Singular value decomposition (SVD) is a general-purpose mathematical analysis tool that has been used in a variety of information-retrieval applications. As the size and complexity of retrieval collections increase, it is crucial for our analysis tools to scale accordingly. To this end, we have studied the application of a new theoretically justiied SVD approximation algorithm to the problem of...

In vitro neuronal networks are known to fire in Synchronized Bursting Events (SBEs), with characteristic temporal width of 100 ms. We treat these events as the principal data atoms of the network. Applying SVD (or PCA) to the spatial information, i.e. activity of neurons per burst, we demonstrate characteristic changes that take place over time scales of hours. We consider this as evidence for ...

Subspace-based methods rely on singular value decomposition (SVD) of the sample covariance matrix (SCM) to compute the array signal or noise subspace. For large array, triditional subspace-based algorithms inevitably lead to intensive computational complexity due to both calculating SCM and performing SVD of SCM. To circumvent this problem, a NyströmBased algorithm for array subspace estimation...

Cerebral small vessel disease (SVD) is a major contributor to stroke, and a leading cause of cognitive impairment and dementia. Despite the devastating effects of cerebral SVD, the pathogenesis of cerebral SVD is still not completely understood. Moreover, there are no specific pharmacological strategies for its prevention or treatment. Cerebral SVD is characterized by marked functional and stru...

A data set with n measurements on p variables can be represented by an n × p data matrix X. In highdimensional settings where p is large, it is often desirable to work with a low-rank approximation to the data matrix. The most prevalent low-rank approximation is the singular value decomposition (SVD). Given X, an n × p data matrix, the SVD factorizes X as X = UDV ′, where U ∈ Rn×n and V ∈ Rp×p ...

The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including ...

Most of the research on dictionary learning has focused on developing algorithms under the assumption that data is available at a centralized location. But often the data is not available at a centralized location due to practical constraints like data aggregation costs, privacy concerns, etc. Using centralized dictionary learning algorithms may not be the optimal choice in such settings. This ...

White matter lesion (WML) in magnetic resonance imaging is commonly observed in patients with cerebral small vessel disease (SVD), but the pathological mechanism of WML in SVD is still unclear. We observed the metabolism and microscopic anatomy of white matter in SVD patients. Twelve subjects clinically diagnosed with SVD and 6 normal control subjects were examined with magnetic resonance spect...

We develop a dictionary learning algorithm by minimizing the `1 distortion metric on the data term, which is known to be robust for non-Gaussian noise contamination. The proposed algorithm exploits the idea of iterative minimization of weighted `2 error. We refer to this algorithm as `1-K-SVD, where the dictionary atoms and the corresponding sparse coefficients are simultaneously updated to min...

Singular value decomposition (SVD) is a matrix decomposition algorithm that returns the optimal (in the sense of squared error) low-rank decomposition of a matrix. SVD has found widespread use across a variety of machine learning applications, where its output is interpreted as compact and informative representations of data. The Netflix Prize challenge, and collaborative filtering in general, ...