Efficient Support Vector Regression with Weighted Constraints

Wang, Ling; Fu, Dong Mei

doi:10.1007/978-3-642-25992-0_82

Cited by 1 publication

(9 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We slightly modify the technique, for setting the OF‐weights, proposed in the work of Wang and Fu by using the new sample's features, x 0 , instead of using the average of training samples. Then, the OF‐weights are set in the following way:

{italicλ}_{italici} = \{\begin{matrix} center \\ center {((), 1 - \frac{italicD ((),, {italicx}_{italici}, x_{0}) - D_{\min}}{D_{\max} - D_{\min}})}^{2} + σ, & center ε < D (x_{i}, {italicx}_{0}) < {italicD}_{italicmax} \\ center 1, & center D (x_{i}, {italicx}_{0}) < ε \end{matrix}, i = 1, 2, \dots, n,

where

{italicD}_{italicmax} = \max (({}, italicD ((),, {italicx}_{italici}, x_{0}) : italici = 1, 2, \dots, italicn))

and

{italicD}_{italicmin} = \min (({}, italicD ((),, {italicx}_{italici}, x_{0}) : italici = 1, 2, \dots, italicn)) .

σ and ε are two parameters.…”

Section: Doubly Weighted Svrmentioning

confidence: 99%

“…As analyzed in Section 5, OF‐weights are suitable for reducing the influence of outliers because OF‐weights directly shrink the estimated coefficients in the estimated functions. And we recommend to adopt the method, for setting the CF‐weights, proposed in the work of Wang and Fu …”

Section: Doubly Weighted Svrmentioning

confidence: 99%

“…The evolution ended when the optimization procedure ran 100 generations or the best fitness was smaller than 10 − 1 . To set the parameters σ and ε for the OF‐weights, we refer to the simulation section in the work of Wang and Fu . The results are summarized in Table .…”

Section: Application Of Dwsvr In the Real Estate Marketmentioning

confidence: 99%

“…In this section, we will describe the basics and the formulations of the SVR 1 and the SVR with OF-weights introduced in, for example, the work of Wang and Fu. 6 The details about solving SVR problems will be discussed in Section 4, as the connection between the LASSO and the SVR is directly discovered during the process in which the primal form of the SVR is transformed into the dual form. In the following sections, we will introduce the weights added as slack variables in constraints.…”

Section: Classic Svr and Objective Function Weightsmentioning

confidence: 99%

“…5 Additionally, various techniques were also designed for general use. For example, Wang and Fu 6 proposed to use the Mahalanobis distance in the kernel-induced feature space to set up observation weights. Similar to this idea, the aim of the techniques of adding weights for general use is to get rid of outliers and to achieve good prediction performance; see, for example, Xu et al, 5 Huang and Shen, 7 Tang and Zhang, 8 Mei and Zhang, 9 Qing et al, 10 and Xu and Wang.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Weighted Support Vector Regression

Han

Clemmensen

2014

Quality & Reliability Eng

View full text Add to dashboard Cite

We propose a new type of weighted support vector regression (SVR), motivated by modeling local dependencies in time and space in prediction of house prices. The classic weights of the weighted SVR are added to the slack variables in the objective function (OF‐weights). This procedure directly shrinks the coefficient of each observation in the estimated functions; thus, it is widely used for minimizing influence of outliers. We propose to additionally add weights to the slack variables in the constraints (CF‐weights) and call the combination of weights the doubly weighted SVR. We illustrate the differences and similarities of the two types of weights by demonstrating the connection between the Least Absolute Shrinkage and Selection Operator (LASSO) and the SVR. We show that an SVR problem can be transformed to a LASSO problem plus a linear constraint and a box constraint. We demonstrate the capabilities of the doubly weighted approach through an example of prediction of house prices. The weight functions in the house pricing model depend on the geographical distance to the house of interest and the difference in time of sale (CF‐weights) as well as the differences lying in variables (OF‐weights), such as house size and number of floors. The results illustrate that the combination of the two types of weights describes the relative importance of observations very well and lowers the influence of possible outliers. Therefore, it enables the SVR models to have good performance. Copyright © 2014 John Wiley & Sons, Ltd.

show abstract