Probabilistic local reconstruction for k-NN regression and its application to virtual metrology in semiconductor manufacturing

Seung kyung Lee, Pilsung Kang, Sungzoon Cho

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)427-439
Number of pages13
JournalNeurocomputing
Volume131
DOIs
Publication statusPublished - 2014 May 5
Externally publishedYes

Bibliographical note

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.

Keywords

  • Bayesian kernel model
  • K-NN regression
  • Locally linear reconstruction

ASJC Scopus subject areas

  • Computer Science Applications
  • Cognitive Neuroscience
  • Artificial Intelligence

Fingerprint

Dive into the research topics of 'Probabilistic local reconstruction for k-NN regression and its application to virtual metrology in semiconductor manufacturing'. Together they form a unique fingerprint.

Cite this