Comparing representational geometries using whitened unbiased-distance-matrix similarity

arxiv:2007.02789

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Representation alignment · 2020-07-06

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1. Part 1
2. Part 2
3. Part 3
4. Part 4
5. Part 5
6. Part 6

Contents

• Comparing representational geometries using whitened unbiased-distance-matrix similarity
• Abstract
• keywords
• 1 Introduction
• 2 Results
• 2.1 Basic Definitions
• 2.2 Biased and unbiased estimates for the squared Euclidean distance
• 2.3 Variance of distance estimates
• 2.4 Model comparison using RDM correlations or cosine similarity
• 2.5 Using RDM cosine similarity prevents bias in model selection
• 2.6 RDM cosine similarity exploits informative zero-point
• 2.7 Covariance of distance estimates
• 2.8 RDM comparison in whitened RDM-space
• 2.9 Influence of RDM whitening on model comparisons
• 2.10 Factors influencing the advantage of RDM whitening
• 2.11 Interpretation of the WUC
• 2.12 Extension of the WUC to flexible RDM models
• 2.13 Relationship to other multivariate dependence measures
• 3 Discussion
• 3.1 Dealing with bias and covariance of distance estimators
• 3.2 When should the whitened unbiased RDM cosine similarity be used?
• 3.3 Probabilistic versions of RSA
• 3.4 Influence of spatial noise correlations
• 3.5 Electrophysiological and other non-Gaussian data
• 3.6 Summary
• 4 Methods
• 4.1 Extended definitions
• 4.2 Bias of distance estimates
• 4.3 Variance of distance estimates
• 4.4 Spatial pre-whitening and Mahalanobis distances
• 4.5 Simulations
• 5 acknowledgements
• 6 Appendix
• 6.1 Derivation of variance-covariance matrix of the distance estimate
• 6.1.1 Expectations of products of random variables
• 6.1.2 Expectations of the product of normal matrices
• 6.1.3 Averaging across partitions
• 6.2 Unbalanced designs
• 6.3 Simulations with spatially correlated noise
• Instructions for reporting errors