  Tensor decomposition, a collection of factorization techniques for
multidimensional arrays, are among the most general and powerful tools for
scientific analysis. However, because of their increasing size, today's data
sets require more complex tensor decomposition involving factorization with
multiple matrices and diagonal tensors such as DEDICOM or PARATUCK2.
Traditional tensor resolution algorithms such as Stochastic Gradient Descent
(SGD), Non-linear Conjugate Gradient descent (NCG) or Alternating Least Square
(ALS), cannot be easily applied to complex tensor decomposition or often lead
to poor accuracy at convergence. We propose a new resolution algorithm, called
VecHGrad, for accurate and efficient stochastic resolution over all existing
tensor decomposition, specifically designed for complex decomposition. VecHGrad
relies on gradient, Hessian-vector product and adaptive line search to ensure
the convergence during optimization. Our experiments on five real-world data
sets with the state-of-the-art deep learning gradient optimization models show
that VecHGrad is capable of converging considerably faster because of its
superior theoretical convergence rate per step. Therefore, VecHGrad targets as
well deep learning optimizer algorithms. The experiments are performed for
various tensor decomposition including CP, DEDICOM and PARATUCK2. Although it
involves a slightly more complex update rule, VecHGrad's runtime is similar in
practice to that of gradient methods such as SGD, Adam or RMSProp.
