Topics in Sparse Approximation PDF Download

Author: Joel Aaron Tropp
Publisher:
ISBN:
Category : Algebras, Linear
Languages : en
Pages :

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Author: Vladimir Temlyakov
Publisher: Birkhäuser
ISBN: 3034808909
Category : Mathematics
Languages : en
Pages : 261

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This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and does not require a broad background in the field.

Author: Ben Adcock
Publisher: SIAM
ISBN: 161197688X
Category : Mathematics
Languages : en
Pages : 310

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Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

Author: Peter A. Flach
Publisher: Springer
ISBN: 3642334601
Category : Computers
Languages : en
Pages : 879

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This two-volume set LNAI 7523 and LNAI 7524 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: ECML PKDD 2012, held in Bristol, UK, in September 2012. The 105 revised research papers presented together with 5 invited talks were carefully reviewed and selected from 443 submissions. The final sections of the proceedings are devoted to Demo and Nectar papers. The Demo track includes 10 papers (from 19 submissions) and the Nectar track includes 4 papers (from 14 submissions). The papers grouped in topical sections on association rules and frequent patterns; Bayesian learning and graphical models; classification; dimensionality reduction, feature selection and extraction; distance-based methods and kernels; ensemble methods; graph and tree mining; large-scale, distributed and parallel mining and learning; multi-relational mining and learning; multi-task learning; natural language processing; online learning and data streams; privacy and security; rankings and recommendations; reinforcement learning and planning; rule mining and subgroup discovery; semi-supervised and transductive learning; sensor data; sequence and string mining; social network mining; spatial and geographical data mining; statistical methods and evaluation; time series and temporal data mining; and transfer learning.

Author: Sabri Arik
Publisher: Springer
ISBN: 3319265555
Category : Computers
Languages : en
Pages : 710

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The four volume set LNCS 9489, LNCS 9490, LNCS 9491, and LNCS 9492 constitutes the proceedings of the 22nd International Conference on Neural Information Processing, ICONIP 2015, held in Istanbul, Turkey, in November 2015. The 231 full papers presented were carefully reviewed and selected from 375 submissions. The 4 volumes represent topical sections containing articles on Learning Algorithms and Classification Systems; Artificial Intelligence and Neural Networks: Theory, Design, and Applications; Image and Signal Processing; and Intelligent Social Networks.

Author: Andrew Fitzgibbon
Publisher: Springer
ISBN: 3642337155
Category : Computers
Languages : en
Pages : 877

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The seven-volume set comprising LNCS volumes 7572-7578 constitutes the refereed proceedings of the 12th European Conference on Computer Vision, ECCV 2012, held in Florence, Italy, in October 2012. The 408 revised papers presented were carefully reviewed and selected from 1437 submissions. The papers are organized in topical sections on geometry, 2D and 3D shapes, 3D reconstruction, visual recognition and classification, visual features and image matching, visual monitoring: action and activities, models, optimisation, learning, visual tracking and image registration, photometry: lighting and colour, and image segmentation.

Author: Frans Coenen
Publisher: Springer Science & Business Media
ISBN: 1848821719
Category : Computers
Languages : en
Pages : 372

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The papers in this volume are the refereed technical papers presented at AI-2008, the Twenty-eighth SGAI International Conference on Innovative Techniques and Applications of Artificial Intelligence, held in Cambridge in December 2008. They present new and innovative developments in the field, divided into sections on CBR and Classification, AI Techniques, Argumentation and Negotiation, Intelligent Systems, From Machine Learning To E-Learning and Decision Making. The volume also includes the text of short papers presented as posters at the conference. This is the twenty-fifth volume in the Research and Development series. The series is essential reading for those who wish to keep up to date with developments in this important field. The Application Stream papers are published as a companion volume under the title Applications and Innovations in Intelligent Systems XVI.

Author: Michael Elad
Publisher: Springer Science & Business Media
ISBN: 1441970118
Category : Mathematics
Languages : en
Pages : 376

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Book Description
A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.

Author: Kurt Jetter
Publisher: Elsevier
ISBN: 9780080462042
Category : Mathematics
Languages : en
Pages : 356

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This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry. A collection of articles of highest scientific standard An excellent introduction and overview of recent topics from multivariate approximation A valuable source of references for specialists in the field A representation of the state-of-the-art in selected areas of multivariate approximation A rigorous mathematical introduction to special topics of interdisciplinary research

Author: Qiang Zhang
Publisher: Springer Nature
ISBN: 303102253X
Category : Technology & Engineering
Languages : en
Pages : 133

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The last few years have witnessed fast development on dictionary learning approaches for a set of visual computing tasks, largely due to their utilization in developing new techniques based on sparse representation. Compared with conventional techniques employing manually defined dictionaries, such as Fourier Transform and Wavelet Transform, dictionary learning aims at obtaining a dictionary adaptively from the data so as to support optimal sparse representation of the data. In contrast to conventional clustering algorithms like K-means, where a data point is associated with only one cluster center, in a dictionary-based representation, a data point can be associated with a small set of dictionary atoms. Thus, dictionary learning provides a more flexible representation of data and may have the potential to capture more relevant features from the original feature space of the data. One of the early algorithms for dictionary learning is K-SVD. In recent years, many variations/extensions of K-SVD and other new algorithms have been proposed, with some aiming at adding discriminative capability to the dictionary, and some attempting to model the relationship of multiple dictionaries. One prominent application of dictionary learning is in the general field of visual computing, where long-standing challenges have seen promising new solutions based on sparse representation with learned dictionaries. With a timely review of recent advances of dictionary learning in visual computing, covering the most recent literature with an emphasis on papers after 2008, this book provides a systematic presentation of the general methodologies, specific algorithms, and examples of applications for those who wish to have a quick start on this subject.