Prediction of Mixtures

The problem of predicting time series originating from mixtures of signals from independent dynamical systems is considered. We show that the problem of finding representations for the dynamics of such systems is hard if the mixing structure of the system is not taken into account. If, on the contrary, the sources can be unmixed in a preprocessing step the complexity of system identification may be drastically reduced. This is demonstrated using chaotic maps. It is shown that applications of methods for blind separation of sources can substantially improve both: prediction performance and prediction horizon.

[1]  D. Katz,et al.  Surface Tensions of Methane-Propane Mixtures , 1943 .

[2]  Yoshua Bengio,et al.  Credit Assignment through Time: Alternatives to Backpropagation , 1993, NIPS.

[3]  L. E. Scriven,et al.  Semiempirical theory of surface tension of binary systems , 1980 .

[4]  Ashok N. Srivastava,et al.  Nonlinear gated experts for time series: discovering regimes and avoiding overfitting , 1995, Int. J. Neural Syst..

[5]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[6]  Mohammad R. Riazi,et al.  Simple equation of state accurately predicts hydrocarbon densities , 1993 .

[7]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[8]  F. Montel,et al.  A simple correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light hydrocarbon systems , 1992 .

[9]  D. Chandler,et al.  Liquid State Physics: A Statistical Mechanical Introduction , 1974 .

[10]  K. Pawelzik,et al.  Optimal Embeddings of Chaotic Attractors from Topological Considerations , 1991 .

[11]  M. Wertheim,et al.  Correlations in the liquid–vapor interface , 1976 .

[12]  G. Ali Mansoori,et al.  Surface tension prediction for pure fluids , 1996, 1802.02201.

[13]  K. Pawelzikzy,et al.  Improving Short-term Prediction with Competing Experts , 1995 .

[14]  Schuster,et al.  Separation of a mixture of independent signals using time delayed correlations. , 1994, Physical review letters.

[15]  G. Saville,et al.  Computer simulation of the gas/liquid surface , 1975 .

[16]  H. Lawrence Clever,et al.  Surface Tensions of Binary Mixtures of Isooctane with Benzene, Cyclohexane, and n-Dodecane at 30°1 , 1964 .

[17]  T. Y. Kwak,et al.  Van der Waals mixing rules for cubic equations of state: applications for supercritical fluid extraction modelling , 1986 .

[18]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[19]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[20]  J. C. Randall,et al.  The Surface Tension and Density of Binary Hydrocarbon Mixtures: Benzene-n-Hexane and Benzene-n-Dodecane , 1966 .

[21]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[22]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[23]  Rudower Chaussee,et al.  Competing Predictors Segment andIdentify Switching , 1994 .

[24]  R. Massoudi,et al.  Effect of pressure on the surface tension of n-hexane. Adsorption of low molecular weight gases on n-hexane at 25.deg. , 1975 .

[25]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[26]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[27]  L. E. Scriven,et al.  An approximate theory of interfacial tensions of multicomponent systems: Applications to binary liquid‐vapor tensions , 1978 .

[28]  Klaus-Robert Müller,et al.  Annealed Competition of Experts for a Segmentation and Classification of Switching Dynamics , 1996, Neural Computation.

[29]  G. C. Benson,et al.  Surface tensions of binary liquid systems. II. Mixtures of alcohols , 1972 .

[30]  John S. Rowlinson,et al.  Fluid Interfacial Phenomena , 1987 .

[31]  Klaus-Robert Müller,et al.  Analysis of switching dynamics with competing neural networks , 1995 .