Thin-plate smoothing spline
WebThe ANUSPLIN package provides a facility for transparent analysis and interpolation of noisy multi-variate data using thin plate smoothing splines, through comprehensive statistical analyses, data diagnostics and … WebApr 6, 2006 · In the model formula, cr represents a cubic smoothing spline, cc a periodic cubic spline, te a tensor product spline and tprs a thin plate regression spline, and d represents the basis dimensions that were used for each model term (for tensor product smooths, d is a vector, d[i] gives the dimension of the ith marginal basis that is used in ...
Thin-plate smoothing spline
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WebThin Plate Spline is scalar invariant, which means if you scale x and y by the same factor, the result should be the same. However, if you scale x and y differently, then the result will be different. This is common characteristics among radial basis functions. Some radial basis functions are not even scalar invariant. Share Improve this answer WebSeven marginal spline types are supported: linear, cubic, different cubic, cubic periodic, cubic thin-plate, ordinal, and nominal. Random effects and parametric effects are also supported. Response can be Gaussian or non-Gaussian: Binomial, Poisson, Gamma, Inverse Gaussian, or Negative Binomial.
http://web.mit.edu/~r/current/arch/i386_linux26/lib/R/library/mgcv/html/smooth.construct.tp.smooth.spec.html Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. They were introduced to geometric design by Duchon. They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and shortly known as the TPS-RPM algorithm. See more The name thin plate spline refers to a physical analogy involving the bending of a thin sheet of metal. Just as the metal has rigidity, the TPS fit resists bending also, implying a penalty involving the smoothness of the … See more TPS has been widely used as the non-rigid transformation model in image alignment and shape matching. An additional application is the … See more • Explanation for a simplified variation problem • TPS at MathWorld • TPS in C++ See more The thin plate spline has a natural representation in terms of radial basis functions. Given a set of control points $${\displaystyle \{c_{i},i=1,2,\ldots ,K\}}$$, a radial basis function defines a spatial mapping which maps any location $${\displaystyle x}$$ in … See more • Elastic map (a discrete version of the thin plate approximation for manifold learning) • Inverse distance weighting • Polyharmonic spline (the thin plate spline is a special case of a … See more
WebDec 1, 2006 · The method discretises the bivariate thin plate smoothing spline equations using hierarchical biquadratic B-splines, and uses a nested grid multigrid procedure to solve the system. To optimise smoothness, a double iteration is incorporated, whereby the estimate of the spline solution and the estimate of the optimal smoothing parameter are ... WebThe smoothing parameter determines the relative weight to place on the contradictory demands of having f be smooth or having f be close to the data. For p = 0, f is the least …
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WebJan 1, 1991 · Thin plate smoothing splines are widely used to spatially interpolate surface climate, however, their application to large data sets is limited by computational efficiency. janice hardy fiction universityWebhere: Thin-plate splines Similar to feature-space model-based statistical vs. empirical prediction I e.g., linear regression model vs. random forest D G Rossiter (CU) Empirical … janice hardy show don\u0027t tellWebAug 14, 2015 · Emerging thought and people leader who aspire to provide strategic leadership and innovate to help company increase profit, minimize waste, lower cost and … janice hanna authorWebApr 11, 2024 · The variables showing the highest importance from the random forests were modeled using the smoothing thin-plate spline in the R package fields [102, 106]. These splines solve a minimization problem that fits piecewise cubic polynomials with continuous first and second derivatives. The median cubic smoothing spline is the robust version of … janice hardy\u0027s fiction universityWebSpline Construction. Create splines including B-form, tensor-product, NURBs, and other rational splines. Using the Curve Fitter app or the fit function, you can fit cubic spline interpolants, smoothing splines, and thin-plate splines. Other Curve Fitting Toolbox™ functions allow more specialized control over spline construction. janice harding imagesWebFeb 23, 2012 · Thin-plate splines with automatic optimal smoothing parameter selection via generalized cross-validation (GCV) have a number of desirable properties (Wahba, 1990). GCV provides an efficient and objective method to determine the correct degree of smoothing for optimally separating a smooth function from white noise. janice harrington obituaryWebApr 11, 2024 · Semiparametric modeling techniques, such as generalized additive models (GAM), employ thin-plate splines to generate a basis expansion on the distances between spatial grid cells and knots placed over the study area to generate a smoothing matrix comparable to a GAM smooth that can account for the random effects of spatial … janice harper obituary