We propose a new algorithm for the symmetric eigenproblem that computes eigenvalues and eigenvectors with high relative accuracy for the largest class of symmetric, definite and indefinite, matrices known so far. The algorithm is divided into two stages: the first one computes a singular value decomposition (SVD) with high relative accuracy, and the second one obtains eigenvalues and eigenvecto...

Singular-value decomposition (SVD) of a linear imaging system gives information on the null and measurement components of object and image and provides a method for object reconstruction from image data. We apply SVD to through-focus imaging systems that produce several two-dimensional images of a three-dimensional object. Analytical expressions for the singular functions are derived in the geo...

Latent semantic indexing (LSI) is an application of numerical method called singular value decomposition (SVD), which discovers latent semantic in documents by creating concepts from existing terms. The application area is not limited to text retrieval, many applications such as image compression are known. We propose usage of SVD as a possible data mining method and lattice size reduction tool...

Data distortion is a critical component to preserve privacy in security-related data mining applications, such as in data miningbased terrorist analysis systems. We propose a sparsified Singular Value Decomposition (SVD) method for data distortion. We also put forth a few metrics to measure the difference between the distorted dataset and the original dataset. Our experimental results using syn...

In this paper we present a novel technique for wavelet-based corner detection using singular value decomposition (SVD). Here SVD facilitates the selection of global natural scale in discrete wavelet transform. We define natural scale as the level associated with most prominent (dominant) eigenvalue. Eigenvector corresponding to dominant eigenvalue is considered as the natural scale. The corners...

For a set of 1D vectors, standard singular value decomposition (SVD) is frequently applied. For a set of 2D objects such as images or weather maps, we form 2DSVD, which computes principal eigenvectors of rowrow and column-column covariance matrices, exactly as in the standard SVD. We study optimality properties of 2DSVD as low-rank approximation and show that it provides a framework unifying tw...

The singular value decomposition, or SVD , has been studied in the past as a tool for detecting and understanding patterns in a collection of documents. We show how the matrices produced by the SVD calculation can be interpreted, allowing us to spot patterns of characters that indicate particular topics in a corpus. A test collection, consisting of two days of AP newswire tra c, is used as a ru...

Abstract. We propose a novel and constructive algorithm that decomposes an arbitrary tensor into a finite sum of orthonormal rank-1 outer factors. The algorithm, named TTr1SVD, works by converting the tensor into a rank-1 tensor train (TT) series via singular value decomposition (SVD). TTr1SVD naturally generalizes the SVD to the tensor regime and delivers elegant notions of tensor rank and err...

We present a new mechanism for detecting shared bottlenecks between end-to-end paths in a network. Our mechanism, which only needs one-way delays from endpoints as an input, is based on the well known linear algebraic approach SVD (Singular Value Decomposition). Clusters of flows which share a bottleneck are extracted from SVD results by applying an outlier detection method. Simulations with va...

We investigate a multiple input multiple output (MIMO) relay broadcast channel (RBC) with full cooperation between users. A beamforming and combining design is proposed based on singular value decomposition (SVD) of the channel matrix between users. Then, users can simultaneously relay each other’s information on the same frequency band with zero interference from each antenna’s transmit signal...