Abstract: b'We study the optimization problem for decomposing $d$ dimensional\nfourth-order Tensors with $k$ non-orthogonal components. We derive\n\\textit{deterministic} conditions under which such a problem does not have\nspurious local minima. In particular, we show that if $\\kappa =\n\\frac{\\lambda_{max}}{\\lambda_{min}} < \\frac{5}{4}$, and incoherence coefficient\nis of the order $O(\\frac{1}{\\sqrt{d}})$, then all the local minima are globally\noptimal. Using standard techniques, these conditions could be easily\ntransformed into conditions that would hold with high probability in high\ndimensions when the components are generated randomly. Finally, we prove that\nthe tensor power method with deflation and restarts could efficiently extract\nall the components within a tolerance level $O(\\kappa \\sqrt{k\\tau^3})$ that\nseems to be the noise floor of non-orthogonal tensor decomposition.<pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad><pad>'