Cerebral small vessel disease (SVD), including white matter hyperintensities (WMH), lacunes and microbleeds, and brain atrophy, are related to cognitive impairment. However, these magnetic resonance imaging (MRI) markers for SVD do not account for all the clinical variances observed in subjects with SVD. Here, we investigated the relation between conventional MRI markers for SVD, network effici...

Here, {W,Z} are the dictionary and the coefficients, respectively, and zk is the kth column of Z. K, q, and λ are user selected parameters controlling the power of the model. More recently, many models with additional structure have been proposed. For example, in [9, 2], the dictionary elements are arranged in groups and the sparsity is on the group level. In [3, 5, 7], the dictionaries are con...

Networks are becoming a unifying framework for modeling complex systems and network inference problems are frequently encountered in many fields. Here, I develop and apply a generative approach to network inference (RCweb) for the case when the network is sparse and the latent (not observed) variables affect the observed ones. From all possible factor analysis (FA) decompositions explaining the...

Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has shifted of the emphasis in frame theory toward sparse l1-minimization problems. In this paper, we apply frame theory to the sparse representation of signals i...

This work presents a new algorithm for dictionary learning. Existing algorithms such as MOD and K-SVD often fail to find the best dictionary because they get trapped in a local minimum. Olshausen and Field’s Sparsenet algorithm relies on a fixed step projected gradient descent. With the right step, it can avoid local minima and converge towards the global minimum. The problem then becomes to fi...

This paper develops an efficient online algorithm for learning multiple consecutive tasks based on the KSVD algorithm for sparse dictionary optimization. We first derive a batch multi-task learning method that builds upon K-SVD, and then extend the batch algorithm to train models online in a lifelong learning setting. The resulting method has lower computational complexity than other current li...

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized SVD (TNrSVD) algorithm is an MPO implementation of the randomized SVD algorithm that is able to compute dominant singular values and their corresponding sin...

Swine vesicular disease (SVD) was first observed in Italy in 1966, and was initially diagnosed as foot and mouth disease (FMD). The causative agent of SVD was classified as an Enterovirus within the family Picornaviridae. It was included in the list of diseases notifiable to the World Organisation for Animal Health (OIE) because of the similarity of its lesions to those produced by FMD; however...