A MATLAB Wrapper for Machine Learning, with another wrapper for neuroimaging data analysis
These functions require the following packages:
To get started, have a look at the demo scripts "ML_demo.m" and "ML4NI_demo.m".
Generally, an analysis proceeds in the following steps: Given features Y, classes x or targets x,
- create a cross-validation (CV) matrix by calling
CV = ML_CV(x, k, mode)wherekis the number of cross-validation folds andmodeis the desired cross-validation strategy (typehelp ML_CVfor more info); AND - a) perform support vector classification (SVC) by calling
SVC = ML_SVC(x, Y, CV, C)OR
b) perform support vector regression (SVR) by callingSVR = ML_SVR(x, Y, CV, C)
whereCis the SVM cost parameter andCVis the cross-validation matrix; - call
ML_SVM_res(SVC, 'perf')orML_SVM_res(SVR, 'perf')to visualize decoding results; - add input arguments
permandsubs(SVC only) to generate permutations and/or perform subsampling.
To directly apply SVC or SVR to neuroimaging data (i.e. scans), use the function "ML4NI_SVM.m" (type help ML4NI_SVM for more info or see below).
function CV = ML_CV(c, k, mode)
% _
% Cross-Validation Folds for Machine Learning Analysis
% FORMAT CV = ML_CV(c, k, mode)
%
% c - an n x 1 vector of class labels (1, 2, 3 etc.)
% k - an integer larger than 1, the number of CV folds
% mode - a string indicating the cross-validation mode
% o 'kf' - k-folds cross-validation across all points
% o 'kfc' - k-folds cross-validation on points per class
% o 'loo' - leave-one-out cross-validation across all points
% o 'looc' - leave-one-out cross-validation on points per class
%
% CV - an n x k matrix indicating training (1) and test (2)
% data for each cross-validation foldfunction SVC = ML_SVC(x, Y, CV, C, perm, subs)
% _
% Cross-Validated Support Vector Machine for Classification
% FORMAT SVC = ML_SVC_ext(x, Y, CV, C, perm, subs)
%
% x - an n x 1 vector of class labels (1, 2, 3 etc.)
% Y - an n x v matrix of predictor variables
% CV - an n x k matrix of cross-validation folds
% C - a scalar, the cost parameter of the SVM
% perm - an integer, the number of permutations
% subs - an integer, the number of subsamples
%
% SVC - a structure specifying the calibrated SVM
% o data - the data for the SVM (x, Y)
% o m - the number of classes (=max(x))
% o N - a 1 x m vector, number of points per class
% o pars - parameters of the SVM (CV, C)
% o opt - options for LibSVM's svmtrain
% o perm - the number of permutations
% o subs - the number of subsamples
% o pred - predictions of the SVM
% o is - an ne x subs matrix of subsampling indices
% o ip - an ne x perm x subs array of permutation indices
% o xt - an ne x perm x subs array of true class labels
% o xp - an ne x perm x subs vector of predicted class labels
% ( where ne is the effective number of data points, i.e.
% n, if subs == 0; m x [min(N)-mod(min(N),10)], if subs > 1 )
% o perf - predictive performance of the SVM
% o DA - a 1 x perm x subs array of decoding accuracies
% o BA - a 1 x perm x subs array of balanced accuracies
% o CA - an m x perm x subs array of class accuracies
% o DA_CI - a 1 x 2 x subs array of 90% confidence intervals for DA
% o BA_CI - a 1 x 2 x subs array of 90% confidence intervals for BA
% o CA_CI - an m x 2 x subs array of 90% confidence intervals for CA
% o DA_pp - the permutation p-value for decoding accuracy
% o BA_pp - the permutation p-value for balanced accuracy
% o CA_pp - the permutation p-values for class accuracies
% o CM - an m x m x subs array of confusion matrices
% ( CM(c2,c1,i) corresponds to the proportion of observations
% from class c1 classified into class c2 in subsample i )function SVR = ML_SVR(x, Y, CV, C, perm)
% _
% Cross-Validated Support Vector Machine for Regression
% FORMAT SVR = ML_SVR_ext(x, Y, CV, C, perm)
%
% x - an n x 1 vector of target values
% Y - an n x v matrix of predictor variables
% CV - an n x k matrix of cross-validation folds
% C - a scalar, the cost parameter of the SVM
% perm - an integer, the number of permutations
%
% SVR - a structure specifying the calibrated SVM
% o data - the data for the SVM (x, Y)
% o pars - parameters of the SVM (CV, C)
% o opt - options for LibSVM's svmtrain
% o perm - the number of permutations
% o pred - predictions of the SVM
% o ip - an n x perm matrix of permutation indices
% o xt - an n x perm matrix of true target values
% o xp - an n x perm matrix of predicted target values
% o perf - predictive performance of the SVM
% o r - a 1 x perm vector of predictive correlations
% o r_p - parametric p-value for predictive correlation
% o r_CI - 90% confidence interval for predictive correlation
% o r_pp - permutation p-value for predictive correlation
% o r_cv - 90% critical values for predictive correlation
% o R2 - the coefficient of determination (=r^2, "R-squared")
% o MAE - mean absolute error between true and predicted
% o MSE - mean squared error between true and predicted
% o m - slope of the line going through points (xt,xp)
% o n - intercept of the line going through points (xt,xp)function ML4NI_SVM(SVM_dir, mask_img, data_imgs, c, x, X, preproc, options)
% _
% Support Vector Machine for Neuroimaging Data
% FORMAT ML4NI_SVM(SVM_dir, mask_img, data_imgs, c, x, X, preproc, options)
% SVM_dir - a string indicating the results directory
% mask_img - a string indicating the mask image (optional)
% data_imgs - an N x 1 cell array of data image filepaths
% c - an N x 1 vector of class labels (1, 2, 3 etc.)
% x - an N x 1 vector of target values (real numbers)
% X - an N x p matrix of additional covariates (optional)
% preproc - a 1 x S structure of preprocessing steps
% o op - a string indicating the operation (see below)
% o cov - a vector indexing covariates to use (from X)
% options - a structure specifying SVM options
% o SVM_type - a string indicating SVM type ('SVC' or 'SVR')
% o C - a scalar, the SVM hyper-parameter
% o CV_mode - a string indicating CV mode (see "help ML_CV")
% o k - an integer, the number of CV folds
% o perm - an integer, the number of permutations
% o subs - an integer, the number of subsamples (for SVC)