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In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
Word embeddings -- distributed representations of words -- in deep learning are beneficial for many tasks in natural language processing (NLP). However, different embedding sets vary greatly in quality and characteristics of the captured…
Large-scale multi-relational embedding refers to the task of learning the latent representations for entities and relations in large knowledge graphs. An effective and scalable solution for this problem is crucial for the true success of…
Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and…
We show an analog to the Fast Johnson-Lindenstrauss Transform for Nearest Neighbor Preserving Embeddings in $\ell_2$. These are sparse, randomized embeddings that preserve the (approximate) nearest neighbors. The dimensionality of the…
Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of…
Modern AI is opening the door to collective decision-making in which participants express their views as free-form text rather than voting on a fixed set of candidates. A natural idea is to embed these opinions in a vector space so that the…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the…
Representation Learning of words and Knowledge Graphs (KG) into low dimensional vector spaces along with its applications to many real-world scenarios have recently gained momentum. In order to make use of multiple KG embeddings for…
Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often…
Knowledge graph embedding models (KGEMs) developed for link prediction learn vector representations for entities in a knowledge graph, known as embeddings. A common tacit assumption is the KGE entity similarity assumption, which states that…
Entity alignment is to find identical entities in different knowledge graphs (KGs) that refer to the same real-world object. Embedding-based entity alignment techniques have been drawing a lot of attention recently because they can help…
Word embeddings learnt from large corpora have been adopted in various applications in natural language processing and served as the general input representations to learning systems. Recently, a series of post-processing methods have been…
We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
This is a draft of a monograph to appear in the Springer series "Encyclopaedia of Mathematical Sciences", subseries "Invariant Theory and Algebraic Transformation Groups". The subject is homogeneous spaces of algebraic groups and their…
There has been an intense recent activity in embedding of very high dimensional and nonlinear data structures, much of it in the data science and machine learning literature. We survey this activity in four parts. In the first part we cover…
We study Goodwillie-Weiss embedding calculus through its relationship with Goodwillie's functor calculus. Specifically, building on a result of Tillmann and Weiss, we construct a functorial complement for \(T_{n}\)-embeddings that takes…