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Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called…

We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear…

Recently, several clustering algorithms have been used to solve variety of problems from different discipline. This dissertation aims to address different challenging tasks in computer vision and pattern recognition by casting the problems…

Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based $\gamma$-quasi-clique model offers a flexible alternative by…

Combinatorial optimization problems are encountered in many practical contexts such as logistics and production, but exact solutions are particularly difficult to find and usually NP-hard for considerable problem sizes. To compute…

A popular paradigm for 3D point cloud registration is by extracting 3D keypoint correspondences, then estimating the registration function from the correspondences using a robust algorithm. However, many existing 3D keypoint techniques tend…

Message Passing Neural Networks (MPNNs) are a staple of graph machine learning. MPNNs iteratively update each node's representation in an input graph by aggregating messages from the node's neighbors, which necessitates a memory complexity…

Named entity discovery (NED) is an important information retrieval problem that can be decomposed into two sub-problems. The first sub-problem, named entity recognition (NER), aims to tag pre-defined sets of words in a vocabulary (called…

We introduce a mixed integer program (MIP) for assigning importance scores to each neuron in deep neural network architectures which is guided by the impact of their simultaneous pruning on the main learning task of the network. By…

Graph convolutional networks (GCNs) have achieved promising performance on various graph-based tasks. However they suffer from over-smoothing when stacking more layers. In this paper, we present a quantitative study on this observation and…

In this paper, we propose a learning-based image fragment pair-searching and -matching approach to solve the challenging restoration problem. Existing works use rule-based methods to match similar contour shapes or textures, which are…

Matching local features across images is a fundamental problem in computer vision. Targeting towards high accuracy and efficiency, we propose Seeded Graph Matching Network, a graph neural network with sparse structure to reduce redundant…

A physics-informed machine learning framework based on holomorphic neural networks is introduced for detecting cracks in two-dimensional solids from strain or displacement data. Crack detection is formulated as an inverse problem in which…

Recovering an image from a noisy observation is a key problem in signal processing. Recently, it has been shown that data-driven approaches employing convolutional neural networks can outperform classical model-based techniques, because…

Critical nodes in networks are extremely vulnerable to malicious attacks to trigger negative cascading events such as the spread of misinformation and diseases. Therefore, effective moderation of critical nodes is very vital for mitigating…

Community detection refers to the task of discovering closely related subgraphs to understand the networks. However, traditional community detection algorithms fail to pinpoint a particular kind of community. This limits its applicability…

Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…

Graph Convolutional Networks (GCNs) have received increasing attention in the machine learning community for effectively leveraging both the content features of nodes and the linkage patterns across graphs in various applications. As…

Mining dense subgraphs on multi-layer graphs is an interesting problem, which has witnessed lots of applications in practice. To overcome the limitations of the quasi-clique-based approach, we propose d-coherent core (d-CC), a new notion of…