Brain age prediction with improved least squares twin SVR

Abstract

Alzheimer's disease (AD) is the prevalent form of dementia and shares many aspects with the aging pattern of abnormal brain. Several studies have shown that early prediction and treatment initiation can slow the progression of dementia's and hence, the quality of life of those subjects can be improved. We propose a novel regression model trained on a normal brain age pattern to predict the brain age of the new subjects. If the brain age delta (difference between the predicted and chronological age) is positive that implies accelerated atrophy and hence, a risk factor for possible conversion to AD. Machine learning models like support vector regression (SVR) based models have been successfully employed in the regression problems. However, SVR is computationally inefficient than twin support vector machine based models. Hence, different twin support vector machine based models like twin SVR (TSVR), <formula><tex>$\varepsilon$</tex></formula>-TSVR and Lagrangian TSVR (LTSVR) models have been used for the regression problems. <formula><tex>$\varepsilon$</tex></formula>-TVSR and LTSVR models seek a pair of <formula><tex>$\varepsilon$</tex></formula>-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 risk and hence may be prone to overfitiing. 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 <formula><tex>$l_2$</tex></formula> norm instead of <formula><tex>$l_1$</tex></formula>. Also, we introduce different Lagrangian function to avoid the computation of matrix inverses. The advantages of the proposed ILSTSVR modes are summarised as: i) No matrix inversions are involved in the proposed ILSTSVR model. ii) Structural risk minimization (SRM) principle is embodied in proposed ILSTSVR model which is the marrow of statistical learning and thus avoids the issues of overfitting. We evaluated the proposed ILSTSVR model on the subjects including cognitively healthy, mild cognitive impairment and Alzheimer's disease subjects for brain-age estimation. Experimental evaluation and statistical tests demonstrate the efficiency of the proposed ILSTSVR model for the brain-age prediction. IEEE