In Alzheimer’s disease (AD) diagnosis, joint feature selection for predicting disease labels (classification) and estimating cognitive scores (regression) with neuroimaging data has received increasing attention. In this paper, we propose a model named Shared Manifold regularized Joint Feature Selection (SMJFS) that performs classification and regression in a unified framework for AD diagnosis. For classification, unlike the existing works that build least squares regression models which are insufficient in the ability of extracting discriminative information for classification, we design an objective function that integrates linear discriminant analysis and subspace sparsity regularization for acquiring an informative feature subset. Furthermore, the local data relationships are learned according to the samples’ transformed distances to exploit the local data structure adaptively. For regression, in contrast to previous works that overlook the correlations among cognitive scores, we learn a latent score space to capture the correlations and employ the latent space to design a regression model with $\ell _{2,1}$ -norm regularization, facilitating the feature selection in regression task. Moreover, the missing cognitive scores can be recovered in the latent space for increasing the number of available training samples. Meanwhile, to capture the correlations between the two tasks and describe the local relationships between samples, we construct an adaptive shared graph to guide the subspace learning in classification and the latent cognitive score learning in regression simultaneously. An efficient iterative optimization algorithm is proposed to solve the optimization problem. Extensive experiments on three datasets validate the discriminability of the features selected by SMJFS.

中文翻译：

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阿尔茨海默病诊断中用于关节分类和回归的共享流形正则化关节特征选择

在阿尔茨海默病（AD）诊断中，利用神经影像数据预测疾病标签（分类）和估计认知评分（回归）的联合特征选择受到越来越多的关注。在本文中，我们提出了一种名为共享流形正则化联合特征选择（SMJFS）的模型，该模型在 AD 诊断的统一框架中执行分类和回归。对于分类，与构建最小二乘回归模型的现有工作在提取分类判别信息的能力方面不足不同，我们设计了一个集成线性判别分析和子空间稀疏正则化的目标函数来获取信息丰富的特征子集。此外，根据样本的变换距离来学习局部数据关系，以自适应地利用局部数据结构。对于回归，与之前忽视认知分数之间的相关性的工作相比，我们学习潜在分数空间来捕获相关性，并利用潜在空间来设计回归模型 $\ell _{2,1}$ -范数正则化，促进回归任务中的特征选择。此外，可以在潜在空间中恢复丢失的认知分数，以增加可用训练样本的数量。同时，为了捕获两个任务之间的相关性并描述样本之间的局部关系，我们构建了一个自适应共享图来同时指导分类中的子空间学习和回归中的潜在认知得分学习。提出了一种高效的迭代优化算法来解决优化问题。对三个数据集的大量实验验证了 SMJFS 选择的特征的可区分性。