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Kernel principal component analysis (KPCA) generalizes the traditional PCA to the nonlinear dimensionality reduction method by incorporating kernel techniques.
On the other hand, with kernel techniques DKLLE extracts the nonlinear feature information when mapping input data into some high dimensional feature space.
By incorporating the kernel techniques into factor analysis, the superiority of KFA method is demonstrated to tackle the uncertainty and non-Gaussian features in the vibration measurements for feature selection and fusion.
The dk-NN AD proposed by Sahigara et al. [12], uses the k-NN principle associated with the concept of adaptive kernel techniques in KDE to detect local neighbourhoods within the data.
By doing so, one can optimize in linear space and avoid computational complexities of kernel techniques, thus making the proposed method suitable for scaling to larger quantities of training data.
When no linear separation of the training data is possible, SVM can work effectively in combination with kernel techniques such as quadratic, polynomial or radial basis function (RBF), so that the hyperplane defining the SVM corresponds to a non-linear decision boundary in the input space [ 14].
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To handle non-linearly separable distributions between different classes, we further develop a non-linear extension of UOOTF based on the kernel technique.
(2) By incorporating the kernel technique into the factor analysis, a new feature selection method (KFA) is presented to exploit the nonlinear representative features with non-Gaussian distributions.
Finally, using the kernel technique, the spectral feature and the spatial feature were jointly used for the classification through a support vector machine (SVM) formulation.
Kernel discriminant analysis, which employs the kernel technique to perform linear discriminant analysis in a high-dimensional feature space, is developed to extract the significant nonlinear features which maximise the between-class variance and minimise the within-class variance.
Network structures can be incorporated into standard methods by defining an appropriate similarity measure between sequences and then employ a kernel technique, such as Support Vector Machines (SVM) [ 4] to classify the response.
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