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The study of neuronal selectivity in a sub-voxel scale using indirect methods such as adaptation requires the averaging of fMRI responses over many trials and participants. Averaging takes place in such a way that could obscure much of the information present in the spatial pattern of individual brain responses. Another characteristic is that fMRI responses are considered separately in individual voxels. Time courses are first extracted in individual voxels and then averaged together to obtain a mean response within a region of interest (ROI). Because each voxel is treated as a separate entity as far as statistical analysis is concerned, conventional fMRI analyses are considered as univariate.

However, fMRI data are fundamentally multivariate; a single acquisition in time contains information at thousands of spatial locations. In contrast to conventional univariate analyses, recent studies have shown that sensitivity of fMRI paradigms can increase significantly by taking into account patterns of activity present across many voxels at the same time (Cox and Savoy 2003; Haynes and Rees 2006; Norman et al. 2006). An example of the rationale behind pattern-classification techniques is given in Figure 1.18. By considering fMRI responses in many voxels simultaneously, instead of analysing one location at a time, multi-variate pattern analyses (MVPA) take into account the fine-grained information in individual voxels. Given the goal of detecting the presence of a particular mental state in the brain, the primary advantage of MVPA methods over univariate methods is increased sensitivity. Conventional fMRI analysis techniques try to find voxels showing a statistically significant response to the experimental conditions. To increase sensitivity to a particular condition, these methods spatially average across voxels that respond significantly to that condition.

Figure 1.18 Hypothetical fMRI activity in two voxels in (a) an ideal univariate situation. The activity in voxel 2 is plotted versus the activity in voxel 1 and each point corresponds to a single fMRI measurement. Voxel 2 is more active in the first condition, but it is not active in the second condition. Because the projected distributions of the responses do not overlap, a conventional univariate analysis could easily discriminate the responses measured under the two conditions. However, in situation (b) both voxels are relatively active in both conditions and the projection of the responses overlap. In this case conventional analyses would be hard to discriminate fMRI activity. Nevertheless, data from each condition occupy a distinct region of the two-dimensional space. A linear decision boundary can be used to distinguish the response distributions. In panel (c) a linear decision boundary would not be sufficient to discriminate responses, therefore, a non-linear classification would be required (modified from Cox and Savoy 2003; Haynes and Rees 2006) .

Although this approach reduces noise, it also reduces signal in two important ways: First, voxels with weaker responses to a particular condition might carry some information about the presence/ absence of that condition. Second, spatial averaging blurs out fine-grained spatial patterns that might discriminate

(a) (b) (c)

stimulus ₁

between experimental conditions. Like conventional methods, the MVPA approach also seeks to boost sensitivity by looking at the contributions of multiple voxels. To avoid the signal-loss issues mentioned above, MVPA methods make use of small differences in the fMRI response of different voxels thought to result from small biases in the spatial distribution of the neural subpopulations sampled by each voxel. By ÔlearningÕ the pattern of these small biases across a large number of voxels in an independent training set, multi-variate pattern analysis can successfully discriminate between stimuli in a novel set of trials.

Several reports have shown that such multivariate techniques can reliably distinguish between responses to different stimuli, where more conventional, voxel-wise univariate approaches, or signal averaging across whole ROIs could not. MVPA techniques have been used to decode the orientation of gratings (Haynes and Rees 2005; Kamitani and Tong 2005), direction of motion (Kamitani and Tong 2006), object categories (Eger et al. 2008; Haushofer et al. 2008; Haxby et al. 2001), to study visual categorisation (Li et al. 2007) and also the encoding of global form (Ostwald et al. 2008). Some of the aforementioned papers went well beyond by predicting from the fMRI patterns of activity the orientation of invisible or masked stimuli, thus, performing a kind of Ôbrain-readingÕ.

Classification performance depends a great deal on the number and choice of voxels included in the analysis (Cox and Savoy 2003; Ku et al. 2008). First, the number of voxels (features) defines the dimensionality of the problem. Classification performance decreases dramatically as the number of features exceeds the number of training points, therefore, it is necessary to choose only an appropriate subset of the total voxel population. Second, voxels that contain little information about the discrimination being made only add unrelated noise to the classifier and degrade performance. As a result, many pattern recognition applications contain a Ôfeature selectionÕ step in which only a subset of voxels is

selected that contains enough information to perform the classification. Of course, the type of the feature selection procedure depends on whether the analysis is restricted to predefined ROIs or it includes locations across the whole brain.

Once a set of voxels has been selected for pattern classification, data are stored into pattern matrices corresponding to the pattern of activity across the selected voxels at a particular time in the experiment. Brain patterns are then labeled according to which experimental condition generated the pattern. This labeling procedure needs to account for the fact that the hemodynamic response measured by the scanner is delayed in time, relative to the neural event under investigation.

Once the fMRI responses are stored into pattern matrices, a subset of these labeled patterns (the train sample) are fed into a multivariate pattern classification algorithm. Based on these patterns, the classification algorithm learns a function that maps between voxel activity patterns and experimental conditions. After the classifier is trained, the next step tests the generalisation of the function. Given a new pattern of brain activity, not previously presented to the classifier (the test sample), can the trained classifier correctly determine the experimental condition associated with that pattern?

In machine learning literature there is an enormous range of classification algorithms that can be potentially used in MVPA studies (Duda et al. 2001). The majority of MVPA studies have used linear classifiers, including correlation-based classifiers (Haxby et al. 2001), neural networks without a hidden layer (Polyn et al. 2005), linear discriminant analysis (LDA) (Haynes and Rees 2006; Haynes and Rees 2005), linear support vector machines (SVM) (Cox and Savoy 2003; Kamitani and Tong 2005), and Gaussian Naive Bayes classifiers (Mitchell et al. 2003). All these classifiers compute a weighted sum of voxel activity values. This

weighted sum is then passed through a decision function, which creates a threshold for saying whether or not a category is present.

Because these techniques are relatively new and not fully understood, users should be extremely cautious about the interpretation of MVPA results (Bartels et al. 2008). Another major concern about MVPA methods is the extent to which Ôbrain readingÕ experiments are ethically acceptable in view of the potential use of this technology towards human rights violation in the future. All in all, MVPA methods have evolved extensively in the last few years and it is expected that MVPA methods will continue to evolve, as better algorithms become available in the coming years. Improvements in the spatial resolution of fMRI will make it possible to resolve even finer-grained cognitive distinctions. For all of these reasons, it is believed that MVPA has a bright future as a tool for characterising how information is represented and processed in the brain.