Quantile estimators with orthogonal pinball loss function

2018 ◽  
Vol 37 (3) ◽  
pp. 401-417 ◽  
Author(s):  
Lean Yu ◽  
Zebin Yang ◽  
Ling Tang
Keyword(s):  
Loss Function ◽  
Pinball Loss ◽  
Quantile Estimators

Pinball Loss Twin Support Vector Clustering

2021 ◽  
Vol 17 (2s) ◽  
pp. 1-23
Author(s):  
M. Tanveer ◽  
Tarun Gupta ◽  
Miten Shah ◽  
Keyword(s):  
Loss Function ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Structural Mri ◽  
Twin Support Vector Machine ◽  
Support Vector ◽  
Support Vector Clustering ◽  
Hinge Loss ◽  
Pinball Loss ◽  
Vector Clustering

Twin Support Vector Clustering (TWSVC) is a clustering algorithm inspired by the principles of Twin Support Vector Machine (TWSVM). TWSVC has already outperformed other traditional plane based clustering algorithms. However, TWSVC uses hinge loss, which maximizes shortest distance between clusters and hence suffers from noise-sensitivity and low re-sampling stability. In this article, we propose Pinball loss Twin Support Vector Clustering (pinTSVC) as a clustering algorithm. The proposed pinTSVC model incorporates the pinball loss function in the plane clustering formulation. Pinball loss function introduces favorable properties such as noise-insensitivity and re-sampling stability. The time complexity of the proposed pinTSVC remains equivalent to that of TWSVC. Extensive numerical experiments on noise-corrupted benchmark UCI and artificial datasets have been provided. Results of the proposed pinTSVC model are compared with TWSVC, Twin Bounded Support Vector Clustering (TBSVC) and Fuzzy c-means clustering (FCM). Detailed and exhaustive comparisons demonstrate the better performance and generalization of the proposed pinTSVC for noise-corrupted datasets. Further experiments and analysis on the performance of the above-mentioned clustering algorithms on structural MRI (sMRI) images taken from the ADNI database, face clustering, and facial expression clustering have been done to demonstrate the effectiveness and feasibility of the proposed pinTSVC model.

scholarly journals Stochastic Subgradient for Large-Scale Support Vector Machine Using the Generalized Pinball Loss Function

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1652
Author(s):  
Wanida Panup ◽  
Rabian Wangkeeree
Keyword(s):  
Support Vector Machine ◽  
Loss Function ◽  
Gradient Descent ◽  
Large Scale ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Support Vector ◽  
Hinge Loss ◽  
Gradient Descent Algorithm ◽  
Pinball Loss

In this paper, we propose a stochastic gradient descent algorithm, called stochastic gradient descent method-based generalized pinball support vector machine (SG-GPSVM), to solve data classification problems. This approach was developed by replacing the hinge loss function in the conventional support vector machine (SVM) with a generalized pinball loss function. We show that SG-GPSVM is convergent and that it approximates the conventional generalized pinball support vector machine (GPSVM). Further, the symmetric kernel method was adopted to evaluate the performance of SG-GPSVM as a nonlinear classifier. Our suggested algorithm surpasses existing methods in terms of noise insensitivity, resampling stability, and accuracy for large-scale data scenarios, according to the experimental results.

scholarly journals Forecasting the Intra-Day Spread Densities of Electricity Prices

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 687 ◽  
Author(s):  
Ekaterina Abramova ◽  
Derek Bunn
Keyword(s):  
Loss Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Density Functions ◽  
Shape Parameters ◽  
Electricity Prices ◽  
Dynamic Density ◽  
Cumulative Distribution Functions ◽  
Pinball Loss ◽  
Best Fitting

Intra-day price spreads are of interest to electricity traders, storage and electric vehicle operators. This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast the German electricity price spreads between different hours of the day, as revealed in the day-ahead auctions. The four specifications of the density functions are dynamic and conditional upon exogenous drivers, thereby permitting the location, scale and shape parameters of the densities to respond hourly to such factors as weather and demand forecasts. The best fitting and forecasting specifications for each spread are selected based on the Pinball Loss function, following the closed-form analytical solutions of the cumulative distribution functions.

General twin support vector machine with pinball loss function

2019 ◽  
Vol 494 ◽  
pp. 311-327 ◽  
Author(s):  
M. Tanveer ◽  
A. Sharma ◽  
P.N. Suganthan
Keyword(s):  
Support Vector Machine ◽  
Loss Function ◽  
Twin Support Vector Machine ◽  
Support Vector ◽  
Pinball Loss
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