Representational similarity analysis
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1 School of Psychology Representational similarity analysis Dr Ian Charest
2 Representational similarity analysis representational dissimilarity matrices (RDMs) stimulus (e.g. images, sounds, other experimental conditions) representational pattern (e.g. voxels, neurons, model units) brain representation (e.g. fmri pattern dissimilarities) behaviour (e.g. dissimilarity judgments) representational dissimilarity a c t i v i t y d i s s i m i l a r i t y stimulus description (e.g. pixel-based dissimilarity) computational model representation (e.g. face-detector model) Charest et al. 2014, 2015, Kriegeskorte & Kievit 2013, see also: Edelman et al. 1998, Laakso & Cottrell 2000, Op de Beeck et al. 2001, Haxby et al. 2001, Aguirre 2007, Kriegeskorte et al. 2008
3 Why investigate representational geometries?
4 downstream neurons can read out the same information from these codes neuron 1 neuron 3 same geometry same information same format neuron 1 neuron 3 neuron 2 neuron 2 Representational geometry The geometry of the points in a high-dimensional response pattern space, which are thought to represent particular. slide kindly provided by N. Kriegeskorte
5 category information...for linear readout...for nonlinear readout...inherently categorical Kriegeskorte & Kievit 2013
6 Kriegeskorte & Kievit 2013
7 The representational similarity trick representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? brain model experimental...
8 The representational similarity trick representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? subject 1 subject 2 experimental...
9 The representational similarity trick representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? brain behaviour experimental...
10 The representational similarity trick representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? region 1 region 2 experimental...
11 The representational similarity trick representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? fmri cell recording experimental...
12 The representational similarity trick representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? fmri MEG experimental...
13 Kriegeskorte, 2008 The RSA trick
14
15 Relating brain and model RDMs representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? brain model experimental...
16 Deep convolutional neural network state of the art in computer vision trained with stochastic gradient descent supervised with 1.2 million category-labeled images 60 million parameters and 650,000 neurons Is this network functionally similar to the brain? Krizhevsky et al convolutional fully connected
17 highest accuracy any model can achieve accuracy of human IT dissimilarity matrix prediction [group-average of Kendall s τ a ] other subjects average as model SE (stimulus bootstrap) accuracy above chance p<0.001 (subjects and as fixed effects) convolutional fully connected SVM discriminants Khaligh-Razavi & Kriegeskorte (2014), Nili et al (RSA Toolbox) weighted combination of fully connected layers and SVM discriminants
18 model comparison (stimulus bootstrap) highest accuracy any model can achieve accuracy of human IT dissimilarity matrix prediction [group-average of Kendall s τ a ] other subjects average as model SE (stimulus bootstrap) accuracy above chance p<0.001 (subjects and as fixed effects) convolutional fully connected SVM discriminants Khaligh-Razavi & Kriegeskorte (2014), Nili et al (RSA Toolbox) weighted combination of fully connected layers and SVM discriminants
19 Comparing brain RDMs between people representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? subject 1 subject 2 experimental...
20 animate inanimate bodies faces places objects Charest et al PNAS
21 Stimuli Objects from the subject s own photo-album animate bodies faces inanimate places objects Charest et al PNAS
22 Comparing brain RDMs between people day 1 day 2 subject 1 subject similarity matrix day 2 subject 2 s 1 s 1 s 2 s 3 s 4 s 5 s 20 s 2 correlation within-subject (ws) day 1 s 3 s 4 between-subject (bs) individuation index ( ws - bs )? s 5 s 20 Charest et al PNAS
23 Charest et al PNAS
24 Representational geometries in human inferior temporal cortex Neurotypicals ASC
25 Comparing brain RDMs and behavioural RDMs representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? brain behaviour experimental...
26 Comparing brain RDMs and behavioural RDMs brain behaviour subject 1 subject similarity matrix day 2 subject 2 s 1 s 1 s 2 s 3 s 4 s 5 s 20 s 2 correlation within-subject (ws) day 1 s 3 s 4 between-subject (bs) individuation index ( ws - bs )? s 5 s 20 Charest et al PNAS
27 Charest et al PNAS
28 RSA Representational Dissimilarity Matrix (RDM) dissimilarity 100 [ percentile of distance ] compute the dissimilarity (e.g. 1 correlation) voxels representational pattern (population code representation) human inferior temporal (hit)... experimental Charest et al PNAS
29 RSA Representational Dissimilarity Matrix (RDM) dissimilarity 100 [ percentile of distance ] compute the dissimilarity (e.g. 1 correlation) linear discriminant analysis EEG Channel amplitudes representational pattern (population code representation) EEG activity-pattern at time t... experimental
30 RSA
31 EEG contains rich topographic information from which you can distinguish mental states
32 EEG contains rich topographic information from which you can distinguish mental states bodies faces places objects
33 bodies faces places objects
34 Personally meaningful objects elicit activity patterns that are distinguishable from unfamiliar objects familiar unfamiliar
35 Personally meaningful objects elicit activity patterns that are distinguishable from unfamiliar objects
36 Personally meaningful objects elicit activity patterns that are distinguishable from unfamiliar objects
37 Personally meaningful objects elicit activity patterns that are distinguishable from unfamiliar objects
38 Personally meaningful objects elicit activity patterns that are distinguishable from unfamiliar objects
39 Object familiarity decoding from EEG activity patterns unfamiliar objects familiar objects signifiant above-chance decoding
40 Object familiarity decoding from EEG activity patterns
41 Object familiarity decoding from EEG activity patterns
42 Comparing individuals representations day 1 day 2 subject 1 subject similarity matrix subject 2 s 1 s 2 s 1 s 2 s 3 s 4 s 5 s 20 day 2 correlation within-subject (ws) between-subject (bs) individuation index ( ws - bs )? day 1 s 3 s 4 s 5 s 20 Charest et al PNAS
43 Comparing individuals representations
44
45 Comparing RDMs between measurement modalities representational distance matrix (RDM)! dissimilarity (e.g. 1-correlation across space) activity patterns? fmri MEG experimental...
46 Cichy et al Nature Neuroscience
47
48 How can we best measure representational distances?
49 Distance estimates are positively biased pattern2 data dist data noise pattern1 data noise pattern1 true dist true pattern2 true dist data neuron 2 neuron 1 dist true
50 Distances are positively biased just like training-set decoding accuracies!
51 compute decoding accuracy? or just do a t test? condition 1 condition 2 linear discriminant t value (LD-t) run A run B Kriegeskorte et al. 2007, Nili et al. 2014
52 data set A data set B Unbiased distance estimates through crossvalidation S2 S2 S1 S2 S1 S1 true distance = 0 true distance = 1 average angle = 90 average angle < 90 E(inner product) = 0 E(inner product) > 0
53 Unbiased distance estimates through crossvalidation Run 1 Training Run 2 Testing Estimated activity patterns Training Testing True activity patterns Estimated error Walther et al. (2016)
54 Unbiased distance estimates through crossvalidation Run 1 Training Run 2 Testing Estimated activity patterns Training Testing True activity patterns Estimated error Walther et al. (2016)
55 The linear discriminant contrast (LDC) is a crossvalidated variant of the Mahalanobis distance Mahalanobis distance (single data set) training set ( p2 p1) ( p2 p1) Fisher linear discriminant contrast (crossvalidated) T Σ 1 training set ( p2 p1) T Σ 1 ( p2' p1') test set Nili et al. (2014)
56 Crossvalidation removes the bias of distance estimates true distance estimated distance [squared Euclidean] Walther et al. (2016)
57 Crossvalidation removes the bias of distance estimates true distance estimated distance [squared Euclidean] Walther et al. (2016)
58 Test-retest reliability for different dissimilarity measures Walther et al. (2016)
59 no crossvalidation crossvalidation Euclidean distance Mahalanobis distance Centroid connection discriminant contrast Fisher linear discriminant contrast covariance-blind Training-set decoding accuracy Test-set decoding accuracy ceiling-limited and quantized positively biased
60 no crossvalidation crossvalidation Euclidean distance Mahalanobis distance Centroid connection discriminant contrast Fisher linear discriminant contrast covariance-blind Training-set decoding accuracy Test-set decoding accuracy ceiling-limited and quantized positively biased
61 The best of both worlds... Multivariate statistics Machine learning multinormal distribution pattern classifiers continuous measures of multivariate separation crossvalidation inference relying on multinormality nonparametric inference procedures
62 Key insights A1 Representational geometries encapsulate the content and format of brain representations. A2 Representational geometries can be characterised by representational dissimilarity matrices (RDMs). A3 RDMs can easily be compared between brains and models, individuals and species, different brain regions, different measurement modalities, and brain and behaviour. A4 We can statistically compare multiple computational models and assess whether they fully explain the measured brain response patterns.
63
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