Weighted multicategory nonparallel planes SVM classifiers

A hybrid multicategory framework for generating automated trading systems

“…Among the various factors traditionally considered by the researchers from different backgrounds and expertise, technical indicators and oscillators based on historical price data are the most widely used and have been demonstrated to be quite reliable in reflecting the direction of the stock price movements. [46][47][48] 43,49,50 as inputs. On the basis of their importance and capability of capturing the significant market moments, the most relevant indicators may be selected.…”

“…Weighted multicategory generalized eigenvalue proximal SVM (WMGEPSVM) 43 is a nonparallel multicategory classification algorithm that is based on the “One‐vs‐All” approach to construct $$$ K $$$ nonparallel hyperplanes to separate each category from rest of the ($$$ K-1 $$$) categories in such a manner that the separating hyperplane is nearest to its respective category and as far as possible from rest of the categories. To deal with the problem of the unbalanced class data, a modified balancing weight factor has been proposed in 43 for WMGEPSVM.…”

“…Weighted multicategory generalized eigenvalue proximal SVM (WMGEPSVM) 43 is a nonparallel multicategory classification algorithm that is based on the “One‐vs‐All” approach to construct $$$ K $$$ nonparallel hyperplanes to separate each category from rest of the ($$$ K-1 $$$) categories in such a manner that the separating hyperplane is nearest to its respective category and as far as possible from rest of the categories. To deal with the problem of the unbalanced class data, a modified balancing weight factor has been proposed in 43 for WMGEPSVM. WMGEPSVM determines the $$$ K $$$ nonparallel hyperplanes as: $$$$ {\mathbbm{\digamma}}_i^{wmgepsvm}={\omega}_i^T\chi +{b}_i,i=1,2,\dots, K, $$$$ where $$$ {\omega}_i\in {\mathbb{R}}^n $$$ and $$$ {b}_i\in \mathbb{R} $$$.…”

“…WMGEPSVM determines the $$$ K $$$ nonparallel hyperplanes as: $$$$ {\mathbbm{\digamma}}_i^{wmgepsvm}={\omega}_i^T\chi +{b}_i,i=1,2,\dots, K, $$$$ where $$$ {\omega}_i\in {\mathbb{R}}^n $$$ and $$$ {b}_i\in \mathbb{R} $$$. For each category $$$ i $$$ the respective hyperplane $$$ {\mathbbm{\digamma}}_i $$$ is found by solving the following: 43 …”

Critical Review on Biochar‐Supported Catalysts for Pollutant Degradation and Sustainable Biorefinery

“…Biodiesel is a renewable fossil source with properties similar to fossil diesel but with additional advantages of no toxicity and environmentally friendly nature. [ 112–114 ] The production reaction involves esterification and transesterification of free fatty acids (FFAs) and vegetable oils with alcohols (commonly ethanol and methanol) ( Figure ), respectively. [ 115–118 ] There are two sets of catalysts used during the process: homogeneous and heterogeneous.…”