Nonnegative 3-way tensor factorization via conjugate gradient with globally optimal stepsize

International audienceThis paper deals with the minimal polyadic decomposition (also known as canonical decomposition or Parafac) of a 3-way array, assuming each entry is positive. In this case, the low-rank approximation problem becomes well-posed. The suggested approach consists of taking into account the nonnegative nature of the loading matrices directly in the problem parameterization. Then, the three gradient components are derived allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, we focus on the conjugate gradient algorithm, well matched to large problems. The good behaviour of the proposed approach is illustrated through computer simulations in the context of data analysis and compared to other existing approaches

Computing the nonnegative 3-way tensor factorization using Tikhonov regularization

International audienceThis paper deals with the minimum polyadic decomposition of a nonnegative three-way array. The main advantage of the nonnegativity constraint is that the approximation problem becomes well posed. To tackle this problem, we suggest the use of a cost function including penalty terms built with matrix exponentials. Gradient components are then derived, allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, Alternating Least Squares (ALS) and conjugate gradient algorithms are studied and compared with another existing algorithm, thanks to computer simulations performed in the context of data analysis

Computing the polyadic decomposition of nonnegative third order tensors

International audienceComputing the minimal polyadic decomposition (also often referred to as canonical decomposition, or sometimes Parafac) amounts to finding the global minimum of a coercive polynomial in many variables. In the case of arrays with nonnegative entries, the low-rank approximation problem is well posed. In addition, due to the large dimension of the problem, the decomposition can be rather efficiently calculated with the help of preconditioned nonlinear conjugate gradient algorithms, as subsequently shown, if equipped with an algebraic calculation of the globally optimal stepsize in low dimension. Other algorithms are also studied (gradient and quasi-Newton approaches) for comparisons. Two versions of each algorithm are considered: the Enhanced Line Search version (ELS), and the backtracking version alternating with ELS. Computer simulations are provided and demonstrate the good behavior of these algorithms dedicated to nonnegative arrays, compared to others put forward in the literature. Finally, applications in the context of data analysis illustrate various algorithms. The main advantage of the suggested approach is to explicitly take into account the nonnegative nature of the loading matrices in the problem parameterization, instead of enforcing positive entries by projection. According to the experiments we have run, such an approach also happens to be more robust with respect to possible modeling errors

Error Analysis of Low-rank Three-Way Tensor Factorization Approach to Blind Source Separation

International audienceIn tensor factorization approaches to blind separation of multidimensional sources, two formulas for calculating the source tensor have emerged. In practice, it is observed that these two schemes exhibit different levels of robustness against perturbations of the factors involved in the tensor model. Motivated by both practical reasons and the will to better figure this out, we present error analyses in source tensor estimation performed by low-rank factorization of three-way tensors. To that aim, computer simulations as well as the analytical calculation of the theoretical error are carried out. The conclusions drawn from these numerical and analytical error analyses are supported by the results obtained thanks to tensor-based blind decomposition of an experimental multispectral image of a skin tumor

Pharmacokinetic modelling and development of Bayesian estimators for therapeutic drug monitoring of mycophenolate mofetil in reduced-intensity haematopoietic stem cell transplantation.

International audienceBACKGROUND: Mycophenolate mofetil, a prodrug of mycophenolic acid (MPA), is used during non-myeloablative and reduced-intensity conditioning haematopoetic stem cell transplantation (HCT) to improve engraftment and reduce graft-versus-host disease (GVHD). However, information about MPA pharmacokinetics is sparse in this context and its use is still empirical. OBJECTIVES: To perform a pilot pharmacokinetic study and to develop maximum a posteriori Bayesian estimators (MAP-BEs) for the estimation of MPA exposure in HCT. PATIENTS AND METHODS: Fourteen patients administered oral mycophenolate mofetil 15 g/kg three times daily were included. Two consecutive 8-hour pharmacokinetic profiles were performed on the same day, 3 days before and 4 days after the HCT. One 8-hour pharmacokinetic profile was performed on day 27 after transplantation. For these 8-hour pharmacokinetic profiles, blood samples were collected predose and 20, 40, 60, 90 minutes and 2, 4, 6 and 8 hours post-dose. Using the iterative two-stage (ITS) method, two different one-compartment open pharmacokinetic models with first-order elimination were developed to describe the data: one with two gamma laws and one with three gamma laws to describe the absorption phase. For each pharmacokinetic profile, the Akaike information criterion (AIC) was calculated to evaluate model fitting. On the basis of the population pharmacokinetic parameters, MAP-BEs were developed for the estimation of MPA pharmacokinetics and area under the plasma concentration-time curve (AUC) from 0 to 8 hours at the different studied periods using a limited-sampling strategy. These MAP-BEs were then validated using a data-splitting method. RESULTS: The ITS approach allowed the development of MAP-BEs based either on 'double-gamma' or 'triple-gamma' models, the combination of which allowed correct estimation of MPA pharmacokinetics and AUC on the basis of a 20 minute-90 minute-240 minute sampling schedule. The mean bias of the Bayesian versus reference (trapezoidal) AUCs was 20%. AIC was systematically calculated for the choice of the most appropriate model fitting the data. CONCLUSION: Pharmacokinetic models and MAP-BEs for mycophenolate mofetil when administered to HCT patients have been developed. In the studied population, they allowed the estimation of MPA exposure based on three blood samples, which could be helpful in conducting clinical trials for the optimization of MPA in reduced-intensity HCT. However, prior studies will be needed to validate them in larger populations

Contracting the Wigner kernel of a spin to the Wigner kernel of a particle

A general relation between the Moyal formalisms for a spin and a particle is established. Once the formalism has been set up for a spin, the phase-space description of a particle is obtained from contracting the group of rotations to the oscillator group. In this process, turn into a spin Wigner kernel turns into the Wigner kernel of a particle. In fact, only one out of 22s different possible kernels for a spin shows this behavior

Water analysis with the help of tensor canonical decompositions

Coopération universitaire et scientifique Franco-VietnamienneInternational audienceRaw data are collected in five measurement locations along the Var river. It is assumed that some locations interact with each other, whereas others do not. In such a context, we are interested in determining the contribution of each location and in better understanding the water exchanges that are involved. Organic components can also be identified thanks to methods such as Canonical Polyadic decompositions (CP) (sometimes known as Parafac), applied to 3D fluorescence spectra calculated from the collected samples. The expected impact is a more efficient detection of polluting matters in water

A propos de la Symptomatologie de la Rage bovine au cours de l’actuelle enzootie française

Gravière P., Gammel J., Jean E., Kissel J., Royer C., Vincent P., Goret Pierre. A propos de la symptomatologie de la rage bovine au cours de l'actuelle enzootie française. In: Bulletin de l'Académie Vétérinaire de France tome 122 n°4, 1969. pp. 163-168