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.1350This 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