Tensor sufficient dimension reduction
Focus Article
Published Online: Mar 19 2015
DOI: 10.1002/wics.1350
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Tensor is a multiway array. With the rapid development of science and technology in the past decades, large amount of tensor observations are routinely collected, processed, and stored in many scientific researches and commercial activities nowadays. The colorimetric sensor array (CSA) data is such an example. Driven by the need to address data analysis challenges that arise in CSA data, we propose a tensor dimension reduction model, a model assuming the nonlinear dependence between a response and a projection of all the tensor predictors. The tensor dimension reduction models are estimated in a sequential iterative fashion. The proposed method is applied to a CSA data collected for 150 pathogenic bacteria coming from 10 bacterial species and 14 bacteria from one control species. Empirical performance demonstrates that our proposed method can greatly improve the sensitivity and specificity of the CSA technique. WIREs Comput Stat 2015, 7:178–184. doi: 10.1002/wics.1350 This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Image Data Mining Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical Learning and Exploratory Methods of the Data Sciences > Pattern Recognition
Plotted in the left panel is the projection of 150 pathogenic bacteria on the first two dimension reduction directions. In the right panel, we compare the prediction error of SIR‐450 min (blue line), SIDRA‐450 min (green line) using data collected 450 min after exposing colorimetric sensor array (CSA) to the bacteria and SIDRA_ALL (red line) using all the time points from 120 min to 600 min, where measurement was taken every 30 min.
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Digital images of 10 pathogenic bacteria at full vapor pressure at 300 K.
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