1. First we attempt to reduce dimensionality by eliminating redundant noise in the HSI image. The primary method employed was PCA.

   \begin{equation*} \mathbf{T}_L = \mathbf{X} \mathbf{W}_L \end{equation*}

   Keeping only the first \(L\) principal components, produced by using only the first \(L\) eigenvectors. We attempt to classify using \(L=7\).

2. We then attempt to reduce dimensionality by searching for a spectral dictionary of linearly independent signals using a novel algorithm ATGP, which performs an orthogonal subspace projection on the raw HSI data. ATGP attempts to define each pixel \(\mathbf{Y}\) as the following:

   \begin{equation*} \mathbf{Y}=a_0 P_0+a_1 P_1+...+a_n P_n \end{equation*}

   We then iteratively create a spectral dictionary from the most abundant spectrally distinct signals in each pixel, constrained to some number of targets \(T=7\).

3. OC

Unfortunately the final report cannot be shared publicly