模式分析的核方法

內(nèi)容概要

模式分析是從一批數(shù)據(jù)中尋找普遍關(guān)系的過(guò)程。它逐漸成為許多學(xué)科的核心，從神經(jīng)網(wǎng)絡(luò)到所謂句法模式識(shí)別，從統(tǒng)計(jì)模式識(shí)別到機(jī)器學(xué)習(xí)和數(shù)據(jù)挖掘，模式分析的應(yīng)用覆蓋了從生物信息學(xué)到文檔檢索的廣泛領(lǐng)域。    本書(shū)所描述的核方法為所有這些學(xué)科提供了一個(gè)有力的和統(tǒng)一的框架，推動(dòng)了可以用于各種普遍形式的數(shù)據(jù)(如字符串、向量、文本等)的各種算法的發(fā)展，并可以用于尋找各種普遍的關(guān)系類(lèi)型(如排序、分類(lèi)、回歸和聚類(lèi)等)。    本書(shū)有兩個(gè)主要目的。首先，它為專(zhuān)業(yè)人員提供了一個(gè)包容廣泛的工具箱，其中包含各種易于實(shí)現(xiàn)的算法、核函數(shù)和解決方案。許多算法給出了MATLAB編碼，可適用于許多領(lǐng)域的模式分析任務(wù)。其次，它為學(xué)生和研究人員提供了一個(gè)方便的入門(mén)向?qū)?，去了解基于核的模式分析這個(gè)迅速發(fā)展的領(lǐng)域。書(shū)中舉例說(shuō)朋了如何針對(duì)新的特定應(yīng)用手工寫(xiě)出一個(gè)算法或核函數(shù)，同時(shí)還給出了為完成此任務(wù)所需的初步方案及數(shù)學(xué)工具。    本書(shū)分三部分。第一部分介紹了這個(gè)領(lǐng)域的基本概念，書(shū)中不僅給出了一個(gè)展開(kāi)的入門(mén)例子，而且還闡述了這種方法的主要理論基礎(chǔ)。第二部分包含了若干基于核的算法，從最簡(jiǎn)單的到較復(fù)雜的系統(tǒng)，例如核偏序最小二乘法、正則相關(guān)分析、支持向量機(jī)、主成分分析等。第三部分描述了若干核函數(shù)，從基本的例子到高等遞歸核函數(shù)、從生成模型導(dǎo)出的核函數(shù)(女IIHMM)和基于動(dòng)態(tài)規(guī)劃的串匹配核函數(shù)，以及用于處理文本文檔的特殊核函數(shù)。    本書(shū)適用于所有從事模式識(shí)別、機(jī)器學(xué)習(xí)、神經(jīng)網(wǎng)絡(luò)及其應(yīng)用(從計(jì)算生物學(xué)到文本分析)的研究人員。

作者簡(jiǎn)介

John Shawe-Taylor英國(guó)南安普敦大學(xué)計(jì)算機(jī)科學(xué)系教授。1986年在倫敦大學(xué)皇家勒威學(xué)院獲得博士學(xué)位。他的主要研究領(lǐng)域包括：神經(jīng)網(wǎng)絡(luò)、機(jī)器學(xué)習(xí)、信息論、算法理論、機(jī)器視覺(jué)、語(yǔ)言處理、觸覺(jué)處理等。他還是NeuroCOLT學(xué)會(huì)歐洲組的成員，發(fā)表過(guò)大量技術(shù)論文。
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書(shū)籍目錄

List of code fragmentsPrefacePart I Basic concepts  1 Pattern analysis    1.1 Patterns in data    1.2 Pattern analysis algorithms    1.3 Exploiting patterns    1.4 Summary    1.5 Further reading and advanced topics  2 Kernel methods: an overview    2.1 The overall picture    2.2 Linear regression in a feature space    2.3 Other examples    2.4 The modularity of kernel methods    2.5 Roadmap of the book    2.6 Summary    2.7 Further reading and advanced topics  3 Properties of kernels    3.1 Inner products and positive semi-definite matrices    3.2 Characterisation of kernels    3.3 The kernel matrix    3.4 Kernel construction    3.5 Summary    3.6 Further reading and advanced topics  4 Detecting stable patterns    4.1 Concentration inequalities    4.2 Capacity and regularisation: Rademacher theory    4.3 Pattern stability for kernel-based classes    4.4 A pragmatic approach    4.5 Summary    4.6 Further reading and advanced topicsPart II Pattern analysis algorithms  5 Elementary algorithms in feature space    5.1 Means and distances    5.2 Computing projections: Gram-Schmidt, QR and Cholesky    5.3 Measuring the spread of the data    5.4 Fisher discriminant analysis I    5.5 Summary    5.6 Further reading and advanced topics  6 Pattern analysis using eigen-decompositions    6.1 Singular value decomposition    6.2 Principal components analysis    6.3 Directions of maximum covariance    6.4 The generalised eigenvector problem    6.5 Canonical correlation analysis    6.6 Fisher discriminant analysis II    6.7 Methods for linear regression    6.8 Summary    6.9 Further reading and advanced topics  7 Pattern analysis using convex optimisation    7.1 The smallest enclosing hypersphere    7.2 Support vector machines for classification    7.3 Support vector machines for regression    7.4 On-line classification and regression    7.5 Summary    7.6 Further reading and advanced topics  8 Ranking, clustering and data visualisation    8.1 Discovering rank relations    8.2 Discovering cluster structure in a feature space    8.3 Data visualisation    8.4 Summary    8.5 Further reading and advanced topicsPart III Constructing kernels  9 Basic kernels and kernel types    9.1 Kernels in closed form    9.2 ANOVA kernels    9.3 Kernels from graphs    9.4 Diffusion kernels on graph nodes    9.5 Kernels on sets    9.6 Kernels on real numbers    9.7 Randomised kernels    9.8 Other kernel types    9.9 Summary    9.10 Further reading and advanced topics  10 Kernels for text    10.1 From bag of words to semantic space    10.2 Vector space kernels    10.3 Summary    10.4 Further reading and advanced topics  11 Kernels for structured data: strings, trees, etc.    11.1 Comparing strings and sequences    11.2 Spectrum kernels    11.3 All-subsequences kernels    11.4 Fixed length subsequences kernels    11.5 Gap-weighted subsequences kernels    11.6 Beyond dynamic programming: trie-based kernels    11.7 Kernels for structured data    11.8 Summary    11.9 Further reading and advanced topics  12 Kernels from generative models    12.1 P-kernels    12.2 Fisher kernels    12.3 Summary    12.4 Further reading and advanced topicsAppendix A Proofs omitted from the main textAppendix B Notational conventionsAppendix C List of pattern analysis methodsAppendix D List of kernelsReferencesIndex

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