Dimensionality reduction (DR) is a major issue to improve the efficiency of the classifiers in Hyperspectral images (HSI). Recently, the independent component analysis (ICA) approach to DR has been investigated. But, this signal processing is applied on vectorized images, losing spatial rearrangement. To jointly take advantage of the spatial and spectral information, HSI has been recently represented as tensor. Offering multiple ways to decompose data orthogonally, we develop a new DR method based on multilinear algebra tools and on ICA. The DR is performed on spectral way using ICA jointly to an orthogonal projection onto a lower subspace dimension of the spatial ways. We show the Maximum Likelihood classifier improvement using the proposed method.