Stable Feature Selection from Brain sMRI

Neuroimage analysis usually involves learning thousands or even millions of variables using only a limited number of samples. In this regard, sparse models, e.g. the lasso, are applied to select the optimal features and achieve high diagnosis accuracy. The lasso, however, usually results in independent unstable features. Stability, a manifest of reproducibility of statistical results subject to reasonable perturbations to data and the model (Yu 2013), is an important focus in statistics, especially in the analysis of high dimensional data. In this paper, we explore a nonnegative generalized fused lasso model for stable feature selection in the diagnosis of Alzheimer’s disease. In addition to sparsity, our model incorporates two important pathological priors: the spatial cohesion of lesion voxels and the positive correlation between the features and the disease labels. To optimize the model, we propose an efficient algorithm by proving a novel link between total variation and fast network flow algorithms via conic duality. Experiments show that the proposed nonnegative model performs much better in exploring the intrinsic structure of data via selecting stable features compared with other state-of-the-arts.  Neuroimage analysis is challenging due to its high feature dimensionality and data scarcity. Sparse models such as the lasso (Tibshirani 1996) have gained great reputation in statistics and machine learning, and they have been applied to the analysis of such high dimensional data by exploiting the sparsity property in the absence of abundant data. As a major result, automatic selection of relevant variables/features by such sparse formulation achieves promising performance. For example, in (Liu, Zhang, and Shen 2012), the lasso model was applied to the diagnosis of Alzheimer’s disease (AD) and showed better performance than the support vector machine (SVM), which is one of the state-of-the-arts in brain image classification. However, in statistics, it is known that the lasso does not always provide interpretable results because of its instability (Yu 2013). “Stability” here means the reproducibility of statistical results subject to reasonable perturbations to data and These perturbations include the often used Jacknife, bootstrap and cross-validation.) This unstable behavior of the lasso model is critical in high dimensional data analysis. The resulting irreproducibility of the feature selection are especially undesirable in neuroimage analysis/diagnosis. However, unlike the problems such as registration and classification, the stability issue of feature selection is much less studied in this field. In this paper we propose a model to induce more stable feature selection from high dimensional brain structural Magnetic Resonance Imaging (sMRI) images. Besides sparsity, the proposed model harnesses two important additional pathological priors in brain sMRI: (i) the spatial cohesion of lesion voxels (via inducing fusion terms) and (ii) the positive correlation between the features and the disease labels. The correlation prior is based on the observation that in many brain image analysis problems (such as AD, frontotemporal dementia, corticobasal degeneration, etc), there exist strong correlations between the features and the labels. For example, gray matter of AD is degenerated/atrophied. Therefore, the gray matter values (indicating the volume) are positively correlated with the cognitive scores or disease labels {-1,1}. That is, the less gray matter, the lower the cognitive score. Accordingly, we propose nonnegative constraints on the variables to enforce the prior and name the model as “non-negative Generalized Fused Lasso” (nGFL). It extends the popular generalized fused lasso and enables it to explore the intrinsic structure of data via selecting stable features. To measure feature stability, we introduce the “Estimation Stability” recently proposed in (Yu 2013) and the (multi-set) Dice coefficient (Dice 1945). Experiments demonstrate that compared with existing models, our model selects much more stable (and pathological-prior consistent) voxels. It is worth mentioning that the non-negativeness per se is a very important prior of many practical problems, e.g. (Lee and Seung 1999). Although nGFL is proposed to solve the diagnosis of AD in this work, the model can be applied to more general problems. Incorporating these priors makes the problem novel w.r.t the lasso or generalized fused lasso from an optimization standpoint. Although off-the-shelf convex solvers such as CVX (Grant and Boyd 2013) can be applied to solve the optimization, it hardly scales to high-dimensional problems in feasible time. In this regard, we propose an efficient algoProceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence