We present a novel approach to automatically segment magnetic resonance (MR) images of the human brain into anatomical regions. Our methodology is based on a deep artificial neural network that assigns each voxel in an MR image of the brain to its corresponding anatomical region. The inputs of the network capture information at different scales around the voxel of interest: 3D and orthogonal 2D intensity patches capture the local spatial context while large, compressed 2D orthogonal patches and distances to the regional centroids enforce global spatial consistency. Contrary to commonly used segmentation methods, our technique does not require any non-linear registration of the MR images. To benchmark our model, we used the dataset provided for the MICCAI 2012 challenge on multi-atlas labelling, which consists of 35 manually segmented MR images of the brain. We obtained competitive results (mean dice coefficient 0.725, error rate 0.163) showing the potential of our approach. To our knowledge, our technique is the first to tackle the anatomical segmentation of the whole brain using deep neural networks.

We present a framework for clustering with cluster-specific feature selection. The framework, CRAFT, is derived from asymptotic log posterior formulations of nonparametric MAP-based clustering models. CRAFT handles assorted data, i.e., both numeric and categorical data, and the underlying objective functions are intuitively appealing. The resulting algorithm is simple to implement and scales nicely, requires minimal parameter tuning, obviates the need to specify the number of clusters a priori, and compares favorably with other methods on real datasets.

Gene expression levels in a population vary extensively across tissues. Such heterogeneity is caused by genetic variability and environmental factors, and is expected to be linked to disease development. The abundance of experimental data now enables the identification of features of gene expression profiles that are shared across tissues, and those that are tissue-specific. While most current research is concerned with characterising differential expression by comparing mean expression profiles across tissues, it is also believed that a significant difference in a gene expression's variance across tissues may also be associated to molecular mechanisms that are important for tissue development and function. We propose a sparse multi-view matrix factorisation (sMVMF) algorithm to jointly analyse gene expression measurements in multiple tissues, where each tissue provides a different "view" of the underlying organism. The proposed methodology can be interpreted as an extension of principal component analysis in that it provides the means to decompose the total sample variance in each tissue into the sum of two components: one capturing the variance that is shared across tissues, and one isolating the tissue-specific variances. sMVMF has been used to jointly model mRNA expression profiles in three tissues - adipose, skin and LCL - which are available for a large and well-phenotyped twins cohort, TwinsUK. Using sMVMF, we are able to prioritise genes based on whether their variation patterns are specific to each tissue. Furthermore, using DNA methylation profiles available, we provide supporting evidence that adipose-specific gene expression patterns may be driven by epigenetic effects.

We introduce, test and discuss a method for classifying and clustering data modeled as directed graphs. The idea is to start diffusion processes from any subset of a data collection, generating corresponding distributions for reaching points in the network. These distributions take the form of high-dimensional numerical vectors and capture essential topological properties of the original dataset. We show how these diffusion vectors can be successfully applied for getting state-of-the-art accuracies in the problem of extracting pathways from metabolic networks. We also provide a guideline to illustrate how to use our method for classification problems, and discuss important details of its implementation. In particular, we present a simple dimensionality reduction technique that lowers the computational cost of classifying diffusion vectors, while leaving the predictive power of the classification process substantially unaltered. Although the method has very few parameters, the results we obtain show its flexibility and power. This should make it helpful in many other contexts.

In applications such as recommendation systems and revenue management, it is important to predict preferences on items that have not been seen by a user or predict outcomes of comparisons among those that have never been compared. A popular discrete choice model of multinomial logit model captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to solve a convex relaxation of nuclear norm minimization. We present the convex relaxation approach in two contexts of interest: collaborative ranking and bundled choice modeling. In both cases, we show that the convex relaxation is minimax optimal. We prove an upper bound on the resulting error with finite samples, and provide a matching information-theoretic lower bound.

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space. Stacking the encoder and decoder together constructs an autoencoder, which we term a diffusion net, that performs out-of-sample-extension as well as outlier detection. We introduce new neural net constraints for the encoder, which preserves the local geometry of the points, and we prove rates of convergence for the encoder. Also, our approach is efficient in both computational complexity and memory requirements, as opposed to previous methods that require storage of all training points in both the high-dimensional and the low-dimensional spaces to calculate the out-of-sample-extension and the pre-image.

We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using \emph{Riemannian manifold optimization} as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation of manifold optimization, however, fails spectacularly: it converges to the same solution but vastly slower. Driven by intuition from manifold convexity, we then propose a reparamerization that has remarkable empirical consequences. It makes manifold optimization not only match EM---a highly encouraging result in itself given the poor record nonlinear programming methods have had against EM so far---but also outperform EM in many practical settings, while displaying much less variability in running times. We further highlight the strengths of manifold optimization by developing a somewhat tuned manifold LBFGS method that proves even more competitive and reliable than existing manifold optimization tools. We hope that our results encourage a wider consideration of manifold optimization for parameter estimation problems.

We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probability distribution, which preserves its mean-square norm. We show that unsupervised learning can be casted as an optimization of the space contraction to preserve the volume occupied by unlabeled examples, at each layer of the network. Supervised learning and classification are performed with an averaged scattering, which provides scattering estimations for multiple classes.

Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both the normalized and unnormalized variants in recent random matrix theory literature. However, normalization for spectral clustering is commonly believed to be beneficial [Stat. Comput. 17 (2007) 395-416]. Indeed, our experiments show that normalization improves prediction accuracy. In this paper, for the popular stochastic blockmodel, we theoretically show that normalization shrinks the spread of points in a class by a constant fraction under a broad parameter regime. As a byproduct of our work, we also obtain sharp deviation bounds of empirical principal eigenvalues of graphs generated from a stochastic blockmodel.

Most real-world networks exhibit community structure, a phenomenon characterized by existence of node clusters whose intra-edge connectivity is stronger than edge connectivities between nodes belonging to different clusters. In addition to facilitating a better understanding of network behavior, community detection finds many practical applications in diverse settings. Communities in online social networks are indicative of shared functional roles, or affiliation to a common socio-economic status, the knowledge of which is vital for targeted advertisement. In buyer-seller networks, community detection facilitates better product recommendations. Unfortunately, reliability of community assignments is hindered by anomalous user behavior often observed as unfair self-promotion, or "fake" highly-connected accounts created to promote fraud. The present paper advocates a novel approach for jointly tracking communities while detecting such anomalous nodes in time-varying networks. By postulating edge creation as the result of mutual community participation by node pairs, a dynamic factor model with anomalous memberships captured through a sparse outlier matrix is put forth. Efficient tracking algorithms suitable for both online and decentralized operation are developed. Experiments conducted on both synthetic and real network time series successfully unveil underlying communities and anomalous nodes.