Kernel regression with sparse metric learning
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Publication:3190300
DOI10.3233/IFS-2012-0597zbMATH Open1295.62041arXiv1712.09001MaRDI QIDQ3190300
Publication date: 16 September 2014
Published in: Journal of Intelligent & Fuzzy Systems (Search for Journal in Brave)
Abstract: Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted average of the surrounding training examples. The weights are typically computed by a distance-based kernel function and they strongly depend on the distances between examples. In this paper, we first review the latest developments of sparse metric learning and kernel regression. Then a novel kernel regression method involving sparse metric learning, which is called kernel regression with sparse metric learning (KRSML), is proposed. The sparse kernel regression model is established by enforcing a mixed -norm regularization over the metric matrix. It learns a Mahalanobis distance metric by a gradient descent procedure, which can simultaneously conduct dimensionality reduction and lead to good prediction results. Our work is the first to combine kernel regression with sparse metric learning. To verify the effectiveness of the proposed method, it is evaluated on 19 data sets for regression. Furthermore, the new method is also applied to solving practical problems of forecasting short-term traffic flows. In the end, we compare the proposed method with other three related kernel regression methods on all test data sets under two criterions. Experimental results show that the proposed method is much more competitive.
Full work available at URL: https://arxiv.org/abs/1712.09001
kernel regressiongradient descent algorithmtraffic flow forecastingmixed norm regularizationsparse metric learning
Nonparametric regression and quantile regression (62G08) Learning and adaptive systems in artificial intelligence (68T05)
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