Universal Normalization Enhanced Graph Representation Learning for Gene Network Prediction

Effective gene network representation learning is of great importance in bioinformatics to predict/understand the relation of gene profiles and disease phenotypes. Though graph neural networks (GNNs) have been the dominant architecture for analyzing various graph-structured data like social networks, their predicting on gene networks often exhibits subpar performance. In this paper, we formally investigate the gene network representation learning problem and characterize a notion of \textit{universal graph normalization}, where graph normalization can be applied in an universal manner to maximize the expressive power of GNNs while maintaining the stability. We propose a novel UNGNN (Universal Normalized GNN) framework, which leverages universal graph normalization in both the message passing phase and readout layer to enhance the performance of a base GNN. UNGNN has a plug-and-play property and can be combined with any GNN backbone in practice. A comprehensive set of experiments on gene-network-based bioinformatical tasks demonstrates that our UNGNN model significantly outperforms popular GNN benchmarks and provides an overall performance improvement of 16 $\%$ on average compared to previous state-of-the-art (SOTA) baselines. Furthermore, we also evaluate our theoretical findings on other graph datasets where the universal graph normalization is solvable, and we observe that UNGNN consistently achieves the superior performance

Online Spectral Clustering on Network Streams

Graph is an extremely useful representation of a wide variety of practical systems in data analysis. Recently, with the fast accumulation of stream data from various type of networks, significant research interests have arisen on spectral clustering for network streams (or evolving networks). Compared with the general spectral clustering problem, the data analysis of this new type of problems may have additional requirements, such as short processing time, scalability in distributed computing environments, and temporal variation tracking. However, to design a spectral clustering method to satisfy these requirements certainly presents non-trivial efforts. There are three major challenges for the new algorithm design. The first challenge is online clustering computation. Most of the existing spectral methods on evolving networks are off-line methods, using standard eigensystem solvers such as the Lanczos method. It needs to recompute solutions from scratch at each time point. The second challenge is the parallelization of algorithms. To parallelize such algorithms is non-trivial since standard eigen solvers are iterative algorithms and the number of iterations can not be predetermined. The third challenge is the very limited existing work. In addition, there exists multiple limitations in the existing method, such as computational inefficiency on large similarity changes, the lack of sound theoretical basis, and the lack of effective way to handle accumulated approximate errors and large data variations over time. In this thesis, we proposed a new online spectral graph clustering approach with a family of three novel spectrum approximation algorithms. Our algorithms incrementally update the eigenpairs in an online manner to improve the computational performance. Our approaches outperformed the existing method in computational efficiency and scalability while retaining competitive or even better clustering accuracy. We derived our spectrum approximation techniques GEPT and EEPT through formal theoretical analysis. The well established matrix perturbation theory forms a solid theoretic foundation for our online clustering method. We facilitated our clustering method with a new metric to track accumulated approximation errors and measure the short-term temporal variation. The metric not only provides a balance between computational efficiency and clustering accuracy, but also offers a useful tool to adapt the online algorithm to the condition of unexpected drastic noise. In addition, we discussed our preliminary work on approximate graph mining with evolutionary process, non-stationary Bayesian Network structure learning from non-stationary time series data, and Bayesian Network structure learning with text priors imposed by non-parametric hierarchical topic modeling

Towards a matroid-minor structure theory

This paper surveys recent work that is aimed at generalising the results and techniques of the Graph Minors Project of Robertson and Seymour to matroids