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Update distances.rst
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TamerGezici authored Aug 26, 2024
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Expand Up @@ -108,7 +108,7 @@ The really big advantage of this dissimilarity measure is that it is unbiased. I

* You can perform a t-test of the crossnobis estimates against zero, exactly like you would test the classification accuracy of a decoder against chance performance. Thus, you do not need to perform a decoding analysis to determine where there is reliable information, and then conduct an RSA analysis to make inferences about the shape of the representation. By using the crossnobis dissimilarity, you can do so in one step (see also \ref{unbiasedDistanceCorrelation}.

* Unequal noise across conditions can severely bias RDMs computed with normal distances. For example when you have less trials for one condition than another, the pattern for that condition :math:`\bar{\mathbf{b}}_i` has higher noise variance. Therefore the distance to other conditions will be higher, even though the condition only differs by noise. When two conditions are estimated with correlated noise (for example when they are acquired in close temrpora; proximity with fMRI), their distance will be smaller than when they are collected with independent noise. For example, one cannot compare 'normal' distances within an imaging run to distances across imaging runs (due to correlated noise, the former will be usually smaller). Cross-validation removes these biases, making inference much more robust.
* Unequal noise across conditions can severely bias RDMs computed with normal distances. For example when you have less trials for one condition than another, the pattern for that condition :math:`\bar{\mathbf{b}}_i` has higher noise variance. Therefore the distance to other conditions will be higher, even though the condition only differs by noise. When two conditions are estimated with correlated noise (for example when they are acquired in close temporal proximity with fMRI), their distance will be smaller than when they are collected with independent noise. For example, one cannot compare 'normal' distances within an imaging run to distances across imaging runs (due to correlated noise, the former will be usually smaller). Cross-validation removes these biases, making inference much more robust.

* Having a meaningful zero point (i.e. the true patterns are not different) can help in model comparison, as it provides another informative point (Diedrichsen et al., 2020). To exploit this, it is recommended to use the cosine similarity instead of the Pearson correlation for RDM comparison.

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