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### 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, 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.

### Efficient Sparse Group Feature Selection via Nonconvex Optimization

Sparse feature selection has been demonstrated to be effective in handling high-dimensional data. While promising, most of the existing works use convex methods, which may be suboptimal in terms of the accuracy of feature selection and parameter estimation. In this paper, we expand a nonconvex paradigm to sparse group feature selection, which is motivated by applications that require identifying the underlying group structure and performing feature selection simultaneously. The main contributions of this article are twofold: (1) statistically, we introduce a nonconvex sparse group feature selection model which can reconstruct the oracle estimator. Therefore, consistent feature selection and parameter estimation can be achieved; (2) computationally, we propose an efficient algorithm that is applicable to large-scale problems. Numerical results suggest that the proposed nonconvex method compares favorably against its competitors on synthetic data and real-world applications, thus achieving desired goal of delivering high performance.

### Multidimensional classification of hippocampal shape features discriminates Alzheimer's disease and mild cognitive impairment from normal aging

We describe a new method to automatically discriminate between patients with Alzheimer's disease (AD) or mild cognitive impairment (MCI) and elderly controls, based on multidimensional classification of hippocampal shape features. This approach uses spherical harmonics (SPHARM) coefficients to model the shape of the hippocampi, which are segmented from magnetic resonance images (MRI) using a fully automatic method that we previously developed. SPHARM coefficients are used as features in a classification procedure based on support vector machines (SVM). The most relevant features for classification are selected using a bagging strategy. We evaluate the accuracy of our method in a group of 23 patients with AD (10 males, 13 females, age $\pm$ standard-deviation (SD) = 73 $\pm$ 6 years, mini-mental score (MMS) = 24.4 $\pm$ 2.8), 23 patients with amnestic MCI (10 males, 13 females, age $\pm$ SD = 74 $\pm$ 8 years, MMS = 27.3 $\pm$ 1.4) and 25 elderly healthy controls (13 males, 12 females, age $\pm$ SD = 64 $\pm$ 8 years), using leave-one-out cross-validation. For AD vs controls, we obtain a correct classification rate of 94%, a sensitivity of 96%, and a specificity of 92%. For MCI vs controls, we obtain a classification rate of 83%, a sensitivity of 83%, and a specificity of 84%. This accuracy is superior to that of hippocampal volumetry and is comparable to recently published SVM-based whole-brain classification methods, which relied on a different strategy. This new method may become a useful tool to assist in the diagnosis of Alzheimer's disease.

### WoCE: a framework for clustering ensemble by exploiting the wisdom of Crowds theory

The Wisdom of Crowds (WOC), as a theory in the social science, gets a new paradigm in computer science. The WOC theory explains that the aggregate decision made by a group is often better than those of its individual members if specific conditions are satisfied. This paper presents a novel framework for unsupervised and semi-supervised cluster ensemble by exploiting the WOC theory. We employ four conditions in the WOC theory, i.e., diversity, independency, decentralization and aggregation, to guide both the constructing of individual clustering results and the final combination for clustering ensemble. Firstly, independency criterion, as a novel mapping system on the raw data set, removes the correlation between features on our proposed method. Then, decentralization as a novel mechanism generates high-quality individual clustering results. Next, uniformity as a new diversity metric evaluates the generated clustering results. Further, weighted evidence accumulation clustering method is proposed for the final aggregation without using thresholding procedure. Experimental study on varied data sets demonstrates that the proposed approach achieves superior performance to state-of-the-art methods.

### Improving feature selection algorithms using normalised feature histograms

The proposed feature selection method builds a histogram of the most stable features from random subsets of a training set and ranks the features based on a classifier based cross-validation. This approach reduces the instability of features obtained by conventional feature selection methods that occur with variation in training data and selection criteria. Classification results on four microarray and three image datasets using three major feature selection criteria and a naive Bayes classifier show considerable improvement over benchmark results.