Least Squares Fit

1 Introduction PLS-DA for data analysis in chemistry and OMICS studies. Also included in this package are 3 variable selection methods: 1) target projection (TP) 2) competitive adaptive reweighted sampling (CARS) 3) subwindow permutation analysis (SPA). SPA is based on model pupulation analysis...

1 Introduction This toolbox implements all the routine PLS-related/based algorithms which kind of serves as the basics in chemometrics, including PLS calibration and prediction, leave one out cross validation (LOOCV), K-fold cross validation, Monte Carlo cross validation(MCCV), double cross...

This is a wrapper function to solve optimization problems (using FMINCON) of the form:min w.r.t. X of CostFunc(X) = beta*(W_ls*F(X)) + (1 - beta)*(max(W_mm*F(X)))subject to: A*X


Platforms: Matlab

The code implements the algorithm as given in Chen et. al 1991.It takes max tolerance from the user.It selects Ms significant regressors from the total M regressors.Unfortunately, the error obtained after training the RBF network isn't as expected. Is there a mistake in my code???Please feel free...


Platforms: Matlab

The code implemented a special case of the ellipsoid fitting technique proposed in the paper Least Squares Ellipsoid Specific Fitting, corresponding to case k= 4. Just put the two files in the same directory and run "testFit4". You can change the noise level to observe the fitting accuracy and...


Platforms: Matlab

Demonstrates a way to implement the LSM algorithm.This is done on a example from the book of Astrom and Wittenmark, Adaptive Control, 2nd ed


Platforms: Matlab

This library implements a randomized algorithm for solving the least-squares equation x = arg min norm(A * x - b, 2) or the underdetermined system min(norm(x, 2)) s.t. Ax=b. With high probability the running this o(mn^2) for an m-by-n matrix.For details of the solver see the paper at:Blendenpik:...


Platforms: Matlab

This example solves a complex curve fitting problem that involves parameter pooling and stratification using a nonlinear least-squares approach. This example also takes advantage of some new language features with MATLAB 7. * Anonymous functions * Nested functions


Platforms: Matlab

Solves the linear least squares problem with nonnegative variables using the newton's algorithm in:Portugal, Judice and Vicente, A comparison of block pivoting and interior point algorithms for linear least squares problems with nonnegative variables, Mathematics of Computation, 63(1994), pp....


Platforms: Matlab

Solves the linear least squares problem with nonnegative variables using the predictor-corrector algorithm in:Portugal, Judice and Vicente, A comparison of block pivoting and interior point algorithms for linear least squares problems with nonnegative variables, Mathematics of Computation,...


Platforms: Matlab

A command-line peak fitting program for time-series signals, written as a self-contained Matlab function in a single m-file. Uses an non-linear optimization algorithm to decompose a complex, overlapping-peak signal into its component parts. The objective is to determine whether your signal can be...


Platforms: Matlab

An affine (or first-order) optic flow model has 6 parameters, describing image translation, dilation, rotation and shear. The class affine_flow provides methods to estimates these parameters for two frames of an image sequence.The class implements a least-squares fit of the parameters to...


Platforms: Matlab

Like polyfit.m but includes weighting of each data point.Summary----------------Find a least-squares fit of 1D data y(x) with an nth order polynomial, weighted by w(x).Usage-----P = polyfitweighted(X,Y,N,W) finds the coefficients of a polynomial P(X) of degree N that fits the data Y best in a...


Platforms: Matlab

This function implements a method of using genetic algorithms to optimise the form of a polynomial, i.e. reducing the number of terms required in comparison to a least-squares fit using all possible terms, as described in the following paper:Clegg, J. et al, "The use of a genetic algorithm to...


Platforms: Matlab

For a given real-valued function of one real variable on an interval, the code calculates the best approximation in the uniform (max) norm by a polynomial of a given degree. Approximating in a uniform norm is much computationally harder compared to the standard least squares fit, but gives eye...


Platforms: Matlab

This m-file computes an approximate determination coefficient (R2) for prediction, sayR2pred = 1 - (PRESS/SST)where PRESS = prediction error sum of squares, SST = total sum of squares.This statistic gives some indication of the predictive capability of the regression model. So, we could expect...


Platforms: Matlab

This function either displays Zernike polynomials over a circular, hexagonal, elliptical, rectangular or annular shaped pupil, or fits surface data to these pupil shapes. See Mahajan, V.N., G.-m. Dai, "Orthonormal polynomials in wavefront analysis: analytical solution," J. Opt. Soc. Am. A, Vol....


Platforms: Matlab

A contour of a 2D region is defined by an ordered set of points where the neighboring elements contain the neighboring points. Such representation can be obtained with many techniques such as boundary tracing and chain codes. (In a simple 2D point set or a curve the points do not have to lie in a...


Platforms: Matlab

Performs polynomial fits that pass through a specified point (x0,y0).The application is to give a least squares fit that is 'exact' at a desired data point, e.g. an equilibrium point in a nonlinear equation of motion implemented via polynomial approximation. Discussion of theory included in...


Platforms: Matlab

polyfitweighted2.m and polyval2.m---------polyfitweighted2.m: Find a least-squares fit of 2D data z(x,y) with an n th order polynomial, weighted by w(x,y).polyval2.m: Evaluate 2D polynomial produced by polyfitweighted2.m.Usage polyfitweighted2-----P = polyfitweighted2(X,Y,Z,N,W) finds the...


Platforms: Matlab