A fast and recursive algorithm for clustering large datasets with kk-medians

Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the $k$-means algorithm, a new class of recursive stochastic gradient algorithms designed for the $k$-medians loss criterion is proposed. By their recursive nature, these algorithms are very fast and are well adapted to deal with large samples of data that are allowed to arrive sequentially. It is proved that the stochastic gradient algorithm converges almost surely to the set of stationary points of the underlying loss criterion. A particular attention is paid to the averaged versions, which are known to have better performances, and a data-driven procedure that allows automatic selection of the value of the descent step is proposed. The performance of the averaged sequential estimator is compared on a simulation study, both in terms of computation speed and accuracy of the estimations, with more classical partitioning techniques such as $k$-means, trimmed $k$-means and PAM (partitioning around medoids). Finally, this new online clustering technique is illustrated on determining television audience profiles with a sample of more than 5000 individual television audiences measured every minute over a period of 24 hours.Comment: Under revision for Computational Statistics and Data Analysi

Multiuser Detection For Asynchronous ARGOS Signals

In this paper, we investigate the application of multiuser detection techniques to a Low Polar Orbit (LPO) mobile satellite used in the ARGOS system. These techniques are used to mitigate the multiple access interference in the uplink transmission of the system. Unlike CDMA, due to the Doppler Effect, each signal has a different received carrier frequency and a different propagation delay. Multiuser detection techniques are proposed for asynchronous transmission in ARGOS system: the maximum likelihood detector, the conventional detector, and the sequential interference cancellation detector, as solutions to tackle the interference effects. Bit Error Rate performance graphs are shown for these techniques

Non Data Aided Parameter Estimation for Multi-User ARGOS Receivers

In this paper, parameter estimators are analyzed in the context of Successive Interference Cancelation (SIC) receivers for the ARGOS system. A Non Data Aided (NDA) feed forward estimator is proposed for the amplitude and the carrier phase parameters. Time delays are assumed to be known. A Window Accumulator (WA) is used to reduce the influence of the additive noise. In the presence of frequency offset, the window length L cannot be chosen arbitrarily large but an optimal length Lopt can be determined. However, because the estimator induces a different optimal length for each parameter, a trade-off must be made. We show that a window length of around 35 samples induces mean square errors (MSEs) lower than 0.012 for both parameters. The MSE of the proposed estimator is also compared to the Modified Cram´er Rao Bound (MCRB)

Impact of Imperfect Parameter Estimation on the Performance of Multi-User ARGOS Receivers

In this paper, we analyze the performance of Successive Interference Cancelation (SIC) receivers in the context of the ARGOS satellite system. Multi-user SIC receivers are studied in presence of imperfect estimates of signal parameters. We derive performance graphs that show the parameter ranges over which a successful demodulation of all users is possible. First, the graphs are derived in the context of perfect parameter estimation. Then, imperfect parameter estimation is considered. Erroneous estimations affect both the amplitude and the time delay of the received signal. Carrier frequencies are assumed to be accurately measured by the receiver. ARGOS SIC receivers are shown to be both robust to imperfect amplitude estimation and sensitive to imperfect time delay estimation

Numerical simulation of a 3D unsteady two-phase flow in the filling cavity in oxygen of a cryogenic rocket-engine

The feeding of the LOX dome of a cryogenic rocket-engine is a decisive stage of the transient engine ignition. However flight conditions are difficult to reproduce by experimental ground tests. The work reported here is part of an ongoing research effort to develop a robust method for prediction and understanding the LOX dome feeding. In the framework of this project, experiments with substition fluids (air and water) are conducted, without mass and energy transfer. This work presented here intends to reproduce these experiments through incompressible two-phase flow CFD simulations, in an industrial geometry equivalent to the experimental mock-up, made up of a feeding piper, a dome and 122 injectors. More precisely, the aim is to compare the numerical results obtained with NEPTUNE CFD code with the experimental results, through the dome pressure and the mass flow rate of water at the outlet. An important work was made to obtain the same inlet conditions in NEPTUNE CFD code as the experimenters, in order to compare the numerical results with the experimental results for the best. The influence of the interfacial momentum transfer modeling and turbulence modeling are also studied here. The turbulence modeling plays no macroscopic or local role on the mass flow rate of water, on the mass of water in dome and on the dome pressure. The drag model has a major impact on our results as well globally as locally, unlike the turbulence modeling. The Simmer-like model is prefered in comparison to the Large Interface called LIM, because it is in better agreement with experimental data. Moreover, it has to be highlighted that the Simmer-like model is very sensitive to its parameter d, the inclusion diameter