Least square regression with indefinite kernels and coefficient regularization

Sun, Hongwei; Wu, Qiang

doi:10.1016/j.acha.2010.04.001

Cited by 96 publications

(61 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For the least squares regularized regression algorithm, it is known in the literature (e.g. [2,6,11,[16][17][18]20]) that saturation occurs, i.e., for r > 1, the derived learning rate is the same as that for the case r = 1. The index p in our AC plays the same role as r, it reflects the degree of correlation between X and Y with respect to RKHSs (reproducing kernel Hilbert spaces).…”

Section: Resultsmentioning

confidence: 96%

Convergence rate of kernel canonical correlation analysis

Cai

Sun

2011

Sci. China Math.

Self Cite

View full text Add to dashboard Cite

Kernel canonical correlation analysis (CCA) is a nonlinear extension of CCA, which aims at extracting the information shared by two random variables. It has wide applications in many fields, such as information retrieval. This paper gives the convergence rate analysis of kernel CCA under some approximation conditions and some suggestions on how to choose the regularization parameter. The result shows that the convergence rate only depends on two parameters: the rate of regularization parameter and the decay rate of eigenvalues of compact operator V Y X , and it gives better understanding of kernel CCA.

show abstract

Section: Resultsmentioning

confidence: 96%

Convergence rate of kernel canonical correlation analysis

Cai

Sun

2011

Sci. China Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since the analysis for (4.1) with a general kernel is much different from that for (1.1), Sun and Wu [13] considered the coefficient-based regularization scheme for the least square regression. It would be interesting to investigate this kind of algorithms for learning conditional quantile regression.…”

Section: Further Discussionmentioning

confidence: 99%

Conditional quantiles with varying Gaussians

Xiang

2011

Adv Comput Math

View full text Add to dashboard Cite

In this paper we study conditional quantile regression by learning algorithms generated from Tikhonov regularization schemes associated with pinball loss and varying Gaussian kernels. Our main goal is to provide convergence rates for the algorithm and illustrate differences between the conditional quantile regression and the least square regression. Applying varying Gaussian kernels improves the approximation ability of the algorithm. Bounds for the sample error are achieved by using a projection operator, a varianceexpectation bound derived from a condition on conditional distributions and a tight bound for the covering numbers involving the Gaussian kernels.

show abstract

“…Based on the least square regression principle [15,18], a novel quantitative identification method was proposed for CO gas recognition with the PAS experimental system. The relationship between the measured PA signal and the known CO concentration is established using the least square regression method first.…”

Section: The Pas Quantitative Analysis Of Carbon Monoxidementioning

confidence: 99%

Detection of Dissolved Carbon Monoxide in Transformer Oil Using 1.567 μm Diode Laser-Based Photoacoustic Spectroscopy

Zhou

Tang

Zhu

et al. 2015

Journal of Spectroscopy

View full text Add to dashboard Cite

Carbon monoxide (CO) is one of the most important fault characteristic gases dissolved in power transformer oil. With the advantages of high sensitivity and accuracy, long-term stability, and short detection time, photoacoustic spectroscopy (PAS) has been proven to be one promising sensing technology for trace gas recognition. In this investigation, a tunable PAS experimental system based on a distributed-feedback (DFB) diode laser was proposed for recognizing dissolved CO in transformer oil. The molecular spectral line of CO gas detection was selected at 1.567 m in the whole experiment. Relationships between the photoacoustic (PA) signal and gas pressure, temperature, laser power, and CO gas concentration were measured and discussed in detail, respectively. Finally, based on the least square regression theory, a novel quantitative identification method for CO gas detection with the PAS experimental system was proposed. And a comparative research about the gas detection performances performed by the PAS system and gas chromatography (GC) measurement was presented. All results lay a solid foundation for exploring a portable and tunable CO gas PAS detection device for practical application in future.

show abstract

Least square regression with indefinite kernels and coefficient regularization

Cited by 96 publications

References 21 publications

Convergence rate of kernel canonical correlation analysis

Convergence rate of kernel canonical correlation analysis

Conditional quantiles with varying Gaussians

Detection of Dissolved Carbon Monoxide in Transformer Oil Using 1.567 μm Diode Laser-Based Photoacoustic Spectroscopy

Contact Info

Product

Resources

About