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Cumulative broadband network traac is often thought to be well modelled by fractional Brownian motion. However, some traac measurements do not show an agreement with the Gaussian marginal distribution assumption. We show that if connection rates are modest relative to heavy tailed connection length distribution tails, then stable L evy motion is a sensible(More)
The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a prespecified number of R factors and a residual array by minimizing the sum of squares of the latter. It is well known that an optimal solution for CP need not exist. We show that if an optimal CP solution does not exist, then any sequence of CP factors monotonically decreasing the CP(More)
Let X be a real-valued three-way array. The Candecomp/Parafac (CP) decomposition is written as X = Y (1) + · · · + Y (R) + E, where Y (r) are rank-1 arrays and E is a rest term. Each rank-1 array is defined by the outer product of three vectors a (r) , b (r) and c (r) , i.e. y (r) ij k = a (r) i b (r) j c (r) k. These vectors make up the R columns of the(More)
It has been shown that a best rank-R approximation of an order-k tensor may not exist when R ≥ 2 and k ≥ 3. This poses a serious problem to data analysts using tensor decompositions. It has been observed numerically that, generally, this issue cannot be solved by consecutively computing and subtracting best rank-1 approximations. The reason for this is that(More)
The Candecomp/Parafac (CP) method decomposes a three-way array into a prespecified number R of rank-1 arrays, by minimizing the sum of squares of the residual array. The practical use of CP is sometimes complicated by the occurrence of so-called degenerate sequences of solutions, in which several rank-1 arrays become highly correlated in all three modes and(More)
a best rank-1 approximation does not necessarily decrease tensor rank. HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive(More)