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Author: Santosh S. Vempala
Publisher: American Mathematical Soc.
ISBN: 0821837931
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neighbor search, geometric clustering and efficient low-rank approximation. Motivated by the first two applications, an extension of random projection to the hypercube is developed here. Throughout the book, random projection is used as a way to understand, simplify and connect progress on these important and seemingly unrelated problems. The book is suitable for graduate students and research mathematicians interested in computational geometry.
Author: Santosh S. Vempala
Publisher: American Mathematical Soc.
ISBN: 0821837931
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neighbor search, geometric clustering and efficient low-rank approximation. Motivated by the first two applications, an extension of random projection to the hypercube is developed here. Throughout the book, random projection is used as a way to understand, simplify and connect progress on these important and seemingly unrelated problems. The book is suitable for graduate students and research mathematicians interested in computational geometry.
Author: Geoffrey Grant Meredith
Publisher:
ISBN: 9789221028390
Category : Business & Economics
Languages : en
Pages : 214
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Book Description
Intended to help individuals in self development for business ownership, this volume presents personal characteristics, planning and control and the variety and use of resources for the entrepreneur. Includes numerous checklists, formula and graphic analytical devices and practical techniques.
Author: Avrim Blum
Publisher: Cambridge University Press
ISBN: 1108617360
Category : Computers
Languages : en
Pages : 433
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Book Description
This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.
Author: Craig Saunders
Publisher: Springer
ISBN: 3540341382
Category : Computers
Languages : en
Pages : 218
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Book Description
This book constitutes the thoroughly refereed post-proceedings of the PASCAL (pattern analysis, statistical modelling and computational learning) Statistical and Optimization Perspectives Workshop on Subspace, Latent Structure and Feature Selection techniques, SLSFS 2005. The 9 revised full papers presented together with 5 invited papers reflect the key approaches that have been developed for subspace identification and feature selection using dimension reduction techniques, subspace methods, random projection methods, among others.
Author: Mohammad Zoynul Abedin
Publisher: Routledge
ISBN: 1000394123
Category : Business & Economics
Languages : en
Pages : 275
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Book Description
This book introduces machine learning in finance and illustrates how we can use computational tools in numerical finance in real-world context. These computational techniques are particularly useful in financial risk management, corporate bankruptcy prediction, stock price prediction, and portfolio management. The book also offers practical and managerial implications of financial and managerial decision support systems and how these systems capture vast amount of financial data. Business risk and uncertainty are two of the toughest challenges in the financial industry. This book will be a useful guide to the use of machine learning in forecasting, modeling, trading, risk management, economics, credit risk, and portfolio management.
Author: László Erdős
Publisher: American Mathematical Soc.
ISBN: 1470436485
Category : Mathematics
Languages : en
Pages : 239
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Book Description
A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Author: Wei Lu
Publisher: Springer Nature
ISBN: 3030604705
Category : Computers
Languages : en
Pages : 195
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Book Description
This book constitutes the thoroughly refereed post-workshop proceedings of the workshops that were held in conjunction with the 24th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2020, in Singapore, Singapore, in May 2020. The 17 revised full papers presented were carefully reviewed and selected from a total of 50 submissions. The five workshops were as follows: · First International Workshop on Literature-Based Discovery (LBD 2020) · Workshop on Data Science for Fake News (DSFN 2020) · Learning Data Representation for Clustering (LDRC 2020) · Ninth Workshop on Biologically Inspired Techniques for Data Mining (BDM · 2020) · First Pacific Asia Workshop on Game Intelligence & Informatics (GII 2020)
Author: Nora Reyes
Publisher: Springer Nature
ISBN: 3030896579
Category : Computers
Languages : en
Pages : 415
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Book Description
This book constitutes the refereed proceedings of the 14th International Conference on Similarity Search and Applications, SISAP 2021, held in Dortmund, Germany, in September/October 2021. The conference was held virtually due to the COVID-19 pandemic.The 23 full papers presented together with 5 short and 3 doctoral symposium papers were carefully reviewed and selected from 50 submissions. The papers are organized in the topical sections named: Similarity Search and Retrieval; Intrinsic Dimensionality; Clustering and Classification; Applications of Similarity Search; Similarity Search in Graph-Structured Data; Doctoral Symposium.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Ravindran Kannan
Publisher: Now Publishers Inc
ISBN: 1601982747
Category : Computers
Languages : en
Pages : 153
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Book Description
Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.
