Ganaie M A, Tanveer M, Beheshti Iman
IEEE J Biomed Health Inform. 2023 Apr;27(4):1661-1669. doi: 10.1109/JBHI.2022.3147524. Epub 2023 Apr 4.
Alzheimer's disease (AD) is the prevalent form of dementia and shares many aspects with the aging pattern of the abnormal brain. Machine learning models like support vector regression (SVR) based models have been successfully employed in the estimation of brain age. However, SVR is computationally inefficient than twin support vector machine based models. Hence, different twin support vector machine based models like twin SVR (TSVR), ε-TSVR, and Lagrangian TSVR (LTSVR) models have been used for the regression problems. ε-TSVR and LTSVR models seek a pair of ε-insensitive proximal planes for generation of end regressor. However, SVR and TSVR based models have several drawbacks- i) SVR model is computationally inefficient compared to the TSVR based models. ii) Twin SVM based models involve the computation of matrix inverse which is intractable in real world scenario's. iii) Both TSVR and LTSVR models are based on empirical risk minimization principle and hence may be prone to overfitting. iv) TSVR and LTSVR assume that the matrices appearing in their formulation are positive definite which may not be satisfied in real world scenario's. To overcome these issues, we formulate improved least squares twin support vector regression (ILSTSVR). The proposed ILSTSVR modifies the TSVR by replacing the inequality constraints with the equality constraints and minimizes the slack variables using squares of L norm instead of L. Also, we introduce a different Lagrangian function to avoid the computation of matrix inverses. We evaluated the proposed ILSTSVR model on the subjects including cognitively healthy, mild cognitive impairment and Alzheimer's disease for brain-age estimation. Experimental evaluation and statistical tests demonstrate the efficiency of the proposed ILSTSVR model for brain-age prediction.
阿尔茨海默病（AD）是痴呆症的常见形式，在异常大脑的老化模式方面有许多相似之处。基于支持向量回归（SVR）等机器学习模型已成功应用于脑龄估计。然而，SVR在计算效率上低于基于孪生支持向量机的模型。因此，不同的基于孪生支持向量机的模型，如孪生SVR（TSVR）、ε-TSVR和拉格朗日TSVR（LTSVR）模型已被用于回归问题。ε-TSVR和LTSVR模型寻求一对ε-不敏感近端平面以生成最终回归器。然而，基于SVR和TSVR的模型有几个缺点：i）与基于TSVR的模型相比，SVR模型计算效率低下。ii）基于孪生支持向量机的模型涉及矩阵求逆运算，这在实际场景中难以处理。iii）TSVR和LTSVR模型都基于经验风险最小化原则，因此可能容易出现过拟合。iv）TSVR和LTSVR假设其公式中出现的矩阵是正定的，这在实际场景中可能无法满足。为了克服这些问题，我们提出了改进的最小二乘孪生支持向量回归（ILSTSVR）。所提出的ILSTSVR通过用等式约束替换不等式约束来修改TSVR，并使用L范数的平方而不是L来最小化松弛变量。此外，我们引入了一个不同的拉格朗日函数以避免矩阵求逆运算。我们在包括认知健康、轻度认知障碍和阿尔茨海默病的受试者上评估了所提出的ILSTSVR模型用于脑龄估计。实验评估和统计测试证明了所提出的ILSTSVR模型在脑龄预测方面的效率。
