<p dir="ltr">Topological Data Analysis (TDA) with its roots embedded in the field of algebraic topology has successfully found its applications in computational biology, drug discovery, machine learning and in many diverse areas of science. One of its cornerstones, persistent homology, captures topological features latent in the data. Recent progress in TDA allows us to integrate these finer topological features into traditional machine learning and deep learning pipelines. However, the utilization of topological methods within a conventional deep learning framework remains relatively uncharted. This thesis presents four scenarios where computational topology tools are employed to advance machine learning.</p><p dir="ltr">The first one involves integrating persistent homology to explore high-dimensional cytometry data. The second one incorporates Extended persistence in a supervised graph classification framework and demonstrates leveraging TDA in cases where data naturally aligns with higher-order elements by extending graph neural networks to higher-order networks, applied specifically in non-manifold mesh classification. The third and fourth scenarios delve into enhancing graph neural networks through multiparameter persistence.</p>

<p> The dramatic improvement in information and communication technology (ICT) has made an evolution in learning management systems (LMS). The rapid growth in LMSs has caused users to demand more advanced, automated, and intelligent services. CourseNetworking is a next-generation LMS adopting machine learning to add personalization, gamification, and more dynamics to the system. This work tries to come up with two recommender systems that can help improve CourseNetworking services. The first one is a social recommender system helping CourseNetworking to track user interests and give more relevant recommendations. Recently, graph neural network (GNN) techniques have been employed in social recommender systems due to their high success in graph representation learning, including social network graphs. Despite the rapid advances in recommender systems performance, dealing with the dynamic property of the social network data is one of the key challenges that is remained to be addressed. In this research, a novel method is presented that provides social recommendations by incorporating the dynamic property of social network data in a heterogeneous graph by supplementing the graph with time span nodes that are used to define users long-term and short-term preferences over time. The second service that is proposed to add to Rumi services is a hashtag recommendation system that can help users label their posts quickly resulting in improved searchability of content. In recent years, several hashtag recommendation methods are proposed and developed to speed up processing of the texts and quickly find out the critical phrases. The methods use different approaches and techniques to obtain critical information from a large amount of data. This work investigates the efficiency of unsupervised keyword extraction methods for hashtag recommendation and recommends the one with the best performance to use in a hashtag recommender system. </p>

<p>Graph representation learning (GRL) has been increasing used to model and understand data from a wide variety of complex systems spanning social, technological, bio-chemical and physical domains. GRL consists of two main components (1) a parametrized encoder that provides representations of graph data and (2) a learning process to train the encoder parameters. Designing flexible encoders that capture the underlying invariances and characteristics of graph data are crucial to the success of GRL. On the other hand, the learning process drives the quality of the encoder representations and developing principled learning mechanisms are vital for a number of growing applications in self-supervised, transfer and federated learning settings. To this end, we propose a suite of models and learning algorithms for GRL which form the two main thrusts of this dissertation.</p> <p><br></p> <p>In Thrust I, we propose two novel encoders which build upon on a widely popular GRL encoder class called graph neural networks (GNNs). First, we empirically study the prediction performance of current GNN based encoders when applied to graphs with heterogeneous node mixing patterns using our proposed notion of local assortativity. We find that GNN performance in node prediction tasks strongly correlates with our local assortativity metric---thereby introducing a limit. We propose to transform the input graph into a computation graph with proximity and structural information as distinct types of edges. We then propose a novel GNN based encoder that operates on this computation graph and adaptively chooses between structure and proximity information. Empirically, adopting our transformation and encoder framework leads to improved node classification performance compared to baselines in real-world graphs that exhibit diverse mixing.</p> <p>Secondly, we study the trade-off between expressivity and efficiency of GNNs when applied to temporal graphs for the task of link ranking. We develop an encoder that incorporates a labeling approach designed to allow for efficient inference over the candidate set jointly, while provably boosting expressivity. We also propose to optimize a list-wise loss for improved ranking. With extensive evaluation on real-world temporal graphs, we demonstrate its improved performance and efficiency compared to baselines.</p> <p><br></p> <p>In Thrust II, we propose two principled encoder learning mechanisms for challenging and realistic graph data settings. First, we consider a scenario where only limited or even no labelled data is available for GRL. Recent research has converged on graph contrastive learning (GCL), where GNNs are trained to maximize the correspondence between representations of the same graph in its different augmented forms. However, we find that GNNs trained by traditional GCL often risk capturing redundant graph features and thus may be brittle and provide sub-par performance in downstream tasks. We then propose a novel principle, termed adversarial-GCL (AD-GCL), which enables GNNs to avoid capturing redundant information during the training by optimizing adversarial graph augmentation strategies used in GCL. We pair AD-GCL with theoretical explanations and design a practical instantiation based on trainable edge-dropping graph augmentation. We experimentally validate AD-GCL by comparing with state-of-the-art GCL methods and achieve performance gains in semi-supervised, unsupervised and transfer learning settings using benchmark chemical and biological molecule datasets. </p> <p>Secondly, we consider a scenario where graph data is silo-ed across clients for GRL. We focus on two unique challenges encountered when applying distributed training to GRL: (i) client task heterogeneity and (ii) label scarcity. We propose a novel learning framework called federated self-supervised graph learning (FedSGL), which first utilizes a self-supervised objective to train GNNs in a federated fashion across clients and then, each client fine-tunes the obtained GNNs based on its local task and available labels. Our framework enables the federated GNN model to extract patterns from the common feature (attribute and graph topology) space without the need of labels or being biased by heterogeneous local tasks. Extensive empirical study of FedSGL on both node and graph classification tasks yields fruitful insights into how the level of feature / task heterogeneity, the adopted federated algorithm and the level of label scarcity affects the clients’ performance in their tasks.</p>

In recent biomedical research, graph representation learning and cell profiling techniques have emerged as transformative tools for analyzing high-dimensional biological data. The integration of these methods, as investigated in this study, has facilitated an enhanced understanding of complex biological systems, consequently improving drug discovery. The research aimed to decipher connections between chemical structures and cellular phenotypes while incorporating other biological information like proteins and pathways into the workflow. To achieve this, machine learning models' efficacy was examined for classification and regression tasks. The newly proposed graph-level and bio-graph integrative predictors were compared with traditional models. Results demonstrated their potential, particularly in classification tasks. Moreover, the topology of the COVID-19 BioGraph was analyzed, revealing the complex interconnections between chemicals, proteins, and biological pathways. By combining network analysis, graph representation learning, and statistical methods, the study was able to predict active chemical combinations within inactive compounds, thereby exhibiting significant potential for further investigations. Graph-based generative models were also used for molecule generation opening up further research avenues in finding lead compounds. In conclusion, this study underlines the potential of combining graph representation learning and cell profiling techniques in advancing biomedical research in drug repurposing and drug combination. This integration provides a better understanding of complex biological systems, assists in identifying therapeutic targets, and contributes to optimizing molecule generation for drug discovery. Future investigations should optimize these models and validate the drug combination discovery approach. As these techniques continue to evolve, they hold the potential to significantly impact the future of drug screening, drug repurposing, and drug combinations.

<p>Artificial neural networks (ANNs) have achieved extraordinary performance in various domains in recent years. However, some studies reveal that ANNs may be vulnerable in three aspects: label scarcity, perturbations, and open-set emerging classes. Noisy labeling and self-supervised learning approaches address the label scarcity issues, but most of the work couldn't handle the perturbations. Adversarial training methods, topological denoising methods, and mechanism designing methods aim to mitigate the negative effects caused by perturbations. However, adversarial training methods can barely train a robust model under the circumstance of extensive label scarcity; topological denoising methods are not efficient on dynamic data structures; and mechanism designing methods often depend on heuristic explorations. Detection-based methods devote to identifying novel or anomaly instances for further downstream tasks. Nonetheless, such instances may belong to open-set new emerging classes. To embrace the aforementioned challenges, we address the robustness issues of ANNs from two aspects. First, we propose a series of Bayesian label transition models to improve the robustness of Graph Neural Networks (GNNs) in the presence of label scarcity and perturbations in the graph domain. Second, we propose a new non-exhaustive learning model, named NE-GM-GAN, to handle both open-set problems and class-imbalance issues in network intrusion datasets. Extensive experiments with several datasets demonstrate that our proposed models can effectively improve the robustness of ANNs.</p>