  Tensors naturally model many real world processes which generate multi-aspect
data. Such processes appear in many different research disciplines, e.g,
chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor
decompositions such as the Tucker decomposition are used to analyze
multi-aspect data and extract latent factors, which capture the multilinear
data structure. Such decompositions are powerful mining tools, for extracting
patterns from large data volumes. However, most frequently used algorithms for
such decompositions involve the computationally expensive Singular Value
Decomposition.
  In this paper we propose MACH, a new sampling algorithm to compute such
decompositions. Our method is of significant practical value for tensor
streams, such as environmental monitoring systems, IP traffic matrices over
time, where large amounts of data are accumulated and the analysis is
computationally intensive but also in "post-mortem" data analysis cases where
the tensor does not fit in the available memory. We provide the theoretical
analysis of our proposed method, and verify its efficacy in monitoring system
applications.
