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. 2017 Apr 12;7:46368. doi: 10.1038/srep46368

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Copyright © 2017, The Author(s)

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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(a) Performance of uniform-random (RNG), quasi-random (Sobol), and HDMR sampling on for the creation of training sets of 150,000 flow shapes, with a uniform-random sampled test set of 10,000 flowshapes. The classification was for 7-pillar sequences. (b) Performance of HDMR sampling and pseudo-random (RNG) sampling vs. training set size, from 50,000 to 250,000 images in increments of 50,000, with the same testing set as in (a). Error bars indicate standard deviation calculated from 50 randomly generated training sets. Note that while RNG sampling can easily generate additional “random” sets of training data, randomly selecting values for k sampling indices in HDMR could result in clustering that greatly impairs performance. The distribution of posterior entropy for the CNN models in testing performance of the best and worst (c) HDMR and (d) RNG training sets are shown for training set size of 150,000. HDMR sampling shows far lower entropy, even with decreased performance, indicating strong model confidence and significant disturbance rejection capability.

Inline graphic — (a) Performance of uniform-random (RNG), quasi-random (Sobol), and HDMR sampling on for the creation of training sets of 150,000 flow shapes, with a uniform-random sampled test set of 10,000 flowshapes. The classification was for 7-pillar sequences. (b) Performance of HDMR sampling and pseudo-random (RNG) sampling vs. training set size, from 50,000 to 250,000 images in increments of 50,000, with the same testing set as in (a). Error bars indicate standard deviation calculated from 50 randomly generated training sets. Note that while RNG sampling can easily generate additional “random” sets of training data, randomly selecting values for k sampling indices in HDMR could result in clustering that greatly impairs performance. The distribution of posterior entropy for the CNN models in testing performance of the best and worst (c) HDMR and (d) RNG training sets are shown for training set size of 150,000. HDMR sampling shows far lower entropy, even with decreased performance, indicating strong model confidence and significant disturbance rejection capability.