Publication Abstract
Locality Preserving Discriminant Analysis in Kernel Induced Feature Spaces for Hyperspectral Image Classification
Li, W., Prasad, S., Fowler, J. E., & Bruce, L.M. (2011). Locality Preserving Discriminant Analysis in Kernel Induced Feature Spaces for Hyperspectral Image Classification. IEEE Geoscience and Remote Sensing Letters. 8(5), 894-898.
Abstract
Linear discriminant analysis (LDA) has been widely
applied for hyperspectral image (HSI) analysis as a popular
method for feature extraction and dimensionality reduction. Linear
methods such as LDA work well for unimodal Gaussian
class-conditional distributions. However, when data samples between
classes are nonlinearly separated in the input space, linear
methods such as LDA are expected to fail. The kernel discriminant
analysis (KDA) attempts to address this issue by mapping
data in the input space onto a subspace such that Fisher’s ratio
in an intermediate (higher-dimensional) kernel-induced space is
maximized. In recent studies with HSI data, KDA has been shown
to outperform LDA, particularly when the data distributions are
non-Gaussian and multimodal, such as when pixels represent
target classes severely mixed with background classes. In this
letter, a modified KDA algorithm, i.e., kernel local Fisher discriminant
analysis (KLFDA), is studied for HSI analysis. Unlike KDA,
KLFDA imposes an additional constraint on the mapping—it
ensures that neighboring points in the input space stay close-by in
the projected subspace and vice versa. Classification experiments
with a challenging HSI task demonstrate that this approach outperforms
current state-of-the-art HSI-classification methods.