TY - JOUR
T1 - Probabilistic local reconstruction for k-NN regression and its application to virtual metrology in semiconductor manufacturing
AU - Lee, Seung kyung
AU - Kang, Pilsung
AU - Cho, Sungzoon
N1 - Funding Information:
This work was supported by the Brain Korea 21 project in 2006-2011, the Brain Korea 21 PLUS project in 2013, the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2011-0030814), Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT, and Future Planning (2011-0021893) and 2013 Seoul National University Brain Fusion Program Research Grant. This work was also supported by the Engineering Research Institute of SNU.
PY - 2014/5/5
Y1 - 2014/5/5
N2 - The ". locally linear reconstruction" (LLR) provides a principled and k-insensitive way to determine the weights of k-nearest neighbor (k-NN) learning. LLR, however, does not provide a confidence interval for the k neighbors-based reconstruction of a query point, which is required in many real application domains. Moreover, its fixed linear structure makes the local reconstruction model unstable, resulting in performance fluctuation for regressions under different k values. Therefore, we propose a probabilistic local reconstruction (PLR) as an extended version of LLR in the k-NN regression. First, we probabilistically capture the reconstruction uncertainty by incorporating Gaussian regularization prior into the reconstruction model. This prevents over-fitting when there are no informative neighbors in the local reconstruction. We then project data into a higher dimensional feature space to capture the non-linear relationship between neighbors and a query point when a value of k is large. Preliminary experimental results demonstrated that the proposed Bayesian kernel treatment improves accuracy and k-invariance. Moreover, from the experiment on a real virtual metrology data set in the semiconductor manufacturing, it was found that the uncertainty information on the prediction outcomes provided by PLR supports more appropriate decision making.
AB - The ". locally linear reconstruction" (LLR) provides a principled and k-insensitive way to determine the weights of k-nearest neighbor (k-NN) learning. LLR, however, does not provide a confidence interval for the k neighbors-based reconstruction of a query point, which is required in many real application domains. Moreover, its fixed linear structure makes the local reconstruction model unstable, resulting in performance fluctuation for regressions under different k values. Therefore, we propose a probabilistic local reconstruction (PLR) as an extended version of LLR in the k-NN regression. First, we probabilistically capture the reconstruction uncertainty by incorporating Gaussian regularization prior into the reconstruction model. This prevents over-fitting when there are no informative neighbors in the local reconstruction. We then project data into a higher dimensional feature space to capture the non-linear relationship between neighbors and a query point when a value of k is large. Preliminary experimental results demonstrated that the proposed Bayesian kernel treatment improves accuracy and k-invariance. Moreover, from the experiment on a real virtual metrology data set in the semiconductor manufacturing, it was found that the uncertainty information on the prediction outcomes provided by PLR supports more appropriate decision making.
KW - Bayesian kernel model
KW - K-NN regression
KW - Locally linear reconstruction
UR - http://www.scopus.com/inward/record.url?scp=84894105629&partnerID=8YFLogxK
U2 - 10.1016/j.neucom.2013.10.001
DO - 10.1016/j.neucom.2013.10.001
M3 - Article
AN - SCOPUS:84894105629
SN - 0925-2312
VL - 131
SP - 427
EP - 439
JO - Neurocomputing
JF - Neurocomputing
ER -