Light-weight Matlab toolbox for multivariate pattern analysis (MVPA)

• (August 2019) added mv_classify for classification of multi-dimensional datasets (e.g. time-frequency), a Naive Bayes classifier and the kappa metric
• (July 2019) added preprocessing module + precomputed kernels for SVM and kernel FDA
• (May 2019) interface added for LIBSVM and LIBLINEAR
• (Mar 2019) MVPA-Light has been integrated with FieldTrip (see tutorial)
• (Feb 2019) added kernel Fisher Discriminant Analysis and new metrics precision, recall, and f1

1. Installation
2. Overview
3. Classification
4. Examples

In Linux/Mac, open a terminal and check out the repository by typing

git clone https://github.com/treder/MVPA-Light.git

In Windows, you might prefer to perform these steps using a Git client. Alternatively, you can simply download the toolbox. Git makes it easier to keep your local version up-do-date using git pull but it's not essential. Next, the toolbox needs to be added to Matlab's search path. In Matlab, add these lines to your startup.m file:

addpath('C:\git\MVPA-Light\startup')
startup_MVPA_Light

This assumes that the repository is located in C:\git\MVPA-Light, so change the path if necessary. The function startup_MVPA_Light adds the relevant folders and it avoids adding the .git subfolder.

If you do not want to use the startup.m file, you can directly add the MVPA-Light folder and its subfolders to the path using MATLAB's Path tool.

MVPA-Light contains two branches: the master branch (recommended) is the stable branch that should always work. devel is the development branch that contains new features that are either under construction or not tested. The toolbox has been tested with Matlab R2012a and newer. There may be issues with earlier Matlab versions.

MVPA-Light provides functions for the classification of neuroimaging data. It is meant to address the basic issues in MVPA (such as classification across time and generalisation) in a fast and robust way while retaining a slim and readable codebase. For Fieldtrip users, the use of the toolbox will be familiar: The first argument to the main functions is a configuration struct cfg that contains all the parameters. However, the toolbox does not require or use Fieldtrip.

Classifiers can be trained and tested by hand using the train_* and test_* functions. For data with a trial structure, such as ERP datasets, mv_classify_across_time can be used to obtain classification performance for each time point in a trial. mv_classify_timextime implements time generalisation, i.e., training on a specific time point, and testing the classifier on all other time points in a trial. Cross-validation, balancing unequal class proportions, and different performance metrics are automatically implemented in these functions.

A classifier is the main workhorse of MVPA. The input brain data, e.g. channels or voxels, is referred to as features, whereas the output data is a class label. The classifier takes a feature vector as input and assigns it to a class. In MVPA-Light, class labels must be coded as 1 (for class 1), 2 (for class 2), 3 (for class 3), and so on.

In order to learn which features in the data discriminate between the experimental conditions, a classifier needs to be exposed to training data. During training, the classifier's parameters are optimised (analogous to determining the beta's in linear regression). All training functions start with train_ (e.g. train_lda).

Classifier performance is evaluated on a dataset called test data. To this end, the classifier is applied to samples from the test data. The class label predicted by the classifier can then be compared to the true class label in order to quantify classification performance. All test functions start with test_ (e.g. test_lda).

• lda: Regularised Linear Discriminant Analysis (LDA). LDA searches for a projection of the data into 1D such that the class means are separated as far as possible and the within-class variability is as small as possible. To counteract overfitting, ridge regularisation and shrinkage regularisation are available. In shrinkage, the regularisation parameter λ (lambda) rankges from λ=0 (no regularisation) to λ=1 (maximum regularisation). It can also be set to 'auto' to have λ be estimated automatically. For more details on regularised LDA see [Bla2011]. LDA has been shown to be formally equivalent to LCMV beamforming and it can be used for recovering time series of ERP sources [Tre2011]. See train_lda for a full description of the parameters.
• logreg: Logistic regression (LR). LR directly models class probabilities by fitting a logistic function to the data. Like LDA, LR is a linear classifier and hence its operation is expressed by a weight vector w and a bias b. By default, logf regularisation is used to prevent overfitting. It is implemented by data augmentation and does not require hyperparameters. Alternatively, L2-regularisation can be used. It requires setting a positive but unbounded parameter λ (lambda) that controls the L2-penalisation of the classifier weights. It can also be set to 'auto'. In this case, different λ's are tried out using a searchgrid; the value of λ maximising cross-validation performance is then used for training on the full dataset. See train_logreg for a full description of the parameters.
• svm: Support Vector Machine (SVM). The parameter C is the cost parameter that controls the amount of regularisation. It is inversely related to the λ defined above. By default, a linear SVM is used. By setting the .kernel parameter (e.g. to 'polynomial' or 'rbf'), non-linear SVMs can be trained as well. See train_svm for a full description of the parameters.

• ensemble: Uses an ensemble of classifiers trained on random subsets of the features and random subsets of the samples. Can use any classifier with train/test functions as a learner. See train_ensemble for a full description of the parameters.

• kernel_fda : Regularised kernel Fisher Discriminant Analysis (KFDA). This is the kernelized version of LDA. By setting the .kernel parameter (e.g. to 'polynomial' or 'rbf'), non-linear classifiers can be trained. See train_kernel_fda for a full description of the parameters.

• liblinear : interface for the LIBLINEAR toolbox for linear SVM and logistic regression. It is a state-of-the-art implementation of linear SVM and Logistic Regression that is fast due to usage of compiled C code. Follow the installation and compilation instructions on the LIBLINEAR website and the GitHub repository. Refer to train_liblinear to see how to call LIBLINEAR in MVPA-Light.

• libsvm : interface for the LIBSVM toolbox for Support Vector Machines (SVM). It is a state-of-the-art implementation of SVM that is fast due to usage of compiled C code. Follow the installation and compilation instructions on the LIBSVM website and the GitHub repository. Refer to train_libsvm to see how to call LIBSVM in MVPA-Light. (note: LIBSVM provides a function called svmtrain which is overshadowed by a Matlab function of the same name in some Matlab versions. This can lead to execution errors. Type which -all svmtrain to check whether there is indeed multiple versions.)

• multiclass_lda : Regularised multi-class Linear Discriminant Analysis (LDA). The data is first projected onto a (C-1)-dimensional discriminative subspace, where C is the number of classes. A new sample is assigned to the class with the closest centroid in this subspace. See train_multiclass_lda for a full description of the parameters.

• naive_bayes : Gaussian Naive Bayes classifier. Its naive assumption is that, given the class label, the features are independent of each other. This allows the posterior probability to be expressed as univariate densities. At testing time, the maximum a posteriori (MAP) rule is applied to assign a sample to the class with the maximum posterior probability. See train_naive_bayes for a full description of the parameters.

To obtain a realistic estimate of classifier performance and control for overfitting, a classifier should be tested on an independent dataset that has not been used for training. In most neuroimaging experiments, there is only one dataset with a restricted number of trials. K-fold cross-validation makes efficient use of this data by splitting it into k different folds. In each iteration, one of the k folds is held out and used as test set, whereas all other folds are used for training. This is repeated until every fold has been used as test set once. See [Lemm2011] for a discussion of cross-validation and potential pitfalls. Cross-validation is implemented in mv_crossvalidate. Note that the more specialised functions mv_classify_across_time, mv_classify_timextime and mv_searchlight implement cross-validation too. Cross-validation is always controlled by the following parameters:

• cfg.cv: cross-validation type, either 'kfold', 'leaveout' or 'holdout' (default 'kfold')
• cfg.k: number of folds in k-fold cross-validation (default 5)
• cfg.repeat: number of times the cross-validation is repeated with new randomly assigned folds (default 5)
• cfg.p: if cfg.cv is 'holdout', p is the fraction of test samples (default 0.1)
• cfg.stratify: if 1, the class proportions are approximately preserved in each test fold (default 1)

Many neuroimaging datasets have a 3-D structure (trials x channels x time). The start of the trial (t=0) typically corresponds to stimulus or response onset. Classification across time can help identify at which time point in a trial discriminative information shows up. To this end, classification is performed across trials, for each time point separately. This is implemented in the function mv_classify_across_time. It returns classification performance calculated for each time point in a trial. mv_plot_result can be used to plot the result.

Classification across time does not give insight into whether information is shared across different time points. For example, is the information that the classifier uses early in a trial (t=80 ms) the same that it uses later (t=300ms)? In time generalization, this question is answered by training the classifier at a certain time point t. The classifer is then tested at the same time point t but it is also tested at all other time points in the trial [King2014]. mv_classify_timextime implements time generalization. It returns a 2D matrix of classification performance, with performance calculated for each combination of training time point and testing time point. mv_plot_result can be used to plot the result.

Which features contribute most to classification performance? The answer to this question can be used to better interpret the data or to perform feature selection. To this end, mv_searchlight performs cross-validated classification for each feature separately. If there is a spatial structure in the features (e.g. neighbouring eletrodes, neighbouring voxels), groups of features rather than single features can be considered. The result is a classification performance measure for each feature. If the features are e.g. channels, the result can be plotted as a topography.

Neuroimaging datasets can be high dimensional. For instance, time-frequency data can have 4 (e.g. samples x channels x frequencies x times) or more dimensions. The function mv_classify deals with data of an arbitrary number and order of dimensions. It combines and generalizes the capabilities of the other high-level functions and allows for flexible tailoring of classification analysis including frequency x frequency generalization and searchlight across multiple dimensions simultaneously. See example6_classify_multidimensional_data.m for code to get you started.

The hyperparameters for each classifier can be controlled using the cfg.hyperparameter field before calling any of the above functions. To this end, initialize the field using cfg.hyperparameter = []. Then, add the desired parameters, e.g. cfg.hyperparameter.lambda = 0.5 for setting the regularisation parameter or cfg.hyperparameter.kernel = 'polynomial' for defining the kernel in SVM. The hyperparameters for each classifier are specified in the documentation for each train_ function in the folder classifier.

Classifier output comes in form of decision values (=distances to the hyperplane for linear methods) or directly in form of class labels. However, one is often only interested in a performance metric that summarises how well the classifier discriminates between the classes. The following metrics can be calculated by the function mv_calculate_performance:

• accuracy (can be abbreviated as acc): Classification accuracy, representing the fraction correctly predicted class labels.
• auc: Area under the ROC curve. An alternative to classification accuracy that is more robust to imbalanced classes and independent of changes to the classifier threshold.
• confusion: confusion matrix. Rows corresponds to true class labels, columns correspond to predicted class labels. The (i,j)-th element gives the proportion of samples of class i that have been classified as class j.
• dval: Average decision value for each class.
• f1: F1 score is the harmonic average of precision and recall, given by 2 *(precision * recall) / (precision + recall).
• kappa: Cohen's kappa measures the 'inter-rater reliability' between predicted and actual class labels. See here for a discussion on CrossValidated.
• precision: precision is given as the number of true positives divided by true positives plus false positives. For multi-class, it is calculated per class from the confusion matrix by dividing each diagonal element by the row sum.
• recall: recall is given as the number of true positives divided by true positives plus false negatives. For multi-class, it is calculated per class from the confusion matrix by dividing each diagonal element by the respective column sum.
• tval: for two classes, calculates the t-test statistic for unequal sample size, equal variance case, based on the decision values. Can be useful for a subsequent second-level analysis across subjects.
• none: Does not calculate a metric but returns the raw classifier output instead.

There is usually no need to call mv_calculate_performance directly. By setting the cfg.metric field, the performance metric is calculated automatically in mv_crossvalidate, mv_classify_across_time, mv_classify_timextime and mv_searchlight. You can provide a cell array of metrics, e.g. cfg.metric = {'accuracy', 'confusion'} to calculate multiple metrics at once.

Preprocessing refers to operations applied to the data before training the classifier. In some cases, preprocessing operations such as oversampling, PCA, or Common Spatial Patterns (CSP) need to be performed as nested operations within a cross-validation analysis. In nested preprocessing, parameters are estimated on the train data and then applied to the test data. This avoids possible information flow from test set to the train set. A prepocessing pipeline can be added by setting the cfg.preprocess and cfg.preprocess_param fields. Currently implemented preprocessing functions are collected in the preprocess subfolder. See code snippet below and examples/example7_preprocessing.m for examples.

This section gives some basic examples. More detailed examples and data can be found in the examples/ subfolder.

% Load data (in /examples folder)
[dat,clabel] = load_example_data('epoched3');

% Fetch the data from the 100th time sample
X = dat.trial(:,:,100);

% Get default hyperparameters for the classifier
param = mv_get_hyperparameter('lda');

% Train an LDA classifier
cf = train_lda(param, X, clabel);

% Test classifier on the same data and get the predicted labels
predlabel = test_lda(cf, X);

% Calculate classification accuracy
acc = mv_calculate_performance('accuracy','clabel',predlabel,clabel)

See examples/example1_train_and_test.m for more details. In most cases, you would not perform training/testing by hand but rather call one of the high-level functions described below.

cfg = [];
cfg.classifier      = 'lda';
cfg.metric          = 'accuracy';
cfg.cv              = 'kfold';
cfg.k               = 5;
cfg.repeat          = 2;

% Perform 5-fold cross-validation with 2 repetitions.
% As classification performance measure we request accuracy (acc).
acc = mv_crossvalidate(cfg, X, clabel);

See examples/example2_crossvalidate.m for more details.

% Classify across time using default settings
cfg = [];
acc = mv_classify_across_time(cfg, dat.trial, clabel);

See examples/example3_classify_across_time.m for more details.

cfg = [];
cfg.metric     = 'auc';

auc = mv_classify_timextime(cfg, dat.trial, clabel);

See examples/example4_classify_timextime.m for more details.

cfg = [];
acc = mv_searchlight(cfg, dat.trial, clabel);

See examples/example5_searchlight.m for more details.

cfg =  [];
cfg.preprocess = {'pca' 'average_samples'};
acc = mv_classify_across_time(cfg, dat.trial, clabel);

See examples/example7_preprocessing.m for more details.

[Bla2011] Blankertz, B., Lemm, S., Treder, M., Haufe, S., & Müller, K. R. (2011). Single-trial analysis and classification of ERP components - A tutorial. NeuroImage, 56(2), 814–825.

[King2014] King, J.-R., & Dehaene, S. (2014). Characterizing the dynamics of mental representations: the temporal generalization method. Trends in Cognitive Sciences, 18(4), 203–210.

[Lemm2011] Lemm, S., Blankertz, B., Dickhaus, T., & Müller, K. R. (2011). Introduction to machine learning for brain imaging. NeuroImage, 56(2), 387–399.

[Tre2016] Treder, M. S., Porbadnigk, A. K., Shahbazi Avarvand, F., Müller, K.-R., & Blankertz, B. (2016). The LDA beamformer: Optimal estimation of ERP source time series using linear discriminant analysis. NeuroImage, 129, 279–291.