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Online updating regularized kernel
On the other hand, to update the kernel weight, the traditional linear or nonlinear online learning algorithms are extended to RKHS to develop types of kernel online learning algorithms, such as the kernel recursive least square algorithms and the kernel (regularized) least mean square algorithms which incorporate suitable sparsification methods to select their kernel centers.The convergence and stability issues of the learning algorithms are guaranteed with adaptive training methods in terms of external disturbance under the Lyapunov stability theorem.IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems,2014,33(2):279-290. A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes[J]. Journal of Chemical and Pharmaceutical Research,2014,6(7):338-346. IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics,2011,42(2):513-529. Extreme learning machine: Theory and application[J].
A novel unified framework is also proposed for kernel online learning with adaptive kernels.
In this framework, the kernel width is not set as a fixed value in the training process.
The sparsification method performs a role to select a compact dictionary consisting of the kernel function centers.
They are developed according to different measures, such as the mutual information measure, the significance measure, the coherence measure or the cumulative coherence measure, which are used to evaluate the novelty of new training samples.
The Mercer kernel function is applied to perform transformation of feature vectors from a low dimensional space to a high or even infinite dimensional reproducing kernel Hilbert space (RKHS), where linear solutions can be found in the high dimensional feature space.
Kernel methods have been widely applied in batch learning or off-line learning contexts for various applications.
For the problem of Gram matrix expansion in kernel online learning algorithms, a novel sparsification rule is presented by measuring the instantaneous learnable information contained on a data sample for dictionary selection. Online learning with (multiple) kernels: A review[J]. IEEE Transactions on Signal Processing,2015,63(23):6343-6353.
The proposed sparsification method combines the constructive strategy and the pruning strategy in two stages. Online learning with kernel regularized least mean square algorithms[J].
The recurrent term makes the past information reusable for the updating of the algorithm.
To ensure the reuse of the recurrent information indeed accelerates the convergence speed, a hybrid training algorithm is proposed for the recurrent training of the algorithm with guaranteed convergence.