This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N -way array. Decompositions of higher-order tensors (i.e., N -way arrays with N ≥ 3) have applications in psychometrics, chemometrics, signal

that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the dis-tances between

Matching elements of two data schemas or two data instances plays a key role in data warehousing, e-business, or even biochemical applications. In this paper we present a matching algorithm based on a fixpoint computation that is usable across different scenarios. The algorithm takes two graphs

in the biorthogonal, i.e, non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a wavelet-like transform that maps integers to integers.

comes from the role of the Laplacian op erator in providing an optimal emb edding. Th e Laplacian of the graph obtained from the data points may be viewed as an approximation to the Laplace-Beltrami operator defined on the manifold. The emb edding maps for the data come from approximations to a natural

quadtree decomposition and a view-independent visible priority. Our experiments have shown that the morphing can be performed at interactive rates on today’s high-end personal computers. Potential applications of the method include virtual holograms, a walkthrough in a virtual environment, image

, reliability, and scalability. We have built a “crawler” to extract the topology of Gnutella’s application level network. In this paper we analyze the topology graph and evaluate generated network traffic. Our two major findings are that: (1) although Gnutella is not a pure power-law network, its current

A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that find tree-decompositions, algorithms that use tree-decompositions to solve hard problems efficiently, graph minor theory, and some

of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace

DryadLINQ is a system and a set of language extensions that enable a new programming model for large scale distributed computing. It generalizes previous execution environments such as SQL, MapReduce, and Dryad in two ways: by adopting an expressive data model of strongly typed.NET objects