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The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear) optimization problem. This paper is devoted to developing an identification method which aims to find the global optimal solution under mild computational burden. Key to the developed identification algorithm is to transform a bilinear estimation to a rank constrained optimization problem and further a difference of convex programming (DCP) problem. The initial condition for the DCP problem is obtained by solving its convex part of the optimization problem which happens to be a nuclear norm regularized optimization problem. Since the nuclear norm regularized optimization is the closest convex form of the low-rank constrained estimation problem, the obtained initial condition is always of high quality which provides the DCP problem a good starting point. The DCP problem is then solved by the sequential convex programming method. Finally, numerical examples are included to show the effectiveness of the developed identification algorithm., Accepted to IEEE Conference on Decision and Control (CDC) 2015

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a deep learning approach to spectral clustering that overcomes the above shortcomings. Our network, which we call SpectralNet, learns a map that embeds input data points into the eigenspace of their associated graph Laplacian matrix and subsequently clusters them. We train SpectralNet using a procedure that involves constrained stochastic optimization. Stochastic optimization allows it to scale to large datasets, while the constraints, which are implemented using a special-purpose output layer, allow us to keep the network output orthogonal. Moreover, the map learned by SpectralNet naturally generalizes the spectral embedding to unseen data points. To further improve the quality of the clustering, we replace the standard pairwise Gaussian affinities with affinities leaned from unlabeled data using a Siamese network. Additional improvement can be achieved by applying the network to code representations produced, e.g., by standard autoencoders. Our end-to-end learning procedure is fully unsupervised. In addition, we apply VC dimension theory to derive a lower bound on the size of SpectralNet. State-of-the-art clustering results are reported on the Reuters dataset. Our implementation is publicly available at https://github.com/kstant0725/SpectralNet ., Added citations. Accepted to ICLR 2018

We introduce a multiscale approach that combines segmentation with classification to detect abnormal brain structures in medical imagery, and demonstrate its utility in automatically detecting multiple sclerosis (MS) lesions in 3-D multichannel magnetic resonance (MR) images. Our method uses segmentation to obtain a hierarchical decomposition of a multichannel, anisotropic MR scans. It then produces a rich set of features describing the segments in terms of intensity, shape, location, neighborhood relations, and anatomical context. These features are then fed into a decision forest classifier, trained with data labeled by experts, enabling the detection of lesions at all scales. Unlike common approaches that use voxel-by-voxel analysis, our system can utilize regional properties that are often important for characterizing abnormal brain structures. We provide experiments on two types of real MR images: a multichannel proton-density-, T2-, and T1-weighted dataset of 25 MS patients and a single-channel fluid attenuated inversion recovery (FLAIR) dataset of 16 MS patients. Comparing our results with lesion delineation by a human expert and with previously extensively validated results shows the promise of the approach.