Download or read book Topological Embeddings written by and published by Academic Press. This book was released on 1973-03-30 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Embeddings

Download or read book Embeddings in Natural Language Processing written by Mohammad Taher Pilehvar and published by Morgan & Claypool Publishers. This book was released on 2020-11-13 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Embeddings have undoubtedly been one of the most influential research areas in Natural Language Processing (NLP). Encoding information into a low-dimensional vector representation, which is easily integrable in modern machine learning models, has played a central role in the development of NLP. Embedding techniques initially focused on words, but the attention soon started to shift to other forms: from graph structures, such as knowledge bases, to other types of textual content, such as sentences and documents. This book provides a high-level synthesis of the main embedding techniques in NLP, in the broad sense. The book starts by explaining conventional word vector space models and word embeddings (e.g., Word2Vec and GloVe) and then moves to other types of embeddings, such as word sense, sentence and document, and graph embeddings. The book also provides an overview of recent developments in contextualized representations (e.g., ELMo and BERT) and explains their potential in NLP. Throughout the book, the reader can find both essential information for understanding a certain topic from scratch and a broad overview of the most successful techniques developed in the literature.

Download or read book Cross Lingual Word Embeddings written by Anders Søgaard and published by Springer Nature. This book was released on 2022-05-31 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of natural language processing (NLP) is English language processing, and while there is good language technology support for (standard varieties of) English, support for Albanian, Burmese, or Cebuano--and most other languages--remains limited. Being able to bridge this digital divide is important for scientific and democratic reasons but also represents an enormous growth potential. A key challenge for this to happen is learning to align basic meaning-bearing units of different languages. In this book, the authors survey and discuss recent and historical work on supervised and unsupervised learning of such alignments. Specifically, the book focuses on so-called cross-lingual word embeddings. The survey is intended to be systematic, using consistent notation and putting the available methods on comparable form, making it easy to compare wildly different approaches. In so doing, the authors establish previously unreported relations between these methods and are able to present a fast-growing literature in a very compact way. Furthermore, the authors discuss how best to evaluate cross-lingual word embedding methods and survey the resources available for students and researchers interested in this topic.

Download or read book Geometry of Semilinear Embeddings written by Mark Pankov and published by World Scientific. This book was released on 2015-05-28 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians. In contrast to classical books, we consider a more general class of semilinear mappings and show that this class is important. A large portion of the material will be formulated in terms of graph theory, that is, Grassmann graphs, graph embeddings, and isometric embeddings. In addition, some relations to linear codes will be described. Graduate students and researchers will find this volume to be self-contained with many examples. Contents:Semilinear Mappings:Division Rings and Their HomomorphismsVector Spaces Over Division RingsSemilinear MappingsSemilinear EmbeddingsMappings of Grassmannians Induced by Semilinear EmbeddingsKreuzer's ExampleDualityCharacterization of Strong Semilinear EmbeddingsProjective Geometry and Linear Codes:Projective SpacesFundamental Theorem of Projective GeometryProof of Theorem 1.2m-independent Subsets in Projective SpacesPGL-subsetsGeneralized MacWilliams TheoremLinear CodesIsometric Embeddings of Grassmann Graphs:Graph TheoryElementary Properties of Grassmann GraphsEmbeddingsIsometric EmbeddingsProof of Theorem 3.1Equivalence of Isometric EmbeddingsLinearly Rigid Isometric EmbeddingsRemarks on Non-isometric EmbeddingsSome Results Related to Chow's TheoremHuang's TheoremJohnson Graph in Grassmann Graph:Johnson GraphIsometric Embeddings of Johnson Graphs in Grassmann GraphsProof of Theorem 4.2Classification Problem and Relations to Linear CodesCharacterizations of Apartments in Building GrassmanniansCharacterization of Isometric Embeddings:Main Result, Corollaries and RemarksCharacterization of DistanceConnectedness of the Apartment GraphIntersections of J(n, k)-subsets of Different TypesProof of Theorem 5.1Semilinear Mappings of Exterior Powers:Exterior PowersGrassmanniansGrassmann Codes Readership: Graduate students and researchers interested in the field of semilinear embeddings. Keywords:Semilinear Embedding;Grassmannian;Grassmann Graph;Linear Code

Download or read book Embeddings of Decomposition Spaces written by Felix Voigtlaender and published by American Mathematical Society. This book was released on 2023-07-31 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract. https://www.ams.org/bookstore/pspdf/memo-287-1426-abstract.pdf

Download or read book Finding Communities in Social Networks Using Graph Embeddings written by Mosab Alfaqeeh and published by Springer Nature. This book was released on with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Build Powerful Search with Embeddings A Practical Guide to ChromaDB Pinecone written by Anand Vemula and published by Anand Vemula. This book was released on with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Build Powerful Search with Embeddings: A Practical Guide to ChromaDB & Pinecone" is a comprehensive guide that delves into the intricacies of utilizing embeddings for constructing robust search systems, specifically employing ChromaDB and Pinecone technologies. Authored by experts in the field, the book offers practical insights, strategies, and hands-on techniques to harness the full potential of embeddings for enhancing search functionalities. The book begins by elucidating the fundamentals of embeddings, elucidating their significance in transforming raw data into meaningful representations that facilitate efficient search operations. It elucidates how embeddings capture semantic similarities and relationships within data, enabling more accurate and context-aware search results. Central to the book's discourse is the exploration of ChromaDB, a cutting-edge database designed to optimize search operations through embeddings. Readers are guided through the implementation process, learning how to leverage ChromaDB's indexing capabilities to store and retrieve embeddings efficiently. The book provides step-by-step instructions, code snippets, and real-world examples to facilitate comprehension and application. Furthermore, the book introduces Pinecone, a powerful vector database that seamlessly integrates with ChromaDB to deliver high-performance search functionalities at scale. Readers are introduced to Pinecone's features, including its ability to handle dynamic embeddings and support real-time updates, ensuring search systems remain responsive and adaptive to evolving data. One of the book's key strengths lies in its emphasis on practicality. It offers actionable insights and best practices for optimizing search performance, addressing common challenges such as handling large datasets, managing dimensionality, and fine-tuning search parameters. Through case studies and use cases, readers gain valuable insights into real-world applications of embedding-based search systems across various domains. Moreover, the book explores advanced topics such as semantic search, similarity learning, and hybrid search architectures, empowering readers to customize and extend their search systems according to specific requirements and use cases. In summary, "Build Powerful Search with Embeddings: A Practical Guide to ChromaDB & Pinecone" equips readers with the knowledge and tools necessary to harness the transformative potential of embeddings for building advanced search systems. Whether you're a seasoned developer or a data scientist, this book serves as an invaluable resource for mastering embedding-based search technologies and unlocking new possibilities in information retrieval.

Download or read book Differential and Complex Geometry Origins Abstractions and Embeddings written by Raymond O. Wells, Jr. and published by Springer. This book was released on 2017-08-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth-century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash. Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.

Download or read book Hardy Operators Function Spaces and Embeddings written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains. This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.

Download or read book Embeddings and Extensions in Analysis written by J.H. Wells and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this book is a presentation of the major results relating to two geometrically inspired problems in analysis. One is that of determining which metric spaces can be isometrically embedded in a Hilbert space or, more generally, P in an L space; the other asks for conditions on a pair of metric spaces which will ensure that every contraction or every Lipschitz-Holder map from a subset of X into Y is extendable to a map of the same type from X into Y. The initial work on isometric embedding was begun by K. Menger [1928] with his metric investigations of Euclidean geometries and continued, in its analytical formulation, by I. J. Schoenberg [1935] in a series of papers of classical elegance. The problem of extending Lipschitz-Holder and contraction maps was first treated by E. J. McShane and M. D. Kirszbraun [1934]. Following a period of relative inactivity, attention was again drawn to these two problems by G. Minty's work on non-linear monotone operators in Hilbert space [1962]; by S. Schonbeck's fundamental work in characterizing those pairs (X,Y) of Banach spaces for which extension of contractions is always possible [1966]; and by the generalization of many of Schoenberg's embedding theorems to the P setting of L spaces by Bretagnolle, Dachuna Castelle and Krivine [1966].

Download or read book Network Embedding written by Cheng Cheng Yang and published by Springer Nature. This book was released on 2022-05-31 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: heterogeneous graphs. Further, the book introduces different applications of NE such as recommendation and information diffusion prediction. Finally, the book concludes the methods and applications and looks forward to the future directions.

Download or read book Embedding Knowledge Graphs with RDF2vec written by Heiko Paulheim and published by Springer Nature. This book was released on 2023-06-03 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the ideas behind one of the most well-known methods for knowledge graph embedding of transformations to compute vector representations from a graph, known as RDF2vec. The authors describe its usage in practice, from reusing pre-trained knowledge graph embeddings to training tailored vectors for a knowledge graph at hand. They also demonstrate different extensions of RDF2vec and how they affect not only the downstream performance, but also the expressivity of the resulting vector representation, and analyze the resulting vector spaces and the semantic properties they encode.

Download or read book Supervised Machine Learning for Text Analysis in R written by Emil Hvitfeldt and published by CRC Press. This book was released on 2021-10-22 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Text data is important for many domains, from healthcare to marketing to the digital humanities, but specialized approaches are necessary to create features for machine learning from language. Supervised Machine Learning for Text Analysis in R explains how to preprocess text data for modeling, train models, and evaluate model performance using tools from the tidyverse and tidymodels ecosystem. Models like these can be used to make predictions for new observations, to understand what natural language features or characteristics contribute to differences in the output, and more. If you are already familiar with the basics of predictive modeling, use the comprehensive, detailed examples in this book to extend your skills to the domain of natural language processing. This book provides practical guidance and directly applicable knowledge for data scientists and analysts who want to integrate unstructured text data into their modeling pipelines. Learn how to use text data for both regression and classification tasks, and how to apply more straightforward algorithms like regularized regression or support vector machines as well as deep learning approaches. Natural language must be dramatically transformed to be ready for computation, so we explore typical text preprocessing and feature engineering steps like tokenization and word embeddings from the ground up. These steps influence model results in ways we can measure, both in terms of model metrics and other tangible consequences such as how fair or appropriate model results are.

Download or read book Embedding Problems in Symplectic Geometry written by Felix Schlenk and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.

Download or read book Graph Embedding Methods for Multiple Omics Data Analysis written by Chen Qingfeng and published by Frontiers Media SA. This book was released on 2021-11-08 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Embedding Artificial Intelligence into ERP Software written by Siar Sarferaz and published by Springer Nature. This book was released on with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Disc Embedding Theorem written by Stefan Behrens and published by Oxford University Press. This book was released on 2021-07-15 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on Fields medal winning work of Michael Freedman, this book explores the disc embedding theorem for 4-dimensional manifolds. This theorem underpins virtually all our understanding of topological 4-manifolds. Most famously, this includes the 4-dimensional Poincaré conjecture in the topological category. The Disc Embedding Theorem contains the first thorough and approachable exposition of Freedman's proof of the disc embedding theorem, with many new details. A self-contained account of decomposition space theory, a beautiful but outmoded branch of topology that produces non-differentiable homeomorphisms between manifolds, is provided, as well as a stand-alone interlude that explains the disc embedding theorem's key role in all known homeomorphism classifications of 4-manifolds via surgery theory and the s-cobordism theorem. Additionally, the ramifications of the disc embedding theorem within the study of topological 4-manifolds, for example Frank Quinn's development of fundamental tools like transversality are broadly described. The book is written for mathematicians, within the subfield of topology, specifically interested in the study of 4-dimensional spaces, and includes numerous professionally rendered figures.