Enhancing Local Linear Models Using Functional Connectivity for Brain State Decoding

Enhancing Local Linear Models Using Functional Connectivity for Brain State Decoding

Orhan Fırat, Mete Özay, Itır Önal, Ilke Öztekin, Fatoş T. Yarman Vural
DOI: 10.4018/ijcini.2013070103
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The authors propose a statistical learning model for classifying cognitive processes based on distributed patterns of neural activation in the brain, acquired via functional magnetic resonance imaging (fMRI). In the proposed learning machine, local meshes are formed around each voxel. The distance between voxels in the mesh is determined by using functional neighborhood concept. In order to define functional neighborhood, the similarities between the time series recorded for voxels are measured and functional connectivity matrices are constructed. Then, the local mesh for each voxel is formed by including the functionally closest neighboring voxels in the mesh. The relationship between the voxels within a mesh is estimated by using a linear regression model. These relationship vectors, called Functional Connectivity aware Mesh Arc Descriptors (FC-MAD) are then used to train a statistical learning machine. The proposed method was tested on a recognition memory experiment, including data pertaining to encoding and retrieval of words belonging to ten different semantic categories. Two popular classifiers, namely k-Nearest Neighbor and Support Vector Machine, are trained in order to predict the semantic category of the item being retrieved, based on activation patterns during encoding. The classification performance of the Functional Mesh Learning model, which range in 62-68% is superior to the classical multi-voxel pattern analysis (MVPA) methods, which range in 40-48%, for ten semantic categories.
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Mesh Learning And Mesh Arc Descriptors (Mad)

Descriptive Analysis and Motivation for the Mesh Model

In this study, BOLD signals ijcini.2013070103.m01 are measured at time instantsijcini.2013070103.m02, ijcini.2013070103.m03, at voxel coordinates ijcini.2013070103.m04, ijcini.2013070103.m05where ijcini.2013070103.m06 is the number of time samples, and ijcini.2013070103.m07 is the number of voxels. The data set ijcini.2013070103.m08 consists of the voxels ijcini.2013070103.m09, which are distributed in brain in three dimensions. Therefore, the position ijcini.2013070103.m10 of a voxel ijcini.2013070103.m11 at time instant ijcini.2013070103.m12 is a three dimensional vector. At each time instantijcini.2013070103.m13, the participant is processing (either encoding or retrieving) a word belonging to a cognitive process. Therefore, the samples ijcini.2013070103.m14 has an object label at each time instance. In Mesh Learning (Ozay, Öztekin, Öztekin, & Vural, 2012), the cognitive states are modeled by local meshes for each individual voxel, called seed voxel ijcini.2013070103.m15, which is defined in a neighborhood system ijcini.2013070103.m16 (see Figure 1). In this mesh, voxel ijcini.2013070103.m17 is connected to ijcini.2013070103.m18-nearest neighboring voxels ijcini.2013070103.m19 by the arcs with weights ijcini.2013070103.m20. Therefore, the relationship among the BOLD signals measured at each voxel, are represented by the arc weights. ijcini.2013070103.m21-nearest neighbors, ijcini.2013070103.m22, are defined as the spatially-nearest neighbors to the seed voxel, where the distances between the voxels are computed using Euclidean distances between the spatial coordinates ijcini.2013070103.m23 of the voxels in brain. The arc weights ijcini.2013070103.m24 of the mesh are estimated by the following linear regression equation:ijcini.2013070103.m25, (1)

Figure 1.

The Star Mesh, which represents the voxel intensity valuesijcini.2013070103.m41 at the center and its 4-nearest neighbors. Blue node represents the center voxel and the orange nodes represent the surrounding voxels.

where ijcini.2013070103.m26 indicates the error of voxel ijcini.2013070103.m27 at time instant ijcini.2013070103.m28, which is minimized for estimating the arc weights ijcini.2013070103.m29. This procedure is conducted by minimizing the expected square error defined as follows,
(2) where ijcini.2013070103.m31 is the set of p-nearest neighbors of the jth voxel at ijcini.2013070103.m32.

Minimizing Equation (2) with respect to ijcini.2013070103.m33 is accomplished by employing Levinson-Durbin recursion (Vaidyanathan, 2007), where ijcini.2013070103.m34 is the expectation operator. The arc weights ijcini.2013070103.m35, which are computed for each seed voxel at each time instant ijcini.2013070103.m36, is used to form the mesh arc vector ijcini.2013070103.m37. Furthermore, a mesh arc matrix ijcini.2013070103.m38 is constructed by concatenating the mesh arc vectors at each time instant, ijcini.2013070103.m39. Finally, feature matrix ijcini.2013070103.m40 which represents the Mesh Arc Descriptor (MAD), is constructed. The feature matrix, extracted during both memory encoding and retrieval stages is further used in training and testing phases in the classification of cognitive processes, respectively. For the details of the mesh learning algorithm see Fırat et al. (2012) and Özay, Öztekin, Öztekin, and Yarman Vural (2011).

The motivation of representing voxels in the brain by local meshes can be validated by analyzing an individual voxels’ intensity change and the change of the sum of squared difference of intensities ijcini.2013070103.m42 in the neighborhood of that voxel in time. Individual voxel intensity values, which are measured at each time instant, do not possess any discriminative information as illustrated in Figure 2 with red line. Note that the signal intensity value for a voxel is almost constant for each time instant. Since the measurements along the time axis correspond to separate cognitive processes, in most of the problems, it is unlikely to discriminate them by using multi-voxel pattern analysis (MVPA) methods, which classify the voxel intensity values by a machine learning tool. On the contrary, there is a slight variation of the sum of squared distances of intensity values in differing neighbor sizes. The above observation shows that the relationships among voxels carry more information than individual voxel intensity values, at each time instant.

Figure 2.

Sum of squared difference,ijcini.2013070103.m43, of intensity values for a voxel and its N-nearest neighboring voxels over time in log space. The time axis indicates the fMRI measurements from 10 semantic categories.


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