3.1 Feature extraction based on PCA
Principal component analysis (PCA) is a common feature extraction
method. In this paper, the feature extraction matrix was constructed by
background spectra matrix and new measured 1-s spectrum. According to
the PCA, it will present the small variation between the background
spectrum and the new measured 1-s spectrum.
Assume the background spectra matrix wasSb ,Sb was acquired during
the initialization procedure. Sb was am ×n matrix. Where m was the dimension of a
spectrum, n was the number of the background spectra. The new 1-s
spectrum si was collected.Sb and si were combined as
the measure matrix Sm . Sm were a m ×(n+ 1) matrix. With the matrixSm , we has gained the eigenvector set
(v 1,v 2,v 3,…,v m)
and eigenvalue set
(λ 1,λ 2,λ 3,…,λ m) of the matrix. Then arranged the eigenvalue
by the descending order. The maximum eigenvalueλ max and its corresponding eigenvectorv max were acquired. v maxwas a 1×m vector. The feature value Pt of the new
measured 1 s spectrum was the maximum value ofv max between the channel range of (240,290).
Based on the above procedure, the feature value of new measured spectra
at different test position were shown in figure 6.