för noderna består av dynamisk och rumslig information som beräknats av metoder från topologisk dataanalys (TDA). För att inkludera såväl det dynamiska som det rumsliga beroendet av grafen, jämförs flera dynamiska grafmetoder. Genom experiment, kunde vi observera att den mest framgångsrika modellen GConvGRU presterade bäst för länkar skapade genom DTW och noder som innehåller dynamisk information över flera tidssteg.

Real-time prediction of taxi demand in a discrete geographical space is useful as it can minimise service disequilibrium by informing idle drivers of the imbalance, incentivising them to reduce it. This, in turn, can lead to improved efficiency, more stimulating work conditions, and a better customer experience. This study aims to investigate the possibility of utilising an artificial neural network model to make such a prediction for Stockholm. The model was trained on historical demand data and - uniquely - crowd flow data from a cellular provider (aggregated and anonymised). Results showed that the final model could generate very helpful predictions (only off by less than 1 booking on average). External factors - including crowd flow data - had a minor positive impact on performance, but limitations regarding the setup of the zones lead to the study being unable to make a definitive conclusion about whether crowd flow data is effective in improving taxi demand predictors or not. / Prognos av taxiefterfrågan i ett diskret geografiskt utrymme är användbart då det kan minimera obalans mellan utbud och efterfrågan genom att informera lediga taxiförare om obalansen och därmed utjämna den. Detta kan i sin tur leda till förbättrad effektivitet, mer stimulerande arbetsförhållanden och en bättre kundupplevelse. Denna studie ämnar att undersöka möjligheten att använda artificiella neurala nätverk för att göra en sådan prognos för Stockholm. Modellen tränades på historisk data om efterfrågan och - unikt för studien - folkströmsdata (aggregerad och anonymiserad) från en mobiloperatör. Resultaten visade att den slutgiltiga modellen kunde generera användbara prognoser (med ett genomsnittligt prognosfel med mindre än 1 bil per tidsenhet). Externa faktorer – inklusive folkströmsdata – hade en märkbar positiv inverkan på prestandan, men begränsningar rörande framställningen av zonerna ledde till att studien inte kunde dra en definitiv slutsats om huruvida folkströmsdata är effektiva för att förbättra prognoser för taxiefterfrågan eller ej.