The aim of this paper applies greedy kernel principal component analysis (greedy kernel PCA) to deal with training data
reduction and nonlinear feature extraction in classification. Kernel PCA is a nonlinear extension of linear PCA. It shows
a powerful nonlinear feature extraction technique via kernel trick. A disadvantage of kernel PCA, however, is that the
storage of training data in terms of the dot products is too expensive since the size of kernel matrix increases
quadratically with the number of training data. So, a more efficient feature extraction method, greedy kernel PCA, is
proposed to reduce training data and nonlinear feature extraction for classification. The reduced set method aims to find
a new kernel expansion and well approximates the original training data. Simulation results show both kernel PCA and
greedy kernel PCA are more superior to linear PCA in feature extraction. Greedy kernel PCA will tend towards kernel
PCA feature extraction as more percentage of training data is included in the reduced set, whilst greedy kernel PCA
results in lower evaluation cost due to the reduced training set. The experiments show also that greedy kernel PCA can
significantly reduce the complexity while retaining their accuracy in classification.
Hyperspectral remote sensing image classification is a challenging task in remote sensing applications because this
image always has some information redundancy and is easy to be affected by noise or lack of the separability. A semi-supervised
classification method based on principal component analysis (PCA) method and kernel fuzzy C-means
(KFCM) algorithm for hyperspectral remote sensing image is proposed in this paper. First the PCA method finds an
effective representation of spectral signature in a reduced dimensional feature space. Then a semi-supervised kernel-based
FCM algorithm, called SSKFCM algorithm by introducing semi-supervised learning technique and the kernel trick
simultaneously into conventional fuzzy C-means algorithm, is introduced to classify the feature vectors. Finally
numerical experiments are conducted on a hyperspectral remote sensing image that provides digital images of 80 spectral
bands with wavelength rang from 455 nm to 1642 nm. Classification performance is estimated by classification accuracy
and kappa coefficient. The simulation results show that the proposed approach can be effectively applied to
hyperspectral remote sensing image classification.
Fuzzy C-Means (FCM) algorithm is a fuzzy pattern recognition method. Clustering precision of the algorithm is affected
by its equal partition trend for data set of large discrepancy of each class samples number, and the optimal clustering
result of the algorithm mightn't be a right partition in this case. In order to overcome this disadvantage, a Gaussian
function Weighted Fuzzy C-Means (WFCM) algorithm is proposed, which the weighted function is produced by a
Gaussian function calculating dot density of each sample. To certain extent, the WFCM algorithm has not only overcome
the limitation of equal partition trend in fuzzy Cmeans algorithm, but also been favorable convergence and stability. The
calculation of the weighted function and the choice of sample dot density range restriction value for the algorithm are
both objective. When partially supervised information obtained from a few labeled samples is introduced to the WFCM
algorithm, the classification performance of the WFCM algorithm is further enhanced and the convergent speed of
objective function is further accelerated.
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