Fault Detection and Diagnosis in Industrial Systems
Fault Detection and Diagnosis in Industrial Systems
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DOI：
10.1198/tech.2002.s724
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发表时间：
2002-04
期刊：
影响因子：
2.5
通讯作者：
T. McAvoy
中科院分区：
文献类型：
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作者：
T. McAvoy
算法。作者指出，神经网络(包括径向基函数)作为一类向量空间之间的非线性映射，确实可以成为一种有用的降维方法。正如作者所声称的，第9章是“本书的基本目标，即发展构建数据的经验降维映射的方法”(第299页)。文中详细介绍了基于惠特尼嵌入定理的WRN(Whitney归约网络)。然而，正如作者所指出的，在这些全球方法中，“当域维度很大时，就不那么实用了。”局部方法是非线性映射的泰勒展开式。因此，泰勒展开式的线性项可以通过KL过程来应用；还给出了一个局部KL算法(见第326页)。这本书对数据简化提供了有价值的总结。当然，数学理论是数据分析基础的重要组成部分。但由于本书纯粹的数学观点的限制，只讨论了确定最优基数的最小二乘型标准。许多其他方法，包括最大似然法，根本没有提到。这种观点限制了这本书的适用性。
algorithm. The author shows that, as a class of nonlinear mappings between vector spaces, neural networks (including radial basis functions) can indeed be a useful method of dimension reduction. Chapter 9 is, as the author claims, “the basic goal of the book, that is the development of methods for constructing empirical dimensionality-reducing mappings of data” (p. 299). The so-called WRN (Whitney reduction network), based on Whitney’s embedding theorem as a global approach, is covered in detail. However, in these global approaches, as the author notes, “when the domain dimension is large, are far less practical.” The local approach is the Taylor expansion of the nonlinear mapping. Thus the linear term of the Taylor expansion can be applied by the KL procedure; a local KL algorithm is also given (p. 326). This book provides a valuable summary of data reduction. Of course, mathematical theory is an important part of the foundation for data analysis. But due to the limitation of the book’s purely mathematical viewpoint, only the least squares–type criteria are discussed for determining an optimal basis. Many other approaches, including maximum likelihood, are not mentioned at all. This view limits the book’s applicability.