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Generalized shape constrained spline fitting for qualitative analysis of trends
Kris Villez, Venkat Venkatasubramanian,
Published in Elsevier Ltd
2013
Volume: 58
   
Pages: 116 - 134
Abstract

In this work, we present a generalized method for analysis of data series based on shape constraint spline fitting which constitutes the first step toward a statistically optimal method for qualitative analysis of trends. The presented method is based on a branch-and-bound (B&B) algorithm which is applied for globally optimal fitting of a spline function subject to shape constraints. More specifically, the B&B algorithm searches for optimal argument values in which the sign of the fitted function and/or one or more of its derivatives change. We derive upper and lower bounding procedures for the B&B algorithm to efficiently converge to the global optimum. These bounds are based on existing solutions for shape constraint spline estimation via Second Order Cone Programs (SOCPs). The presented method is demonstrated with three different examples which are indicative of both the strengths and weaknesses of this method. © 2013 Elsevier Ltd.

About the journal
JournalData powered by TypesetComputers and Chemical Engineering
PublisherData powered by TypesetElsevier Ltd
ISSN00981354
Open AccessNo
Concepts (14)
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    BOUNDING PROCEDURES
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    Branch and bounds
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    Generalized method
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    Qualitative analysis
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    QUALITATIVE TREND ANALYSIS
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    SECOND ORDER CONE PROGRAMS
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    SECOND-ORDER CONE PROGRAMMING
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    Spline functions
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    Data mining
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    FAILURE ANALYSIS
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    Global optimization
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    Interpolation
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    Optimization
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    Algorithms