Automatic Repeated-loess Decomposition of Data Consisting of Sums of Oscillatory Curves

Repeated loess is a nonparametric procedure that uses progressive smoothing and differencing to decompose data consisting of sums of curves. Smoothing is by locally weighted polynomial regression. Here the procedure was developed so that the decomposition into components was controlled automatically by the number of maxima in each component. The level of smoothing of each component was chosen to maximize the estimated probability of the observed number of maxima. No assumptions were made about the periodicity of components and only very weak assumptions about their shapes. The automatic procedure was applied to simulated data and to experimental data on human visual sensitivity to line orientation.

[1]  J. Wolfe,et al.  The role of categorization in visual search for orientation. , 1992, Journal of experimental psychology. Human perception and performance.

[2]  M. Farge.  Wavelet Transforms and their Applications to Turbulence , 1992 .

[3]  B. Silverman,et al.  Estimating the mean and covariance structure nonparametrically when the data are curves , 1991 .

[4]  T. Gasser,et al.  Residual variance and residual pattern in nonlinear regression , 1986 .

[5]  Christian Marendaz,et al.  Visual Search for Oriented Lines: Anisotropy and Psychophysical Modeling Nature and Dynamics of Reference Frames Nature and Dynamics of Reference Frames in Visual Search for Orientation: Implications for Early Visual Processing , 2022 .

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

[7]  D. Foster,et al.  Asymmetries in oriented-line detection indicate two orthogonal filters in early vision , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[8]  D. Regan,et al.  Periodicity in orientation discrimination and the unconfounding of visual information , 1986, Vision Research.

[9]  Jeffrey D. Hart,et al.  Nonparametric Smoothing and Lack-Of-Fit Tests , 1997 .

[10]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[11]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[12]  G. Orban,et al.  How well do response changes of striate neurons signal differences in orientation: a study in the discriminating monkey , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[13]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[14]  B. Silverman,et al.  Using Kernel Density Estimates to Investigate Multimodality , 1981 .

[15]  William S. Cleveland,et al.  Visualizing Data , 1993 .

[16]  Irma J. Terpenning,et al.  STL : A Seasonal-Trend Decomposition Procedure Based on Loess , 1990 .

[17]  P. Schiller,et al.  Quantitative studies of single-cell properties in monkey striate cortex. II. Orientation specificity and ocular dominance. , 1976, Journal of neurophysiology.

[18]  S Westland,et al.  Multiple groups of orientation–selective visual mechanisms underlying rapid orientated–line detection , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[19]  R. Baddeley,et al.  A statistical analysis of natural images matches psychophysically derived orientation tuning curves , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[20]  G. Henry,et al.  The nature and origin of orientation specificity in neurons of the visual pathways , 1994, Progress in Neurobiology.

[21]  S. Appelle.  Perception and discrimination as a function of stimulus orientation: the "oblique effect" in man and animals. , 1972, Psychological bulletin.

[22]  Dario L. Ringach,et al.  Dynamics of orientation tuning in macaque primary visual cortex , 1997, Nature.

[23]  P. Diggle.  Time Series: A Biostatistical Introduction , 1990 .

[24]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[25]  J. Marron,et al.  SiZer for Exploration of Structures in Curves , 1999 .

[26]  J. Ramsay,et al.  Some Tools for Functional Data Analysis , 1991 .

[27]  S. Thorpe,et al.  Dynamics of orientation coding in area V1 of the awake primate , 1993, Visual Neuroscience.

[28]  W. Cleveland,et al.  Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting , 1988 .

[29]  Thomas A. Louis,et al.  Modeling the Labeling Index Distribution: An Application of Functional Data Analysis , 1995 .

[30]  Cécile Ballaz,et al.  La perception visuelle des orientations et« l'effet de l'oblique » , 2000 .

[31]  R. L. Valois,et al.  The orientation and direction selectivity of cells in macaque visual cortex , 1982, Vision Research.

[32]  J. Marron,et al.  SCALE SPACE VIEW OF CURVE ESTIMATION , 2000 .

[33]  Frederick Robertson Macaulay,et al.  The Smoothing of Time Series , 1931 .

[34]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .