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122 nips-2007-Locality and low-dimensions in the prediction of natural experience from fMRI

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Author: Francois Meyer, Greg Stephens

Abstract: Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. One approach towards illuminating the connection between fMRI and cognitive function is through decoding; how do the time series of voxel activities combine to provide information about internal and external experience? Here we seek models of fMRI decoding which are balanced between the simplicity of their interpretation and the effectiveness of their prediction. We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. We ﬁnd that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features. In particular, we build effective models based on the decorrelated components of cognitive activity in the classically-deﬁned Brodmann areas. For some of the stimuli, the top predictive areas were surprisingly transparent, including Wernicke’s area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions for velocity. Direct sensory experience resulted in the most robust predictions, with the highest correlation (c ∼ 0.8) between the predicted and experienced time series of verbal instructions. Techniques based on non-linear dimensionality reduction (Laplacian eigenmaps) performed similarly. The interpretability and relative simplicity of our approach provides a conceptual basis upon which to build more sophisticated techniques for fMRI decoding and offers a window into cognitive function during dynamic, natural experience. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Locality and low-dimensions in the prediction of natural experience from fMRI Francois G. [sent-1, score-0.209]

2 Abstract Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. [sent-6, score-0.161]

3 One approach towards illuminating the connection between fMRI and cognitive function is through decoding; how do the time series of voxel activities combine to provide information about internal and external experience? [sent-7, score-0.276]

4 We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. [sent-9, score-0.455]

5 We ﬁnd that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features. [sent-10, score-0.282]

6 In particular, we build effective models based on the decorrelated components of cognitive activity in the classically-deﬁned Brodmann areas. [sent-11, score-0.253]

7 For some of the stimuli, the top predictive areas were surprisingly transparent, including Wernicke’s area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions for velocity. [sent-12, score-0.423]

8 Direct sensory experience resulted in the most robust predictions, with the highest correlation (c ∼ 0. [sent-13, score-0.164]

9 8) between the predicted and experienced time series of verbal instructions. [sent-14, score-0.088]

10 The interpretability and relative simplicity of our approach provides a conceptual basis upon which to build more sophisticated techniques for fMRI decoding and offers a window into cognitive function during dynamic, natural experience. [sent-16, score-0.346]

11 1 Introduction Functional Magnetic Resonance Imaging (fMRI) is a non-invasive imaging technique that can quantify changes in cerebral venous oxygen concentration. [sent-17, score-0.138]

12 Changes in the fMRI signal that occur during brain activation are very small (1-5%) and are often contaminated by noise (created by the imaging system hardware or physiological processes). [sent-18, score-0.329]

13 The Experience Based Cognition competition (EBC) [3] offers an opportunity to study complex responses to natural environments, and to test new ideas and new methods for the analysis of fMRI collected in natural environments. [sent-21, score-0.126]

14 t0 t0 ti ti tj T l T tj t Figure 1: We study the variation of the set of features fk (t), k = 1, · · · , K as a function of the dynamical changes in the fMRI signal X(t) = [x1 (t), · · · , xN (t)] during natural experience. [sent-28, score-0.844]

15 The features represent both external stimuli such as the presence of faces and internal emotional states encountered during the exploration of a virtual urban environment (left and right images). [sent-29, score-0.599]

16 We predict the feature functions fk for t = Tl+1 , · · · T , from the knowledge of the entire fMRI dataset X , and the partial knowledge of fk (t) for t = 1, · · · , Tl . [sent-30, score-0.693]

17 In this work we seek a low dimensional representation of the entire fMRI dataset that provides a new set of ‘voxel-free” coordinates to study cognitive and sensory features. [sent-34, score-0.268]

18 We denote a three-dimensional volumes of fMRI composed of a total of N voxels by X(t) = [x1 (t), · · · , xN (t)]. [sent-35, score-0.136]

19 xN (1) · · · xN (T ) where each row n represents a time series xn generated from voxel n and each column j represents a scan acquired at time tj . [sent-46, score-0.261]

20 We call the set of features to be predicted fk , k = 1, , · · · , K. [sent-47, score-0.376]

21 We are interested in studying the variation of the set of features fk (t), k = 1, · · · , K describing the subject experience as a function of the dynamical changes of the brain, as measured by X(t). [sent-48, score-0.555]

22 Formally, we need to build predictions of fk (t) for t = Tl+1 , · · · T , from the knowledge of the entire fMRI dataset X , and the partial knowledge of fk (t) for the training time samples t = 1, · · · , Tl (see Fig. [sent-49, score-0.77]

23 tj ti φ t0 φ D t Figure 2: Low-dimensional parametrization of the set of “brain states”. [sent-51, score-0.268]

24 The parametrization is constructed from the samples provided by the fMRI data at different times, and in different states. [sent-52, score-0.1]

25 2 A voxel-free parametrization of brain states We use here the global information provided by the dynamical evolution of X(t) over time, both during the training times and the test times. [sent-53, score-0.58]

26 We would like to effectively replace each fMRI dataset X(t) by a small set of features that facilitates the identiﬁcation of the brain states, and make the prediction of the features easier. [sent-54, score-0.48]

27 Formally, our goal is to construct a map φ from the voxel space to low dimensional space. [sent-55, score-0.094]

28 As t varies over the training and the test sets, we hope that we explore most of the possible brain conﬁgurations that are useful for predicting the features. [sent-57, score-0.277]

29 The map φ provides a parametrization of the brain states. [sent-58, score-0.343]

30 2 as a smooth surface, is the set of parameters y1 , · · · , yL that characterize the brain dynamics. [sent-61, score-0.243]

31 Note that time does not play any role on D, and neighboring points on D correspond to similar brain states. [sent-63, score-0.243]

32 Equipped with this re-parametrization of the dataset X , the goal is to learn the evolution of the feature time series as a function of the new coordinates [y1 (t), · · · , yL (t)]T . [sent-64, score-0.165]

33 Each feature function is an implicit function of the brain state measured by [y1 (t), · · · , yL (t)]. [sent-65, score-0.243]

34 For a given feature fk , the training data provide us with samples of fk at certain locations in D. [sent-66, score-0.68]

35 The map φ is build by globally computing a new parametrization of the set {X(1), · · · , X(T )}. [sent-67, score-0.143]

36 1 The graph of brain states We represent the fMRI dataset for the training times and test times by a graph. [sent-73, score-0.405]

37 Each vertex i corresponds to a time sample ti , and we compute the distance between two vertices i and j by measuring a distance between X(ti ) and X(tj ). [sent-74, score-0.141]

38 Global changes in the signal due to residual head motion, or global blood ﬂow changes were removed by computing a a principal components analysis (PCA) of the dataset X and removing a small number components. [sent-75, score-0.337]

39 This distance compares all the voxels (white and gray matter, as well as CSF) inside the brain. [sent-77, score-0.113]

40 The Euclidean distance used to construct the graph is only useful locally: we can use it to compare brain states that are very similar, but is unfortunately very sensitive to short-circuits created by the noise in the data. [sent-80, score-0.381]

41 The commute time can be conveniently computed 1 1 from the eigenfunctions φ1 , · · · , φN of N = D 2 PD− 2 , with the eigenvalues −1 ≤ λN · · · ≤ λ2 < λ1 = 1. [sent-83, score-0.152]

42 As proposed in [4, 5, 6], we deﬁne an embedding i → Ik (i) = 1 φk (i) √ , 1 − λk di Because −1 ≤ λN · · · ≤ λ2 < λ1 = 1, we have √ 1 1−λ2 k = 2, · · · , N > √ 1 1−λ3 (4) 1 > · · · √1−λ . [sent-85, score-0.189]

43 We can therefore N φk (j) neglect √1−λ for large k, and reduce the dimensionality of the embedding by using only the ﬁrst k K coordinates in (4). [sent-86, score-0.262]

44 The algorithm for the construction of the embedding is summarized in Fig. [sent-89, score-0.192]

45 Algorithm 1: Construction of the embedding Input: – X(t), t = 1, · · · , T , K: number of eigenfunctions. [sent-91, score-0.161]

46 ﬁnd the ﬁrst K eigenfunctions, φk , of N • Output: For ti = 1 : T – new co-ordinates of X(ti ): yk (ti ) = φ (i) √1 √ k πi 1−λk k = 2, · · · , K + 1 Figure 3: Construction of the embedding A parameter of the embedding (Fig. [sent-94, score-0.403]

47 We expect that for small values of K the embedding will not describe the data with enough precision, and the prediction will be inaccurate. [sent-97, score-0.245]

48 If K is too large, some of the new coordinates will be describing the noise in the dataset, and the algorithm will overﬁt the training data. [sent-98, score-0.105]

49 The quality of the prediction for the features: faces, instruction and velocity is plotted against K. [sent-101, score-0.217]

50 Instructions elicits a strong response in the auditory cortex that can be decoded with as few as 20 coordinates. [sent-102, score-0.124]

51 As expected the performance eventually drops when additional coordinates are used to describe variability that is not related to the features to be decoded. [sent-104, score-0.124]

52 3 Semi-supervised learning of the features The problem of predicting a feature fk at an unknown time tu is formulated as kernel ridge regression problem. [sent-107, score-0.439]

53 The training set {fk (t) for t = 1, · · · , Tl } is used to estimate the optimal choice of weights in the following model, Tl ˆ f (tu ) = α(t)K(y(tu ), y(t)), ˆ t=1 where K is a kernel and tu is a time point where we need to predict. [sent-108, score-0.097]

54 4 Results We compared the nonlinear embedding approach (referred to as global Laplacian) to dimension reduction obtained with a PCA of X . [sent-110, score-0.328]

55 Here the principal components are principal volumes, and for each time t we can expand X(t) onto the principal components. [sent-111, score-0.217]

56 We use fk (t) in a subset to predict fk (t) in the other subset. [sent-113, score-0.646]

57 In order to quantify the stability of the prediction we randomly selected 85 % of the training set (ﬁrst subset), and predicted 85 % of the testing set (other subset). [sent-114, score-0.118]

58 The performance was quantiﬁed with the normalized correlation between the model prediction and the real value of fk , est r = δfk (t), δfk (t) / est 2 δ(fk )2 δfk , (5) where δfk = fk (t) − fk . [sent-117, score-1.215]

59 The approach based on the nonlinear embedding yields very stable results, with low variance. [sent-121, score-0.225]

60 For both global methods the optimal performance is reached with less than 50 coordinates. [sent-122, score-0.103]

61 For most features, the nonlinear embedding performed better than global PCA. [sent-125, score-0.328]

62 3 From global to local While models based on global features leverage predictive components from across the brain, cognitive function is often localized within speciﬁc regions. [sent-126, score-0.453]

63 The Brodmann areas were deﬁned almost a century ago (see e. [sent-128, score-0.128]

64 While the areas are characterized structurally many also have distinct functional roles and we use these roles to provide useful interpretations of our predictive models. [sent-130, score-0.243]

65 Though the partitioning of cortical regions remains an open and challenging problem, the Brodmann areas represent a transparent compromise between dimensionality, function and structure. [sent-131, score-0.229]

66 Using data supplied by the competition, we warp each brain into standard Talairach coordinates and locate the Brodmann area corresponding to each voxel. [sent-132, score-0.383]

67 Within each Brodmann region, differing in size from tens to thousands of elements, we build the covariance matrix of voxel time series using all three virtual reality episodes. [sent-133, score-0.326]

68 We then project the voxel time series onto the eigenvectors of the covariance matrix (principal components) and build a simple, linear stimulus decoding model using the top n modes ranked by their eigenvalues, n est fk (t) = k wi mk (t). [sent-134, score-0.875]

69 The weights are chosen to minimize the RMS error on the training k set and have a particularly simple form here as the modes are decorrelated, wi = S(t)mk (t) . [sent-136, score-0.168]

70 9 〈r〉 faces instructions velocity 0 1 100 global Laplacian faces instructions velocity 0 1 200 100 global eigenmodes 200 (d) (c) 48 0. [sent-140, score-1.167]

71 (a) nonlinear embedding, (b) global principal components, (c) local (Brodmann area) principal components. [sent-142, score-0.325]

72 In all cases we ﬁnd that the prediction is remarkably low-dimensional, saturating with less than 100 features. [sent-143, score-0.167]

73 (d) stability and interpretability of the optimal Brodmann areas used for decoding the presence of faces. [sent-144, score-0.313]

74 All three areas are functionally associated with visual processing. [sent-145, score-0.158]

75 Brodmann area 22 (Wernicke’s area) is the best predictor of instructions (not shown). [sent-146, score-0.252]

76 The connections between anatomy, function and prediction add an important measure of interpretability to our decoding models. [sent-147, score-0.24]

77 the real stimulus averaged over the two virtual reality episodes and we use the region with the lowest training error to make the prediction. [sent-148, score-0.283]

78 In principle, we could use a large number of modes to make a prediction with n limited only by the number of training samples. [sent-149, score-0.205]

79 In practice the predictive power of our linear model saturates for a remarkably low number of modes in each region. [sent-150, score-0.155]

80 In Fig 4(c) we demonstrate the performance of the model on the number of local modes for three stimuli that are predicted rather well (faces, instructions and velocity). [sent-151, score-0.417]

81 For many of the well-predicted stimuli, the best Brodmann areas were also stable across subjects and episodes offering important interpretability. [sent-152, score-0.206]

82 For example, in the prediction of instructions (which the subjects received through headphones), the top region was Brodmann Area 22, Wernicke’s area, which has long been associated with the processing of human language. [sent-153, score-0.341]

83 For the prediction of the face stimulus the best region was usually visual cortex (Brodmann Areas 17 and 19) and for the prediction of velocity it was Brodmann Area 7, known to be important for the coordination of visual and motor activity. [sent-154, score-0.502]

84 Using modes derived from Laplacian eigenmaps we were also able to predict an emotional state, the self-reporting of fear and anxiety. [sent-155, score-0.175]

85 Interestingly, in this case the best predictions came from higher cognitive areas in frontal cortex, Brodmann Area 11. [sent-156, score-0.236]

86 While the above discussion highlights the usefulness of classical anatomical location, many aspects of cognitive experience are not likely to be so simple. [sent-157, score-0.194]

87 Local decoders do well on stimuli related to objects while nonlinear global methods better capture stimuli related to emotion. [sent-160, score-0.397]

88 to look for ways of combining the intuition derived from single classical location with more global methods that are likely to do better in prediction. [sent-161, score-0.103]

89 As a step in this direction, we modify our model to include multiple Brodmann areas n est fk (t) = l wi ml (t), i (7) l∈A i=1 where A represents a collection of areas. [sent-162, score-0.561]

90 To make a prediction using the modiﬁed model we ﬁnd the top three Brodmann areas as before (ranked by their training correlation with the stimulus) and then incorporate all of the modes in these areas (nA in total) in the linear model of Eq 7. [sent-163, score-0.497]

91 The combined model leverages both the interpretive power of single areas and also some of the interactions between them. [sent-165, score-0.128]

92 For ease of comparison, we also show the best global results (both nonlinear Laplacian and global principal components). [sent-168, score-0.333]

93 For many (but not all) of the stimuli, the local, low-dimensional linear model is signiﬁcantly better than both linear and nonlinear global methods. [sent-169, score-0.167]

94 4 Discussion Incorporating the knowledge of functional, cortical regions, we used fMRI to build low-dimensional models of natural experience that performed surprisingly well at predicting many of the complex stimuli in the EBC competition. [sent-170, score-0.283]

95 In addition, the regional basis of our models allows for transparent cognitive interpretation, such as the emergence of Wernicke’s area for the prediction of auditory instructions in the virtual environment. [sent-171, score-0.634]

96 Other well-predicted experiences include the presence of body parts and faces, both of which were decoded by areas in visual cortex. [sent-172, score-0.276]

97 In future work, it will be interesting to examine whether there is a well-deﬁned cognitive difference between stimuli that can be decoded with local brain function and those that appear to require more global techniques. [sent-173, score-0.658]

98 We also learned in this work that nonlinear methods for embedding datasets, inspired by manifold learning methods [4, 5, 6], outperform linear techniques in their ability to capture the complex dynamics of fMRI. [sent-174, score-0.225]

99 Finally, our particular use of Brodmann areas and linear methods represent only a ﬁrst step towards combining prior knowledge of broad regional brain function with the construction of models for the decoding of natural experience. [sent-175, score-0.564]

100 Extrinsic and intrinsic systems in the posterior cortex of the human brain revealed during natural sensory stimulation. [sent-187, score-0.391]

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