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

29 Citations (Scopus)


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
Publication statusPublished - 2014 May 5
Externally publishedYes


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

ASJC Scopus subject areas

  • Computer Science Applications
  • Cognitive Neuroscience
  • Artificial Intelligence


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