We propose a new method to estimate plant biodiversity with Rényi and Rao indexes through the so called High Order Singular Value Decomposition (HOSVD) of tensors. Starting from NASA multispectral images we evaluate biodiversity and we compare original biodiversity estimates with those realised via the HOSVD compression methods for big data. Our strategy turns out to be extremely powerful in terms of storage memory and precision of the outcome. The obtained results are so promising that we can support the efficiency of our method in the ecological framework
