  The online analysis of multi-way data stored in a tensor $\mathcal{X} \in
\mathbb{R} ^{I_1 \times \dots \times I_N} $ has become an essential tool for
capturing the underlying structures and extracting the sensitive features which
can be used to learn a predictive model. However, data distributions often
evolve with time and a current predictive model may not be sufficiently
representative in the future. Therefore, incrementally updating the
tensor-based features and model coefficients are required in such situations. A
new efficient tensor-based feature extraction, named NeSGD, is proposed for
online $CANDECOMP/PARAFAC$ (CP) decomposition. According to the new features
obtained from the resultant matrices of NeSGD, a new criteria is triggered for
the updated process of the online predictive model. Experimental evaluation in
the field of structural health monitoring using laboratory-based and real-life
structural datasets show that our methods provide more accurate results
compared with existing online tensor analysis and model learning. The results
showed that the proposed methods significantly improved the classification
error rates, were able to assimilate the changes in the positive data
distribution over time, and maintained a high predictive accuracy in all case
studies.
