Online Prediction of Time Series Data With Kernels

Abstract

Abstract-Kernel-based algorithms have been a topic of considerable interest in the machine learning community over the last ten years. Their attractiveness resides in their elegant treatment of nonlinear problems. They have been successfully applied to pattern recognition, regression and density estimation. A common characteristic of kernel-based methods is that they deal with kernel expansions whose number of terms equals the number of input data, making them unsuitable for online applications. Recently, several solutions have been proposed to circumvent this computational burden in time series prediction problems. Nevertheless, most of them require excessively elaborate and costly operations. In this paper, we investigate a new model reduction criterion that makes computationally demanding sparsification procedures unnecessary. The increase in the number of variables is controlled by the coherence parameter, a fundamental quantity that characterizes the behavior of dictionaries in sparse approximation problems. We incorporate the coherence criterion into a new kernel-based affine projection algorithm for time series prediction. We also derive the kernel-based normalized LMS algorithm as a particular case. Finally, experiments are conducted to compare our approach to existing methods.

Nonlinear unmixing of hyperspectral images using radial basis functions and orthogonal least squares

“…Future works include the adaptive update of the weights and centers for unsupervised spectral unmixing. Dictionary learning algorithms [10] could also be investigated for center selection in radial basis function networks.…”

Analisis Dan Implementasi Model Peramalan Berbasis Algoritma Moving Avarage Untuk Nilai Tukar Rupiah Terhadap Dolar

“…Sedangkan peramalan bulanan lebih kurang akurat karena kurangnya sampel data. Richard, Bermudez dan Honeine [6] membahas seberapa cocok algoritma time series ini terhadap data kernel yang telah dikumpulkan kedalam aplikasi online. Sehingga aplikasi tersebut bisa menjadi pembanding cocok tidaknya algoritma time series dimasukan kedalam aplikasi online.…”

Theoretical Analyses on 2-Norm-Based Multiple Kernel Regressors

“…(4). Note that the original kernels K 1 and K 2 are no longer reproducing kernels of the RKHS corresponding to the kernel K = K 1 + K 2 .…”

“…The kernel method [1]- [3] is widely recognized as one of powerful tools in the field of machine learning, such as pattern recognition, regression estimation and density estimation; and it has been imported into the field of signal processing such as system identification problems [4], [5]. So far, many kernel-based learning machines have been proposed such as the support vector machines [3], [6] and the kernel ridge regressors [2].…”