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What is Shape Constraints

Encyclopedia of Data Science and Machine Learning
The constraints of quadratic programming, representing Convex Nonparametric Least Square, are used to provide the estimated regression function's concavity or convexity.
Published in Chapter:
Convex Nonparametric Least Squares for Predictive Maintenance
William Chung (City University of Hong Kong, Hong Kong) and Iris M. H. Yeung (City University of Hong Kong, Hong Kong)
Copyright: © 2023 |Pages: 17
DOI: 10.4018/978-1-7998-9220-5.ch158
Abstract
A nonparametric regression method, convex nonparametric least square (CNLS), as a machine learning approach is introduced and discussed to the application of predictive maintenance. With the industrial internet of things sensors, predictive maintenance (PdM) becomes viable to identify maintenance issues in real time by predicting the next error of the system. Machine learning (ML) methods, such as support vector machine (SVM), are popular to develop the prediction model for PdM. On the other hand, regression-based methods are considered inappropriate due to their pre-defined function forms and the non-linear nature of the PdM models. The convex nonparametric least squares (CNLS) method can overcome the above shortcomings of the regression-based methods. One of the attractive properties of the CNLS method is its regression-based analysis without pre-defined non-linear function forms. In addition, the CNLS method does not need to find the appropriate Kernel function like the SVM. Hence, the CNLS method is introduced for developing a predicting model for PdM.
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