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Harmonic and Applied Analysis
  • Language: en
  • Pages: 316

Harmonic and Applied Analysis

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science. This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on Applied Harmonic Analysis, held at the University of Genova in 2017 and 2019. Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers. Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.

Topology
  • Language: en
  • Pages: 383

Topology

This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; con- nectedness and compactness; Alexandrov compactification; quotient topol- ogies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. This second edition contains a new chapter with a topological introduction to sheaf cohomology and applications. It also corrects some inaccuracies and some additional exercises are proposed. The textbook is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

Empirical Inference
  • Language: en
  • Pages: 295

Empirical Inference

This book honours the outstanding contributions of Vladimir Vapnik, a rare example of a scientist for whom the following statements hold true simultaneously: his work led to the inception of a new field of research, the theory of statistical learning and empirical inference; he has lived to see the field blossom; and he is still as active as ever. He started analyzing learning algorithms in the 1960s and he invented the first version of the generalized portrait algorithm. He later developed one of the most successful methods in machine learning, the support vector machine (SVM) – more than just an algorithm, this was a new approach to learning problems, pioneering the use of functional ana...

Advances in Knowledge Discovery and Data Mining
  • Language: en
  • Pages: 902

Advances in Knowledge Discovery and Data Mining

  • Type: Book
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  • Published: 2006-03-10
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  • Publisher: Springer

This book constitutes the refereed proceedings of the 10th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2006, held in Singapore in April 2006. The 67 revised full papers and 33 revised short papers presented together with 3 invited talks were carefully reviewed and selected from 501 submissions. The papers are organized in topical sections on Classification, Ensemble Learning, Clustering, Support Vector Machines, Text and Document Mining, Web Mining, Bio-Data Mining, and more.

Machine Learning and Knowledge Discovery in Databases
  • Language: en
  • Pages: 648

Machine Learning and Knowledge Discovery in Databases

  • Type: Book
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  • Published: 2010-08-17
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  • Publisher: Springer

Annotation. This book constitutes the refereed proceedings of the joint conference on Machine Learning and Knowledge Discovery in Databases: ECML PKDD 2010, held in Barcelona, Spain, in September 2010. The 120 revised full papers presented in three volumes, together with 12 demos (out of 24 submitted demos), were carefully reviewed and selected from 658 paper submissions. In addition, 7 ML and 7 DM papers were distinguished by the program chairs on the basis of their exceptional scientific quality and high impact on the field. The conference intends to provide an international forum for the discussion of the latest high quality research results in all areas related to machine learning and knowledge discovery in databases. A topic widely explored from both ML and DM perspectives was graphs, with motivations ranging from molecular chemistry to social networks.

Mixed Boundary Problems in Solid Mechanics
  • Language: en
  • Pages: 173

Mixed Boundary Problems in Solid Mechanics

The book covers a wide range of subjects and techniques related to mixed boundary problems of elasticity from basic concepts to special techniques that are unlikely to appear in traditional university graduate courses. This book may also be of interest to industrial researchers who encounter defects such as cracks and inclusions of different materials in mechanisms under different localization and type of loading. So the topics present the application of mathematical mechanics of solid bodies notably in elasticity, showing the interconnection of elasticity and temperature that would normally treated independently. Theoretical and experimental results are expected to be useful for researchers...

Further with Knowledge Graphs
  • Language: en
  • Pages: 284

Further with Knowledge Graphs

  • Type: Book
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  • Published: 2021-09-23
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  • Publisher: IOS Press

The field of semantic computing is highly diverse, linking areas such as artificial intelligence, data science, knowledge discovery and management, big data analytics, e-commerce, enterprise search, technical documentation, document management, business intelligence, and enterprise vocabulary management. As such it forms an essential part of the computing technology that underpins all our lives today. This volume presents the proceedings of SEMANTiCS 2021, the 17th International Conference on Semantic Systems. As a result of the continuing Coronavirus restrictions, SEMANTiCS 2021 was held in a hybrid form in Amsterdam, the Netherlands, from 6 to 9 September 2021. The annual SEMANTiCS confere...

Regularization, Optimization, Kernels, and Support Vector Machines
  • Language: en
  • Pages: 528

Regularization, Optimization, Kernels, and Support Vector Machines

  • Type: Book
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  • Published: 2014-10-23
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  • Publisher: CRC Press

Regularization, Optimization, Kernels, and Support Vector Machines offers a snapshot of the current state of the art of large-scale machine learning, providing a single multidisciplinary source for the latest research and advances in regularization, sparsity, compressed sensing, convex and large-scale optimization, kernel methods, and support vector machines. Consisting of 21 chapters authored by leading researchers in machine learning, this comprehensive reference: Covers the relationship between support vector machines (SVMs) and the Lasso Discusses multi-layer SVMs Explores nonparametric feature selection, basis pursuit methods, and robust compressive sensing Describes graph-based regular...

A Compact Course on Linear PDEs
  • Language: en
  • Pages: 267

A Compact Course on Linear PDEs

This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations.

Introduction to the Thermomechanics of Continua and Hyperbolic Systems
  • Language: en
  • Pages: 193