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Person# Effrosyni Simou

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Related research domains (3)

Machine learning

Machine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machin

Graph (abstract data type)

In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics.
A graph data str

Experiment

An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effe

Related publications (5)

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In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph-structured descriptions. In such settings, it is desirable to design representation learning algorithms that can take into account the information captured by the underlying structure. This thesis focuses on providing new methods to ingrain geometrical information in end-to-end deep learning architectures for graphs through the use of elements from Optimal Transport theory.First, we consider the setting where the data can be described by a fixed graph. In this setting, each datapoint corresponds to a node of the graph and the edges among nodes signify their pairwise relations. We propose an autoencoder architecture that consists of a linear layer in the encoder and a novel Wasserstein barycentric layer at the decoder. Our proposed barycentric layer takes into account the underlying geometry through the diffusion distance of the graph and provides a way to obtain structure-aware, non-linear interpolations, which lead to directly interpretable node embeddings that are stable to perturbations of the graph structure. Further, the embeddings obtained with our proposed autoencoder achieve competitive or superior results compared to state-of-the-art methods in node classification tasks.Second, we consider the setting where the data consist of multiple graphs. In that setting, the graphs can be of varying size and, therefore, a global pooling operation is needed in order to obtain representations of fixed size and enable end-to-end learning with deep networks. We propose a global pooling operation that optimally preserves the statistical properties of the representations. In order to do so, we take into account the geometry of the representation space and introduce a global pooling layer that minimizes the Wasserstein distance between a graph representation and its pooled counterpart, of fixed size. This is achieved by performing a Wasserstein gradient flow with respect to the pooled representation. Our proposed method demonstrates promising results in the task of graph classification.Overall, in this thesis we provide new methods for incorporating geometrical information in end-to-end deep learning architectures for graph structured data. We believe that our proposals will contribute to the development of algorithms that learn meaningful representations and that take fully into account the geometry of the data under consideration.

Pascal Frossard, Effrosyni Simou

In order to perform network analysis tasks, representations that capture the most relevant information in the graph structure are needed. However, existing methods learn representations that cannot be interpreted in a straightforward way and that are relatively unstable to perturbations of the graph structure. We address these two limitations by proposing node2coords, a representation learning algorithm for graphs, which learns simultaneously a low-dimensional space and coordinates for the nodes in that space. The patterns that span the low dimensional space reveal the graph's most important structural information. The coordinates of the nodes reveal the proximity of their local structure to the graph structural patterns. We measure this proximity with Wasserstein distances that permit to take into account the properties of the underlying graph. Therefore, we introduce an autoencoder that employs a linear layer in the encoder and a novel Wasserstein barycentric layer at the decoder. Node connectivity descriptors, which capture the local structure of the nodes, are passed through the encoder to learn a small set of graph structural patterns. In the decoder, the node connectivity descriptors are reconstructed as Wasserstein barycenters of the graph structural patterns. The optimal weights for the barycenter representation of a node's connectivity descriptor correspond to the coordinates of that node in the low-dimensional space. Experimental results demonstrate that the representations learned with node2coords are interpretable, lead to node embeddings that are stable to perturbations of the graph structure and achieve competitive or superior results compared to state-of-the-art unsupervised methods in node classification.

In several machine learning tasks for graph structured data, the graphs under consideration may be composed of a varying number of nodes. Therefore, it is necessary to design pooling methods that aggregate the graph representations of varying size to representations of fixed size which can be used in downstream tasks, such as graph classification. Existing graph pooling methods offer no guarantee with regards to the similarity of a graph representation and its pooled version. In this work we address this limitation by proposing FlowPool, a pooling method that optimally preserves the statistics of a graph representation to its pooled counterpart by minimizing their Wasserstein distance. This is achieved by performing a Wasserstein gradient flow with respect to the pooled graph representation. We propose a versatile implementation of our method which can take into account the geometry of the representation space through any ground cost. This implementation relies on the computation of the gradient of the Wasserstein distance with recently proposed implicit differentiation schemes. Our pooling method is amenable to automatic differentiation and can be integrated in end-to-end deep learning architectures. Further, FlowPool is invariant to permutations and can therefore be combined with permutation equivariant feature extraction layers in GNNs in order to obtain predictions that are independent of the ordering of the nodes. Experimental results demonstrate that our method leads to an increase in performance compared to existing pooling methods when evaluated in graph classification tasks.

2021