Dangers of geometric filtering

Abstract We argue that there are unrecognised dangers in the popular and powerful geometric filtering method. Carelessly applied, geometric filtering can produce apparent structure in data which is pure noise, or can cause severe distortions in clean deterministic data. The explanations for these effects are straightforward and the dangers are easily avoided by taking simple precautions in the filtering process.

[1]  K. Judd.  An improved estimator of dimension and some comments on providing confidence intervals , 1992 .

[2]  Schwartz,et al.  Singular-value decomposition and the Grassberger-Procaccia algorithm. , 1988, Physical review. A, General physics.

[3]  Kevin Judd,et al.  ESTIMATING DIMENSIONS WITH CONFIDENCE , 1991 .

[4]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[5]  P. Grassberger.  Do climatic attractors exist? , 1986, Nature.

[6]  P. Grassberger,et al.  A simple noise-reduction method for real data , 1991 .

[7]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[8]  J. D. Farmer,et al.  ON DETERMINING THE DIMENSION OF CHAOTIC FLOWS , 1981 .

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

[10]  Yorke,et al.  Noise reduction in dynamical systems. , 1988, Physical review. A, General physics.

[11]  G. P. King,et al.  Topological dimension and local coordinates from time series data , 1987 .

[12]  H. Abarbanel,et al.  Local false nearest neighbors and dynamical dimensions from observed chaotic data. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  T. Sauer.  A noise reduction method for signals from nonlinear systems , 1992 .

[14]  J. D. Farmer,et al.  Optimal shadowing and noise reduction , 1991 .

[15]  K. Judd.  Estimating dimension from small samples , 1994 .

[16]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.