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Fast validation of LDA classifiers for cross-validation and permutation testing + new MVPA toolbox

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In multivariate pattern analysis (MVPA) of neuroimaging data, it is often important to establish whether a given classification performance is statistically significant. Unfortunately, one of the most popular approaches, permutation testing, is computationally expensive, since a classifier has to be trained and tested thousands of times. For Linear Discriminant Analysis (LDA) classifiers, this problem can be circumvented by exploiting its relationship with linear regression. An update rule can be used to calculate the classifier outputs in each cross-validation fold without ever re-training the classifier. Remarkably, since the hat matrix is independent of the class labels, this approach immediately extends to permutations. The approach can be generalised to multi-class LDA via the notion of optimal scoring. The update rule allows for drastic computational improvements especially in large feature spaces. Analyses using simulations and a publicly available MEG dataset (Wakeman and Henson, 2015) demonstrate speed improvements of several orders of magnitude over the classical re-training approach while providing identical results.

The function will be implemented in MVPA -Light (github.com/treder/MVPA-Light), an easy-to-use toolbox on multivariate pattern classification in MATLAB . The toolbox provides a fast interface for cross-validation, searchlight analysis, time classification and time x time generalisation. So far, Linear Discriminant Analysis (LDA) with shrinkage regularisation, logistic regression with L2 regularisation, linear and nonlinear Support Vector Machines, multi-class LDA , and ensemble methods have been implemented. To provide a fast, out-of-the-box solution, MVPA -Light uses custom implementations of popular optimisation algorithms such as Dual Coordinate Descent.

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