Author: Claudio Stamile
Publisher: Packt Publishing Ltd
ISBN: 1800206755
Category : Computers
Languages : en
Pages : 338
Book Description
Build machine learning algorithms using graph data and efficiently exploit topological information within your models Key Features Implement machine learning techniques and algorithms in graph data Identify the relationship between nodes in order to make better business decisions Apply graph-based machine learning methods to solve real-life problems Book Description Graph Machine Learning will introduce you to a set of tools used for processing network data and leveraging the power of the relation between entities that can be used for predictive, modeling, and analytics tasks. The first chapters will introduce you to graph theory and graph machine learning, as well as the scope of their potential use. You'll then learn all you need to know about the main machine learning models for graph representation learning: their purpose, how they work, and how they can be implemented in a wide range of supervised and unsupervised learning applications. You'll build a complete machine learning pipeline, including data processing, model training, and prediction in order to exploit the full potential of graph data. After covering the basics, you'll be taken through real-world scenarios such as extracting data from social networks, text analytics, and natural language processing (NLP) using graphs and financial transaction systems on graphs. You'll also learn how to build and scale out data-driven applications for graph analytics to store, query, and process network information, and explore the latest trends on graphs. By the end of this machine learning book, you will have learned essential concepts of graph theory and all the algorithms and techniques used to build successful machine learning applications. What you will learn Write Python scripts to extract features from graphs Distinguish between the main graph representation learning techniques Learn how to extract data from social networks, financial transaction systems, for text analysis, and more Implement the main unsupervised and supervised graph embedding techniques Get to grips with shallow embedding methods, graph neural networks, graph regularization methods, and more Deploy and scale out your application seamlessly Who this book is for This book is for data scientists, data analysts, graph analysts, and graph professionals who want to leverage the information embedded in the connections and relations between data points to boost their analysis and model performance using machine learning. It will also be useful for machine learning developers or anyone who wants to build ML-driven graph databases. A beginner-level understanding of graph databases and graph data is required, alongside a solid understanding of ML basics. You'll also need intermediate-level Python programming knowledge to get started with this book.
Graph Machine Learning
Author: Claudio Stamile
Publisher: Packt Publishing Ltd
ISBN: 1800206755
Category : Computers
Languages : en
Pages : 338
Book Description
Build machine learning algorithms using graph data and efficiently exploit topological information within your models Key Features Implement machine learning techniques and algorithms in graph data Identify the relationship between nodes in order to make better business decisions Apply graph-based machine learning methods to solve real-life problems Book Description Graph Machine Learning will introduce you to a set of tools used for processing network data and leveraging the power of the relation between entities that can be used for predictive, modeling, and analytics tasks. The first chapters will introduce you to graph theory and graph machine learning, as well as the scope of their potential use. You'll then learn all you need to know about the main machine learning models for graph representation learning: their purpose, how they work, and how they can be implemented in a wide range of supervised and unsupervised learning applications. You'll build a complete machine learning pipeline, including data processing, model training, and prediction in order to exploit the full potential of graph data. After covering the basics, you'll be taken through real-world scenarios such as extracting data from social networks, text analytics, and natural language processing (NLP) using graphs and financial transaction systems on graphs. You'll also learn how to build and scale out data-driven applications for graph analytics to store, query, and process network information, and explore the latest trends on graphs. By the end of this machine learning book, you will have learned essential concepts of graph theory and all the algorithms and techniques used to build successful machine learning applications. What you will learn Write Python scripts to extract features from graphs Distinguish between the main graph representation learning techniques Learn how to extract data from social networks, financial transaction systems, for text analysis, and more Implement the main unsupervised and supervised graph embedding techniques Get to grips with shallow embedding methods, graph neural networks, graph regularization methods, and more Deploy and scale out your application seamlessly Who this book is for This book is for data scientists, data analysts, graph analysts, and graph professionals who want to leverage the information embedded in the connections and relations between data points to boost their analysis and model performance using machine learning. It will also be useful for machine learning developers or anyone who wants to build ML-driven graph databases. A beginner-level understanding of graph databases and graph data is required, alongside a solid understanding of ML basics. You'll also need intermediate-level Python programming knowledge to get started with this book.
Publisher: Packt Publishing Ltd
ISBN: 1800206755
Category : Computers
Languages : en
Pages : 338
Book Description
Build machine learning algorithms using graph data and efficiently exploit topological information within your models Key Features Implement machine learning techniques and algorithms in graph data Identify the relationship between nodes in order to make better business decisions Apply graph-based machine learning methods to solve real-life problems Book Description Graph Machine Learning will introduce you to a set of tools used for processing network data and leveraging the power of the relation between entities that can be used for predictive, modeling, and analytics tasks. The first chapters will introduce you to graph theory and graph machine learning, as well as the scope of their potential use. You'll then learn all you need to know about the main machine learning models for graph representation learning: their purpose, how they work, and how they can be implemented in a wide range of supervised and unsupervised learning applications. You'll build a complete machine learning pipeline, including data processing, model training, and prediction in order to exploit the full potential of graph data. After covering the basics, you'll be taken through real-world scenarios such as extracting data from social networks, text analytics, and natural language processing (NLP) using graphs and financial transaction systems on graphs. You'll also learn how to build and scale out data-driven applications for graph analytics to store, query, and process network information, and explore the latest trends on graphs. By the end of this machine learning book, you will have learned essential concepts of graph theory and all the algorithms and techniques used to build successful machine learning applications. What you will learn Write Python scripts to extract features from graphs Distinguish between the main graph representation learning techniques Learn how to extract data from social networks, financial transaction systems, for text analysis, and more Implement the main unsupervised and supervised graph embedding techniques Get to grips with shallow embedding methods, graph neural networks, graph regularization methods, and more Deploy and scale out your application seamlessly Who this book is for This book is for data scientists, data analysts, graph analysts, and graph professionals who want to leverage the information embedded in the connections and relations between data points to boost their analysis and model performance using machine learning. It will also be useful for machine learning developers or anyone who wants to build ML-driven graph databases. A beginner-level understanding of graph databases and graph data is required, alongside a solid understanding of ML basics. You'll also need intermediate-level Python programming knowledge to get started with this book.
Graph Representation Learning
Author: William L. William L. Hamilton
Publisher: Springer Nature
ISBN: 3031015886
Category : Computers
Languages : en
Pages : 141
Book Description
Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Publisher: Springer Nature
ISBN: 3031015886
Category : Computers
Languages : en
Pages : 141
Book Description
Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Graph-Powered Machine Learning
Author: Alessandro Negro
Publisher: Simon and Schuster
ISBN: 163835393X
Category : Computers
Languages : en
Pages : 494
Book Description
Upgrade your machine learning models with graph-based algorithms, the perfect structure for complex and interlinked data. Summary In Graph-Powered Machine Learning, you will learn: The lifecycle of a machine learning project Graphs in big data platforms Data source modeling using graphs Graph-based natural language processing, recommendations, and fraud detection techniques Graph algorithms Working with Neo4J Graph-Powered Machine Learning teaches to use graph-based algorithms and data organization strategies to develop superior machine learning applications. You’ll dive into the role of graphs in machine learning and big data platforms, and take an in-depth look at data source modeling, algorithm design, recommendations, and fraud detection. Explore end-to-end projects that illustrate architectures and help you optimize with best design practices. Author Alessandro Negro’s extensive experience shines through in every chapter, as you learn from examples and concrete scenarios based on his work with real clients! Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Identifying relationships is the foundation of machine learning. By recognizing and analyzing the connections in your data, graph-centric algorithms like K-nearest neighbor or PageRank radically improve the effectiveness of ML applications. Graph-based machine learning techniques offer a powerful new perspective for machine learning in social networking, fraud detection, natural language processing, and recommendation systems. About the book Graph-Powered Machine Learning teaches you how to exploit the natural relationships in structured and unstructured datasets using graph-oriented machine learning algorithms and tools. In this authoritative book, you’ll master the architectures and design practices of graphs, and avoid common pitfalls. Author Alessandro Negro explores examples from real-world applications that connect GraphML concepts to real world tasks. What's inside Graphs in big data platforms Recommendations, natural language processing, fraud detection Graph algorithms Working with the Neo4J graph database About the reader For readers comfortable with machine learning basics. About the author Alessandro Negro is Chief Scientist at GraphAware. He has been a speaker at many conferences, and holds a PhD in Computer Science. Table of Contents PART 1 INTRODUCTION 1 Machine learning and graphs: An introduction 2 Graph data engineering 3 Graphs in machine learning applications PART 2 RECOMMENDATIONS 4 Content-based recommendations 5 Collaborative filtering 6 Session-based recommendations 7 Context-aware and hybrid recommendations PART 3 FIGHTING FRAUD 8 Basic approaches to graph-powered fraud detection 9 Proximity-based algorithms 10 Social network analysis against fraud PART 4 TAMING TEXT WITH GRAPHS 11 Graph-based natural language processing 12 Knowledge graphs
Publisher: Simon and Schuster
ISBN: 163835393X
Category : Computers
Languages : en
Pages : 494
Book Description
Upgrade your machine learning models with graph-based algorithms, the perfect structure for complex and interlinked data. Summary In Graph-Powered Machine Learning, you will learn: The lifecycle of a machine learning project Graphs in big data platforms Data source modeling using graphs Graph-based natural language processing, recommendations, and fraud detection techniques Graph algorithms Working with Neo4J Graph-Powered Machine Learning teaches to use graph-based algorithms and data organization strategies to develop superior machine learning applications. You’ll dive into the role of graphs in machine learning and big data platforms, and take an in-depth look at data source modeling, algorithm design, recommendations, and fraud detection. Explore end-to-end projects that illustrate architectures and help you optimize with best design practices. Author Alessandro Negro’s extensive experience shines through in every chapter, as you learn from examples and concrete scenarios based on his work with real clients! Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Identifying relationships is the foundation of machine learning. By recognizing and analyzing the connections in your data, graph-centric algorithms like K-nearest neighbor or PageRank radically improve the effectiveness of ML applications. Graph-based machine learning techniques offer a powerful new perspective for machine learning in social networking, fraud detection, natural language processing, and recommendation systems. About the book Graph-Powered Machine Learning teaches you how to exploit the natural relationships in structured and unstructured datasets using graph-oriented machine learning algorithms and tools. In this authoritative book, you’ll master the architectures and design practices of graphs, and avoid common pitfalls. Author Alessandro Negro explores examples from real-world applications that connect GraphML concepts to real world tasks. What's inside Graphs in big data platforms Recommendations, natural language processing, fraud detection Graph algorithms Working with the Neo4J graph database About the reader For readers comfortable with machine learning basics. About the author Alessandro Negro is Chief Scientist at GraphAware. He has been a speaker at many conferences, and holds a PhD in Computer Science. Table of Contents PART 1 INTRODUCTION 1 Machine learning and graphs: An introduction 2 Graph data engineering 3 Graphs in machine learning applications PART 2 RECOMMENDATIONS 4 Content-based recommendations 5 Collaborative filtering 6 Session-based recommendations 7 Context-aware and hybrid recommendations PART 3 FIGHTING FRAUD 8 Basic approaches to graph-powered fraud detection 9 Proximity-based algorithms 10 Social network analysis against fraud PART 4 TAMING TEXT WITH GRAPHS 11 Graph-based natural language processing 12 Knowledge graphs
Deep Learning on Graphs
Author: Yao Ma
Publisher: Cambridge University Press
ISBN: 1108831745
Category : Computers
Languages : en
Pages : 339
Book Description
A comprehensive text on foundations and techniques of graph neural networks with applications in NLP, data mining, vision and healthcare.
Publisher: Cambridge University Press
ISBN: 1108831745
Category : Computers
Languages : en
Pages : 339
Book Description
A comprehensive text on foundations and techniques of graph neural networks with applications in NLP, data mining, vision and healthcare.
Graph Neural Networks: Foundations, Frontiers, and Applications
Author: Lingfei Wu
Publisher: Springer Nature
ISBN: 9811660549
Category : Computers
Languages : en
Pages : 701
Book Description
Deep Learning models are at the core of artificial intelligence research today. It is well known that deep learning techniques are disruptive for Euclidean data, such as images or sequence data, and not immediately applicable to graph-structured data such as text. This gap has driven a wave of research for deep learning on graphs, including graph representation learning, graph generation, and graph classification. The new neural network architectures on graph-structured data (graph neural networks, GNNs in short) have performed remarkably on these tasks, demonstrated by applications in social networks, bioinformatics, and medical informatics. Despite these successes, GNNs still face many challenges ranging from the foundational methodologies to the theoretical understandings of the power of the graph representation learning. This book provides a comprehensive introduction of GNNs. It first discusses the goals of graph representation learning and then reviews the history, current developments, and future directions of GNNs. The second part presents and reviews fundamental methods and theories concerning GNNs while the third part describes various frontiers that are built on the GNNs. The book concludes with an overview of recent developments in a number of applications using GNNs. This book is suitable for a wide audience including undergraduate and graduate students, postdoctoral researchers, professors and lecturers, as well as industrial and government practitioners who are new to this area or who already have some basic background but want to learn more about advanced and promising techniques and applications.
Publisher: Springer Nature
ISBN: 9811660549
Category : Computers
Languages : en
Pages : 701
Book Description
Deep Learning models are at the core of artificial intelligence research today. It is well known that deep learning techniques are disruptive for Euclidean data, such as images or sequence data, and not immediately applicable to graph-structured data such as text. This gap has driven a wave of research for deep learning on graphs, including graph representation learning, graph generation, and graph classification. The new neural network architectures on graph-structured data (graph neural networks, GNNs in short) have performed remarkably on these tasks, demonstrated by applications in social networks, bioinformatics, and medical informatics. Despite these successes, GNNs still face many challenges ranging from the foundational methodologies to the theoretical understandings of the power of the graph representation learning. This book provides a comprehensive introduction of GNNs. It first discusses the goals of graph representation learning and then reviews the history, current developments, and future directions of GNNs. The second part presents and reviews fundamental methods and theories concerning GNNs while the third part describes various frontiers that are built on the GNNs. The book concludes with an overview of recent developments in a number of applications using GNNs. This book is suitable for a wide audience including undergraduate and graduate students, postdoctoral researchers, professors and lecturers, as well as industrial and government practitioners who are new to this area or who already have some basic background but want to learn more about advanced and promising techniques and applications.
Graph Algorithms for Data Science
Author: Tomaž Bratanic
Publisher: Simon and Schuster
ISBN: 1617299464
Category : Computers
Languages : en
Pages : 350
Book Description
Graph Algorithms for Data Science teaches you how to construct graphs from both structured and unstructured data. You'll learn how the flexible Cypher query language can be used to easily manipulate graph structures, and extract amazing insights. Graph Algorithms for Data Science is a hands-on guide to working with graph-based data in applications. It's filled with fascinating and fun projects, demonstrating the ins-and-outs of graphs. You'll gain practical skills by analyzing Twitter, building graphs with NLP techniques, and much more. These powerful graph algorithms are explained in clear, jargon-free text and illustrations that makes them easy to apply to your own projects.
Publisher: Simon and Schuster
ISBN: 1617299464
Category : Computers
Languages : en
Pages : 350
Book Description
Graph Algorithms for Data Science teaches you how to construct graphs from both structured and unstructured data. You'll learn how the flexible Cypher query language can be used to easily manipulate graph structures, and extract amazing insights. Graph Algorithms for Data Science is a hands-on guide to working with graph-based data in applications. It's filled with fascinating and fun projects, demonstrating the ins-and-outs of graphs. You'll gain practical skills by analyzing Twitter, building graphs with NLP techniques, and much more. These powerful graph algorithms are explained in clear, jargon-free text and illustrations that makes them easy to apply to your own projects.
Knowledge Graphs
Author: Mayank Kejriwal
Publisher: MIT Press
ISBN: 0262045095
Category : Computers
Languages : en
Pages : 559
Book Description
A rigorous and comprehensive textbook covering the major approaches to knowledge graphs, an active and interdisciplinary area within artificial intelligence. The field of knowledge graphs, which allows us to model, process, and derive insights from complex real-world data, has emerged as an active and interdisciplinary area of artificial intelligence over the last decade, drawing on such fields as natural language processing, data mining, and the semantic web. Current projects involve predicting cyberattacks, recommending products, and even gleaning insights from thousands of papers on COVID-19. This textbook offers rigorous and comprehensive coverage of the field. It focuses systematically on the major approaches, both those that have stood the test of time and the latest deep learning methods.
Publisher: MIT Press
ISBN: 0262045095
Category : Computers
Languages : en
Pages : 559
Book Description
A rigorous and comprehensive textbook covering the major approaches to knowledge graphs, an active and interdisciplinary area within artificial intelligence. The field of knowledge graphs, which allows us to model, process, and derive insights from complex real-world data, has emerged as an active and interdisciplinary area of artificial intelligence over the last decade, drawing on such fields as natural language processing, data mining, and the semantic web. Current projects involve predicting cyberattacks, recommending products, and even gleaning insights from thousands of papers on COVID-19. This textbook offers rigorous and comprehensive coverage of the field. It focuses systematically on the major approaches, both those that have stood the test of time and the latest deep learning methods.
Introduction to Graph Neural Networks
Author: Zhiyuan Zhiyuan Liu
Publisher: Springer Nature
ISBN: 3031015878
Category : Computers
Languages : en
Pages : 109
Book Description
Graphs are useful data structures in complex real-life applications such as modeling physical systems, learning molecular fingerprints, controlling traffic networks, and recommending friends in social networks. However, these tasks require dealing with non-Euclidean graph data that contains rich relational information between elements and cannot be well handled by traditional deep learning models (e.g., convolutional neural networks (CNNs) or recurrent neural networks (RNNs)). Nodes in graphs usually contain useful feature information that cannot be well addressed in most unsupervised representation learning methods (e.g., network embedding methods). Graph neural networks (GNNs) are proposed to combine the feature information and the graph structure to learn better representations on graphs via feature propagation and aggregation. Due to its convincing performance and high interpretability, GNN has recently become a widely applied graph analysis tool. This book provides a comprehensive introduction to the basic concepts, models, and applications of graph neural networks. It starts with the introduction of the vanilla GNN model. Then several variants of the vanilla model are introduced such as graph convolutional networks, graph recurrent networks, graph attention networks, graph residual networks, and several general frameworks. Variants for different graph types and advanced training methods are also included. As for the applications of GNNs, the book categorizes them into structural, non-structural, and other scenarios, and then it introduces several typical models on solving these tasks. Finally, the closing chapters provide GNN open resources and the outlook of several future directions.
Publisher: Springer Nature
ISBN: 3031015878
Category : Computers
Languages : en
Pages : 109
Book Description
Graphs are useful data structures in complex real-life applications such as modeling physical systems, learning molecular fingerprints, controlling traffic networks, and recommending friends in social networks. However, these tasks require dealing with non-Euclidean graph data that contains rich relational information between elements and cannot be well handled by traditional deep learning models (e.g., convolutional neural networks (CNNs) or recurrent neural networks (RNNs)). Nodes in graphs usually contain useful feature information that cannot be well addressed in most unsupervised representation learning methods (e.g., network embedding methods). Graph neural networks (GNNs) are proposed to combine the feature information and the graph structure to learn better representations on graphs via feature propagation and aggregation. Due to its convincing performance and high interpretability, GNN has recently become a widely applied graph analysis tool. This book provides a comprehensive introduction to the basic concepts, models, and applications of graph neural networks. It starts with the introduction of the vanilla GNN model. Then several variants of the vanilla model are introduced such as graph convolutional networks, graph recurrent networks, graph attention networks, graph residual networks, and several general frameworks. Variants for different graph types and advanced training methods are also included. As for the applications of GNNs, the book categorizes them into structural, non-structural, and other scenarios, and then it introduces several typical models on solving these tasks. Finally, the closing chapters provide GNN open resources and the outlook of several future directions.
Data Analytics on Graphs
Author: Ljubisa Stankovic
Publisher:
ISBN: 9781680839821
Category : Data mining
Languages : en
Pages : 556
Book Description
Aimed at readers with a good grasp of the fundamentals of data analytics, this book sets out the fundamentals of graph theory and the emerging mathematical techniques for the analysis of a wide range of data acquired on graph environments. This book will be a useful friend and a helpful companion to all involved in data gathering and analysis.
Publisher:
ISBN: 9781680839821
Category : Data mining
Languages : en
Pages : 556
Book Description
Aimed at readers with a good grasp of the fundamentals of data analytics, this book sets out the fundamentals of graph theory and the emerging mathematical techniques for the analysis of a wide range of data acquired on graph environments. This book will be a useful friend and a helpful companion to all involved in data gathering and analysis.
Machine Learning in Social Networks
Author: Manasvi Aggarwal
Publisher: Springer Nature
ISBN: 9813340223
Category : Technology & Engineering
Languages : en
Pages : 121
Book Description
This book deals with network representation learning. It deals with embedding nodes, edges, subgraphs and graphs. There is a growing interest in understanding complex systems in different domains including health, education, agriculture and transportation. Such complex systems are analyzed by modeling, using networks that are aptly called complex networks. Networks are becoming ubiquitous as they can represent many real-world relational data, for instance, information networks, molecular structures, telecommunication networks and protein–protein interaction networks. Analysis of these networks provides advantages in many fields such as recommendation (recommending friends in a social network), biological field (deducing connections between proteins for treating new diseases) and community detection (grouping users of a social network according to their interests) by leveraging the latent information of networks. An active and important area of current interest is to come out with algorithms that learn features by embedding nodes or (sub)graphs into a vector space. These tasks come under the broad umbrella of representation learning. A representation learning model learns a mapping function that transforms the graphs' structure information to a low-/high-dimension vector space maintaining all the relevant properties.
Publisher: Springer Nature
ISBN: 9813340223
Category : Technology & Engineering
Languages : en
Pages : 121
Book Description
This book deals with network representation learning. It deals with embedding nodes, edges, subgraphs and graphs. There is a growing interest in understanding complex systems in different domains including health, education, agriculture and transportation. Such complex systems are analyzed by modeling, using networks that are aptly called complex networks. Networks are becoming ubiquitous as they can represent many real-world relational data, for instance, information networks, molecular structures, telecommunication networks and protein–protein interaction networks. Analysis of these networks provides advantages in many fields such as recommendation (recommending friends in a social network), biological field (deducing connections between proteins for treating new diseases) and community detection (grouping users of a social network according to their interests) by leveraging the latent information of networks. An active and important area of current interest is to come out with algorithms that learn features by embedding nodes or (sub)graphs into a vector space. These tasks come under the broad umbrella of representation learning. A representation learning model learns a mapping function that transforms the graphs' structure information to a low-/high-dimension vector space maintaining all the relevant properties.