  Dimensionality reduction is an important step in processing the hyperspectral
images (HSI) to overcome the curse of dimensionality problem. Linear
dimensionality reduction methods such as Independent component analysis (ICA)
and Linear discriminant analysis (LDA) are commonly employed to reduce the
dimensionality of HSI. These methods fail to capture non-linear dependency in
the HSI data, as data lies in the nonlinear manifold. To handle this, nonlinear
transformation techniques based on kernel methods were introduced for
dimensionality reduction of HSI. However, the kernel methods involve cubic
computational complexity while computing the kernel matrix, and thus its
potential cannot be explored when the number of pixels (samples) are large. In
literature a fewer number of pixels are randomly selected to partial to
overcome this issue, however this sub-optimal strategy might neglect important
information in the HSI. In this paper, we propose randomized solutions to the
ICA and LDA dimensionality reduction methods using Random Fourier features, and
we label them as RFFICA and RFFLDA. Our proposed method overcomes the
scalability issue and to handle the non-linearities present in the data more
efficiently. Experiments conducted with two real-world hyperspectral datasets
demonstrates that our proposed randomized methods outperform the conventional
kernel ICA and kernel LDA in terms overall, per-class accuracies and
computational time.
