Multi-dimensional Function Approximation and Regression Estimation

Pérez-Cruz, Fernando; Camps‐Valls, Gustau; Soria-Olivas, Emilio; Pérez-Ruixo, Juan José; Figueiras-Vidal, Aníbal R.; Artés‐Rodríguez, Antonio

doi:10.1007/3-540-46084-5_123

Cited by 64 publications

(66 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This work is supported by the Natural Science Foundation of Shandong Province (Grant No: ZR2016AM24) and the Natural Science Min Hou and Liya Fan / IJAMML 6:1 (2017) [1][2][3][4][5][6][7][8][9][10][11][12][13][14] …”

Section: Acknowledgementsmentioning

confidence: 99%

“…Existing methods can be roughly divided into two categories. One is feed forward neural networks, such as ELM and some variants [4][5][6][7], and another is based on single-output support vector regression machine (S-SVR), such as M-SVR [8] and multiple S-SVR model (multiple S-SVR) [9]. Unfortunately, M-SVR and multiple S-SVR are all to ignore the cross relations among output variables and then decrease the accuracy of regression.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi-Output Least Squares TSVR

Hu¹,

Fan²

2017

Int. J. Appl. Math. Mach. Learning

View full text Add to dashboard Cite

In order to improve the regression accuracy of MLS-SVR presented by Xu et al.[10] with a fast training algorithm, this paper proposes a new regression method named as multioutput least squares twin SVR (MLS-TSVR) for multi-output problems. The main advantage of the proposed method is that the relations among output weight vectors are considered as a whole rather than decomposed in MLS-SVR. Experimental results show that MLS-TSVR has a good property on regression accuracy.

show abstract

Section: Acknowledgementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-Output Least Squares TSVR

Hu¹,

Fan²

2017

Int. J. Appl. Math. Mach. Learning

View full text Add to dashboard Cite

show abstract

“…A sample will surely be penalized once its distance from the origin is larger than ε. This insensitive zone can also be found in [14]. However, that work formulates the structured regression as a quadratic-constrained quadratic program, while our formulation solves the same problem in a quadratic program with linear constraints, which makes the learning process faster and lower the computational cost.…”

mentioning

confidence: 93%

Efficient Structured Support Vector Regression

Jia

Wang

Liu

2011

Computer Vision – ACCV 2010

View full text Add to dashboard Cite

Support Vector Regression (SVR) has been a long standing problem in machine learning, and gains its popularity on various computer vision tasks. In this paper, we propose a structured support vector regression framework by extending the max-margin principle to incorporate spatial correlations among neighboring pixels. The objective function in our framework considers both label information and pairwise features, helping to achieve better cross-smoothing over neighboring nodes. With the bundle method, we effectively reduce the number of constraints and alleviate the adverse effect of outliers, leading to an efficient and robust learning algorithm. Moreover, we conduct a thorough analysis for the loss function used in structured regression, and provide a principled approach for defining proper loss functions and deriving the corresponding solvers to find the most violated constraint. We demonstrate that our method outperforms the state-of-the-art regression approaches on various testbeds of synthetic images and real-world scenes. Abstract. Support Vector Regression (SVR) has been a long standing problem in machine learning, and gains its popularity on various computer vision tasks. In this paper, we propose a structured support vector regression framework by extending the max-margin principle to incorporate spatial correlations among neighboring pixels. The objective function in our framework considers both label information and pairwise features, helping to achieve better cross-smoothing over neighboring nodes. With the bundle method, we effectively reduce the number of constraints and alleviate the adverse effect of outliers, leading to an efficient and robust learning algorithm. Moreover, we conduct a thorough analysis for the loss function used in structured regression, and provide a principled approach for defining proper loss functions and deriving the corresponding solvers to find the most violated constraint. We demonstrate that our method outperforms the state-of-the-art regression approaches on various testbeds of synthetic images and real-world scenes.

show abstract

“…In order to deal with MO regression problems, Prez-Cruz et al [4] developed M-SVR. But according to the experimental results in [5], M-SVR is somewhat sensitive to the perturbation of hyper-parameters in some small scale sample problems.…”

Section: Introductionmentioning

confidence: 99%

FAST M-TLS-RSVR AND M-LS-e-TSVR FOR MULTI-OUTPUT REGRESSION

Zhao¹,

Fan²

2017

Int. J. Appl. Math. Mach. Learning

View full text Add to dashboard Cite

This paper focuses on research multi-output regression problems and proposes two novel fast learning algorithms named as fast multi-output twin least squares regularized SVR (FM-TLS-RSVR) and fast multi-output least squaresrespectively. The main advantage of the proposed methods is to consider the cross relations among output vectors as a whole and avoid the singularity of matrices. In addition, the proposed FM-TLS-RSVR also possesses the sparsity. Experiment results indicate that FM-TLS-RSVR and TSVR --LS -FM ε are two effective and competitive multi-output regressors.

show abstract

Multi-dimensional Function Approximation and Regression Estimation

Cited by 64 publications

References 3 publications

Multi-Output Least Squares TSVR

Multi-Output Least Squares TSVR

Efficient Structured Support Vector Regression

FAST M-TLS-RSVR AND M-LS-e-TSVR FOR MULTI-OUTPUT REGRESSION

Contact Info

Product

Resources

About