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Author: Gilbert Strang
Publisher: Wellesley-Cambridge Press
ISBN: 9780692196380
Category : Computers
Languages : en
Pages : 0
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Book Description
Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, the first textbook that teaches linear algebra together with deep learning and neural nets. This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.
Author: Gilbert Strang
Publisher: Wellesley-Cambridge Press
ISBN: 9780692196380
Category : Computers
Languages : en
Pages : 0
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Book Description
Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, the first textbook that teaches linear algebra together with deep learning and neural nets. This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.
Author: Takeshi Furuhashi
Publisher: Physica
ISBN: 3790818372
Category : Computers
Languages : en
Pages : 266
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Book Description
Symbolic processing has limitations highlighted by the symbol grounding problem. Computational processing methods, like fuzzy logic, neural networks, and statistical methods have appeared to overcome these problems. However, they also suffer from drawbacks in that, for example, multi-stage inference is difficult to implement. Deep fusion of symbolic and computational processing is expected to open a new paradigm for intelligent systems. Symbolic processing and computational processing should interact at all abstract or computational levels. For this undertaking, attempts to combine, hybridize, and fuse these processing methods should be thoroughly investigated and the direction of novel fusion approaches should be clarified. This book contains the current status of this attempt and also discusses future directions.
Author: Lars Elden
Publisher: SIAM
ISBN: 0898716268
Category : Computers
Languages : en
Pages : 226
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Book Description
Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.
Author: Le Nguyen Binh
Publisher: CRC Press
ISBN: 142001952X
Category : Science
Languages : en
Pages : 382
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Book Description
The potential of photonic signal processing (PSP) to overcome electronic limits for processing ultra-wideband signals, provide signal conditioning that can be integrated in line with fiber optic systems, and improve signal quality makes this technology extremely attractive for improvement in receiver sensitivity performance. Spanning the current transitional period, Photonic Signal Processing: Techniques and Applications addresses the merging techniques of processing and manipulating signals propagating in the optical domain. The book begins with a historical perspective of PSP and introduces photonic components essential for photonic processing systems, such as optical amplification devices, optical fibers, and optical modulators. The author demonstrates the representation of photonic circuits via a signal flow graph technique adapted for photonic domain. He describes photonic signal processors, such as differentiators and integrators, and their applications for the generation of solitons, and then covers the application of these solitons in optically amplified fiber transmission systems. The book illustrates the compensation dispersion using a photonic processor, the design of optical filters using photonic processor techniques, and the filtering of microwave signals in the optical domain. Exploring methods for the processing of signals in the optical domain, the book includes solutions to photonic circuits that use signal flow techniques and significant applications in short pulse generation, the filtering of signals, differentiation, and the integration of signals. It delineates fundamental techniques on the processing of signals in the optical domain as well as their applications that lead to advanced aspects of performing generation of short pulses, integration, differentiation, and filtering for optical communications systems and networks and processing of ultra-high speed signals.
Author: Kenichi Kanatani
Publisher: Morgan & Claypool Publishers
ISBN: 1636391087
Category : Mathematics
Languages : en
Pages : 157
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Book Description
Linear algebra is one of the most basic foundations of a wide range of scientific domains, and most textbooks of linear algebra are written by mathematicians. However, this book is specifically intended to students and researchers of pattern information processing, analyzing signals such as images and exploring computer vision and computer graphics applications. The author himself is a researcher of this domain. Such pattern information processing deals with a large amount of data, which are represented by high-dimensional vectors and matrices. There, the role of linear algebra is not merely numerical computation of large-scale vectors and matrices. In fact, data processing is usually accompanied with "geometric interpretation." For example, we can think of one data set being "orthogonal" to another and define a "distance" between them or invoke geometric relationships such as "projecting" some data onto some space. Such geometric concepts not only help us mentally visualize abstract high-dimensional spaces in intuitive terms but also lead us to find what kind of processing is appropriate for what kind of goals. First, we take up the concept of "projection" of linear spaces and describe "spectral decomposition," "singular value decomposition," and "pseudoinverse" in terms of projection. As their applications, we discuss least-squares solutions of simultaneous linear equations and covariance matrices of probability distributions of vector random variables that are not necessarily positive definite. We also discuss fitting subspaces to point data and factorizing matrices in high dimensions in relation to motion image analysis. Finally, we introduce a computer vision application of reconstructing the 3D location of a point from three camera views to illustrate the role of linear algebra in dealing with data with noise. This book is expected to help students and researchers of pattern information processing deepen the geometric understanding of linear algebra.
Author: Dan A. Simovici
Publisher: World Scientific
ISBN: 981438349X
Category : Computers
Languages : en
Pages : 878
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Book Description
This comprehensive volume presents the foundations of linear algebra ideas and techniques applied to data mining and related fields. Linear algebra has gained increasing importance in data mining and pattern recognition, as shown by the many current data mining publications, and has a strong impact in other disciplines like psychology, chemistry, and biology. The basic material is accompanied by more than 550 exercises and supplements, many accompanied with complete solutions and MATLAB applications. Key Features Integrates the mathematical developments to their applications in data mining without sacrificing the mathematical rigor Presented applications with full mathematical justifications and are often accompanied by MATLAB code Highlights strong links between linear algebra, topology and graph theory because these links are essentially important for applications A self-contained book that deals with mathematics that is immediately relevant for data mining Book jacket.
Author: Le Nguyen Binh
Publisher: CRC Press
ISBN: 0429792638
Category : Technology & Engineering
Languages : en
Pages : 506
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Book Description
This Second Edition of "Photonic Signal Processing" updates most recent R&D on processing techniques of signals in photonic domain from the fundamentals given in its first edition. Several modern techniques in Photonic Signal Processing (PSP) are described: Graphical signal flow technique to simplify the analysis of the photonic transfer functions, plus its insights into the physical phenomena of such processors. The resonance and interference of optical fields are presented by the poles and zeros of the optical circuits, respectively. Detailed design procedures for fixed and tunable optical filters. These filters, "brick-wall-like", now play a highly important role in ultra-broadband (100GBaud) to spectral shaping of sinc temporal response so as to generate truly Nyquist sampler of the received eye diagrams 3-D PSP allows multi-dimensional processing for highly complex optical signals Photonic differentiators and integrators for dark soliton generations. Optical dispersion compensating processors for ultra-long haul optical transmission systems. Some optical devices essentials for PSP. Many detailed PSP techniques are given in the chapters of this Second Edition.
Author: James L. Mcclelland
Publisher: MIT Press
ISBN: 9780262631105
Category : Psychology
Languages : en
Pages : 636
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Book Description
What makes people smarter than computers? These volumes by a pioneering neurocomputing group suggest that the answer lies in the massively parallel architecture of the human mind. They describe a new theory of cognition called connectionism that is challenging the idea of symbolic computation that has traditionally been at the center of debate in theoretical discussions about the mind. The authors' theory assumes the mind is composed of a great number of elementary units connected in a neural network. Mental processes are interactions between these units which excite and inhibit each other in parallel rather than sequential operations. In this context, knowledge can no longer be thought of as stored in localized structures; instead, it consists of the connections between pairs of units that are distributed throughout the network. Volume 1 lays the foundations of this exciting theory of parallel distributed processing, while Volume 2 applies it to a number of specific issues in cognitive science and neuroscience, with chapters describing models of aspects of perception, memory, language, and thought.
Author: Paolo Atzeni
Publisher: Springer
ISBN: 3642340024
Category : Computers
Languages : en
Pages : 608
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Book Description
This book constitutes the refereed proceedings of the 31st International Conference on Conceptual Modeling, ER 2012, held in Florence, Italy, in October 2012. The 24 regular papers presented together with 13 short papers, 6 poster papers and 3 keynotes were carefully reviewed and selected from 141 submissions. The papers are organized in topical sections on understandability and cognitive approaches; conceptual modeling for datawarehousing and business intelligence; extraction, discovery and clustering; search and documents; data and process modeling; ontology based approaches; variability and evolution; adaptation, preferences and query refinement; queries, matching and topic search; and conceptual modeling in action.
Author: Steve Leibson
Publisher: Elsevier
ISBN: 0080472451
Category : Technology & Engineering
Languages : en
Pages : 341
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Book Description
Microprocessor cores used for SOC design are the direct descendents of Intel's original 4004 microprocessor. Just as packaged microprocessor ICs vary widely in their attributes, so do microprocessors packaged as IP cores. However, SOC designers still compare and select processor cores the way they previously compared and selected packaged microprocessor ICs. The big problem with this selection method is that it assumes that the laws of the microprocessor universe have remained unchanged for decades. This assumption is no longer valid.Processor cores for SOC designs can be far more plastic than microprocessor ICs for board-level system designs. Shaping these cores for specific applications produces much better processor efficiency and much lower system clock rates. Together, Tensilica's Xtensa and Diamond processor cores constitute a family of software-compatible microprocessors covering an extremely wide performance range from simple control processors, to DSPs, to 3-way superscalar processors. Yet all of these processors use the same software-development tools so that programmers familiar with one processor in the family can easily switch to another.This book emphasizes a processor-centric MPSOC (multiple-processor SOC) design style shaped by the realities of the 21st-century and nanometer silicon. It advocates the assignment of tasks to firmware-controlled processors whenever possible to maximize SOC flexibility, cut power dissipation, reduce the size and number of hand-built logic blocks, shrink the associated verification effort, and minimize the overall design risk.· An essential, no-nonsense guide to the design of 21st-century mega-gate SOCs using nanometer silicon.· Discusses today's key issues affecting SOC design, based on author's decades of personal experience in developing large digital systems as a design engineer while working at Hewlett-Packard's Desktop Computer Division and at EDA workstation pioneer Cadnetix, and covering such topics as an award-winning technology journalist and editor-in-chief for EDN magazine and the Microprocessor Report.· Explores conventionally accepted boundaries and perceived limits of processor-based system design and then explodes these artificial constraints through a fresh outlook on and discussion of the special abilities of processor cores designed specifically for SOC design.· Thorough exploration of the evolution of processors and processor cores used for ASIC and SOC design with a look at where the industry has come from, and where it's going.· Easy-to-understand explanations of the capabilities of configurable and extensible processor cores through a detailed examination of Tensilica's configurable, extensible Xtensa processor core and six pre-configured Diamond cores.· The most comprehensive assessment available of the practical aspects of configuring and using multiple processor cores to achieve very difficult and ambitious SOC price, performance, and power design goals.
