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Twin extreme learning machine (TELM) based on the hinge-loss function shows great potential for pattern classification. However, the hinge loss is related to the shortest distance between sets and the corresponding classifier is hence sensitive to noise and unstable for resampling. In contrast, the <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-insensitive zone pinball loss is related to the quantile distance therefore is not sensitive to noise, and the resulting solution is sparse. To improve the performance of TELM, we propose a novel TELM learning framework by introducing <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>-insensitive zone pinball loss function into TELM. Compared to TELM with hinge loss, the proposed SPTELM has the same computational complexity and is insensitive to noise, resampling stability and maintaining the sparsity of the solution. Further, we theoretically analyzed the sparsity, noise insensitivity and time complexity of SPTELM. Experimental results on multiple datasets demonstrate the noise insensitive, retains sparsity of the proposed method.

Sparse Twin Extreme Learning Machine With $\varepsilon$ -Insensitive Zone Pinball Loss