In the last decade, twin support vector machines (TWSVMs) classifiers have been achieved considerable emphasis on pattern classification tasks. However, the TWSVM formulation still suffers from the following two shortcomings: (i) TWSVM deals with the inverse matrix calculation in the Wolfe-dual problems which is intractable for large scale datasets with numerous features and samples. (ii) TWSVM minimizes the empirical risk instead of the structural risk in its formulation. With the advent of huge amounts of data today, these disadvantages render TWSVM as an ineffective choice for pattern classification tasks. In this paper, we propose an efficient large scale least squares twin support vector machines (LS-LSTSVM) for pattern classification which rectifies all the aforementioned shortcomings. The proposed LS-LSTSVM introduces different Lagrangian functions to eliminates the need for calculating the inverse matrices. The proposed LS-LSTSVM also does not employ kernel generated surfaces for the non-linear case, and thus used the kernel trick directly. This ensures that the proposed LS-LSTSVM model is superior to the original TWSVM and LSTSVM. Lastly, the structural risk is minimized in LS-LSTSVM. This exhibits the essence of statistical learning theory, and, consequently, classification accuracy on datasets can be improved due to this change. The proposed LS-LSTSVM is solved using the sequential minimal optimization (SMO) technique which makes it more suitable for large scale problems. We further proved the convergence of the proposed LS-LSTSVM. Exhaustive experiments on several real-world benchmarks and NDC based large scale datasets demonstrate that the proposed LS-LSTSVM is feasible for large datasets, and, in most cases, performed better than existing algorithms.

中文翻译：

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大规模最小二乘双 SVM

在过去十年中，双支持向量机 (TWSVM) 分类器在模式分类任务上取得了相当大的重视。然而，TWSVM 公式仍然存在以下两个缺点： (i) TWSVM 处理沃尔夫对偶问题中的逆矩阵计算，这对于具有大量特征和样本的大规模数据集来说是难以处理的。(ii) TWSVM 在其公式中将经验风险而非结构风险降至最低。随着今天大量数据的出现，这些缺点使 TWSVM 成为模式分类任务的无效选择。在本文中，我们提出了一种高效的大规模最小二乘双支持向量机 (LS-LSTSVM) 用于模式分类，它纠正了上述所有缺点。提出的 LS-LSTSVM 引入了不同的拉格朗日函数，以消除计算逆矩阵的需要。提出的 LS-LSTSVM 也没有为非线性情况使用内核生成的表面，因此直接使用了内核技巧。这确保了所提出的 LS-LSTSVM 模型优于原始的 TWSVM 和 LSTSVM。最后，结构风险在 LS-LSTSVM 中被最小化。这体现了统计学习理论的本质，因此，由于这种变化，可以提高数据集的分类准确性。所提出的 LS-LSTSVM 是使用顺序最小优化 (SMO) 技术解决的，这使得它更适用于大规模问题。我们进一步证明了所提出的 LS-LSTSVM 的收敛性。