Related papers: An Impossibility Theorem for Node Embedding
Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…
We prove that the problem of deciding whether a 2- or 3-dimensional simplicial complex embeds into $\mathbb{R}^3$ is NP-hard. Our construction also shows that deciding whether a 3-manifold with boundary tori admits an $\mathbb{S}^{3}$…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…
An effective aggregation of node features into a graph-level representation via readout functions is an essential step in numerous learning tasks involving graph neural networks. Typically, readouts are simple and non-adaptive functions…
In this paper, the task of cross-network node classification, which leverages the abundant labeled nodes from a source network to help classify unlabeled nodes in a target network, is studied. The existing domain adaptation algorithms…
Node features bolster graph-based learning when exploited jointly with network structure. However, a lack of nodal attributes is prevalent in graph data. We present a framework to recover completely missing node features for a set of…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
Deep learning methods in the literature are commonly benchmarked on image data sets, which may not be suitable or effective baselines for non-image tabular data. In this paper, we take a data-centric view to perform one of the first studies…
Temporal networks are an important type of network whose topological structure changes over time. Compared with methods on static networks, temporal network embedding (TNE) methods are facing three challenges: 1) it cannot describe the…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
Graph homomorphism counts, first explored by Lov\'asz in 1967, have recently garnered interest as a powerful tool in graph-based machine learning. Grohe (PODS 2020) proposed the theoretical foundations for using homomorphism counts in…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context…
Network embedding has recently attracted lots of attentions in data mining. Existing network embedding methods mainly focus on networks with pairwise relationships. In real world, however, the relationships among data points could go beyond…
Network representation learning (NRL) advances the conventional graph mining of social networks, knowledge graphs, and complex biomedical and physics information networks. Over dozens of network representation learning algorithms have been…
Network embedding methods map a network's nodes to vectors in an embedding space, in such a way that these representations are useful for estimating some notion of similarity or proximity between pairs of nodes in the network. The quality…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of…
While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of…