组合数据分析
2011-2
清华大学出版社
（美）休伯特 等著
163
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combinatorial data analysis (cda) refers to a wide class of
methods for the study of relevant data sets in which the
arrangement of a collection of objects is absolutely central.
combinatorial data analysis: optimization by dynamic programming
focuses on the identification of arrangements, which are then
further restricted to where the combinatorial search is carried out
by a recursive optimization process based on the general principles
of dynamic programming (dp).
the authors provide a comprehensive and self-contained review
delineating a very general dp paradigm, or schema, that can serve
two functions. first, the paradigm can be applied in various
special forms to encompass all previously proposed applications
suggested in the classification literature. second, the paradigm
can lead directly to many more novel uses. an appendix is included
as a user's manual for a collection of programs available as
freeware.
the incorporation of a wide variety of cda tasks under one common
optimization framework based on dp is one of this book's strongest
points. the authors include verifiably optimal solutions to
nontrivially sized problems over the array of data analysis tasks
discussed.
this monograph provides an applied documentation source, as well as
an introduction to a collection of associated computer programs,
that will be of interest to applied statisticians and data analysts
as well as notationally sophisticated users.
作者：（美国）休伯特（Lawrence Hubert） （美国）Phipps Arabie （美国）Jacqueline Meulman
preface
1 introduction
2 general dynamic programming paradigm
2.1 an introductory example: linear assignment
2.2 the gdpp
3 cluster analysis
3.1 partitioning
3.1.1 admissibility restrictions on partitions
3.1.2 partitioning based on two-mode proximity matrices
3.2 hierarchical clustering
3.2.1 hierarchical clustering and the optimal fitting of
ultrametrics
3.2.2 constrained hierarchical clustering
4 object sequencing and seriation
4.1 optimal sequencing of a single object set
4.1.1 symmetric one-mode proximity matrices
4.1.2 skew-symmetric one-mode proximity matrices
4.1.3 two-mode proximity matrices
4.1.4 object sequencing for symmetric one-mode proximity matrices
based on the construction of optimal paths
4.2 sequencing an object set subject to precedence
constraints
4.3 construction of optimal ordered partitions
5 heuristic applications of the gdpp
5.1 cluster analysis
5.2 object sequencing and seriation
6 extensions and generalizations
6.1 introduction
6.1.1 multiple data sources
6.1.2 multiple structures
6.1.3 uses for the information in the sets ω1,...,ωk
6.1.4 a priori weights for objects and/or proximities
6.2 prospects
appendix: available programs
bibliography
author index
subject index
版权页：插图：The choice of an ordering that can be imposed to constrain the search domain for optimal partitions could be directly tied to the task of finding an(optimal) sequencing of the objects along a continuum(which is discussed extensively in Chapter 41．Somewhat more generally，one possible data analysis strategY for seeking partitions as close to optimal.as possible would be to construct a preliminary object ordering through some initial ptimization process，and possibly one based on another analysis method that could then constrain the domain of search for an optimal partition．Obviously,if one were successful in generating an appropriate object ordering，partitions that would be optimal when constrained would also be optimal unconstrained．The obvious key here iS to have some mechanism for identifying an appropriate order to give this possible equivalence fbetween an optimal constrained partition and one that lS optimal unconstrained)a chance to succeed．As one explicit example of how such a process might be developed for constructing partitions based on an empmcally generated ordering for the objects，a recent paper by Alpert and Kahng(1995)proposed a three-stage process·First, the objects to be partitioned are embedded in a Euclidean representation with a specific multidimensional scaling strategy(Alpert and Kahng(1995)suggest a method they attribute to Hall(1970)，but that Was actually developed much earlier by Guttman(1968)，who used it to develop——an initial spatial configuration for the objects in his approach to nonmetric multidimensional scaling)．
《组合数据分析:通过动态规划进行优化》：国际著名数学图书·影印版
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少数专门讲解动态规划的书
挺好的，内容也不算多