Analysis

A.2.4.1 Behavioral response

Response latency was determined by the difference between the trigger signals recorded for the on-set of a picture and the button press. Median response latencies of correct responses were deter-mined for each object and were compared across objects and categories by means of Analysis of Variance (ANOVA) with the within-factors CATEGORY and OBJECT, respectively.

A.2.4.2 Data processing and artifact correction

In a first step, external noise was removed by applying a noise-reduction procedure. This procedure eliminates any correlation that the MEG sensors have with any of the reference magnetometer.

BESA2000 software (MEGIS, Munich) was used for all following data processing steps.

The continuously recorded data of each block were combined into one file and ocular and cardiac artifacts were corrected. This correction was based on the MSEC (multiple source eye correction) approach developed by Berg and Scherg (1994). This method uses empirically determined compo-nents to estimate artifact related ocular or cardiac activity from the topographic information of all sensors. For the correction of eye blinks one source vector was used, while for the removal of car-diac artifacts two independent source vectors were applied.

Next, data were converted to epochs of 1000 ms starting 100 ms prior to stimulus onset. Correction of possible baseline differences was achieved by subtracting the mean amplitude of each channel during the pre-stimulus period from each epoch. Each data set was visually inspected to detect sen-sors with a high amount of artifacts. Artifact-loaded channels were replaced by interpolated data based on spherical splines (Perrin et al., 1989). For each channel the mean amplitude during each

A.2.4 : Methods - Analysis

epoch was computed to estimate the goodness of data and to identify any trials with remaining arti-facts due to movement or other sources of noise, which were excluded from further analysis by set-ting an artifact rejection threshold.

For every subject, the event-related magnetic field was averaged for each of the 16 base-level con-cepts and the individual grand mean across all concon-cepts was subtracted from the grand mean of each single concept to remove activity not specifically related to it.

Trials in which the response was erroneous were not included in the averages.

A.2.4.3 Source space analysis

An important issue in the interpretation of electro- and magnetophysiological data is the inference from the recorded signals to the underlying generators in the brain. This problem, known as the 'in-verse problem' (Helmholtz, 1853), is ambiguous: it has no unique solution. That is, a given magnet-ic field recorded can be explained by an infinite number of different configurations of intracranial sources. A solution can only be found by making assumptions about these sources and volume con-duction (Fender, 1987).

In this study, the source current distribution was estimated with a distributed source model, the Minimum Norm Estimate (MNE). While single- or multiple dipole models presuppose that brain activity is localized to one or several small areas, the MNE represents the best solution for the cur-rent if only little a priori information about the source is available (Hämäläinen & Ilmoniemi, 1994;

Michel et al., 2004; Hauk, 2004). The MNE models the cortical source space as a dense grid of n in-dependent, single equivalent current dipoles located on a sphere.

A measured magnetic field can be described by a vector B:

B=L P + ε

where L is a m x n lead field matrix, describing the sensitivity pattern of each of the m magnetome-24

A.2.4 : Methods - Analysis

ters to the primary current P and ε is a noise component.

Even in the case of perfectly accurate data (with ε=0) this system has no unique solution. Several methods to solve the this problem have been suggested. Here, a unique solution was achieved by minimizing the ordinary quadratic L2 norm of the current distribution, or in other words by select-ing the current distribution with the shortest current vector capable of explainselect-ing the measured sig-nals.

As the presence of noise can lead to distortions or unstable estimates of real activity, spatial regular-ization is necessary and Thikhonov-Philips regularregular-ization (Bertero et al., 1988) was applied during the pseudo-inversion of matrix L, which results in suppression of currents with poor coupling to the sensors. This means that the MNE does not represent exactly the measured signals, but deviations are within the range of measurement errors (Sarvas, 1987). The Minimum Norm model consisted of a concentric sphere with a radius of 0.6 relative to the average radius of the cortex. The source space contained a uniformly distributed grid of hypothetical dipoles, each with three orientations at the 655 locations. For illustration and further analysis 197 of the locations covering the whole sphere were selected. All results reported on the following are based on the norm activity (i.e. vec-tor length) of the three orthogonal dipoles at each of the 197 locations. The MNE was computed with MATLAB-based in-house software developed by Olaf Hauk.

A.2.4.4 Spatio-temporal correlations

A.2.4.4.1 Method

As described in the introductory part of this thesis, objects might be represented in the brain in form of specialized areas or in distributed networks with a unique neural signature for a particular base level concept. Given that category-related activity is reflected in the distribution of magnetic fields, base level concepts of the same superordinate category should be more similar than base level

con-A.2.4 : Methods - Analysis

cepts of different superordinate categories. Determining spatio-temporal correlation coefficients permits to compare brain activity evoked by the different base level concepts.

The Pearson correlation coefficient r was computed for each pair wise combination of the 16 base-level concepts. Different subsets of dipole locations (combined to 17 areas, see Figure A-4) and time windows were used. Time windows had a width of 40 ms each and data were analyzed from 90 to 450 ms after stimulus onset (resulting in 9 time windows: 90-130 ms, 130-170 ms, etc).

The correlations were computed after all data points within an area (each including of 8 dipole loca-tions) and time window were represented by a single vector for each concept. As Pearson’s r is not normally distributed, the values were Fisher z transformed to the variable z’:

z’=0.5 * ln(1+r)-ln(1-r)], where ln is the natural logarithm.

26

Figure A-4: Schematic representation of the distribution of 17 areas clustered for analysis. Each of the areas contained 8 dipole locations.Top view, nose up.

A.2.4 : Methods - Analysis

The distribution of z’ is normal with a standard error of: σz’= 3 1

− N .

The z’-transformed coefficients were averaged a) for pairs of base level concepts within the same super-ordinate category, b) for pairs of base-level concepts from different categories.

A.2.4.4.2 Contrast score, Topography of correlations

For graphical illustrations of the spatial distribution of differences between the correlations within and between superordinate categories for each of the areas a contrast score was determined. This contrast score consisted of the sum of the differences between each within-category correlation of a given category and the between-category correlations with the other categories. For each area one contrast score was obtained. Scores were 'mapped' using the center of gravity of each area as an ap-proximate location of the area on the scalp.

A.2.4.5 Unsupervised classification

The primary goal of classification methods is the clustering and visualization of high-dimensional data, based on similarities among different patterns. In this study two different clustering algorithms were applied¹:

a) Self-organizing topographical mapping as a neural network approach b) Hierarchical clustering as a statistical classification approach

A.2.4.5.1 Hierarchical clustering

Hierarchical clustering techniques organize data in nested sequences of groups, which can be dis-played in the form of dendrograms or trees. In this study, a hierarchical algorithm clustered the two most similar high-dimensional vectors in sequential passes (Duda et al., 2000). During each pass the number of vectors is reduced by one by replacing the two composing vectors by the mean of them.

1I am grateful to Prof. Dr. Shlomo Bentin and Dr. Yaron Silberman for providing algorithms and assistance in

A.2.4 : Methods - Analysis

Similarity was defined as the Euclidian distance between two data vectors.

This procedure is deterministic and enables to follow the dynamic formation of clusters.

Hierarchical clustering was performed on the grand average for each base-level concept for the time windows 120-210 ms and 210-450 ms. Each concept was represented by a vector including all data points within a time window and all dipole locations within area. The clustering was performed in-dependently for each hemisphere. Selection of these time windows was based on visual inspection of the data and theoretical considerations. While during the first time window the initial stages of visual processing are completed (Thorpe & Fabre-Thorpe, 2001), the second one is most likely as-sociated with semantic activity.

In addition, Symmetric Uncertainty Coefficients (see Appendix C) were computed (for the outcome of the hierarchical clustering after 12 passes) to quantify the results of the hierarchical clustering procedure.

A.2.4.5.2 Self-organizing topographical mapping (SOM)

SOM is a particular type of neural network, using an unsupervised stochastic iterative learning algo-rithm to discover patterns and categories in the input data by clustering high-dimensional vectorial data.

For each iteration, a data vector is randomly chosen (without replacement) and compared to a set of vectors of the same dimension organized on a (usually) two-dimensional grid. At each comparison, the vector on the grid that is the most similar to the data vector (based on a high-dimensional metric function) is algorithmically modified, becoming even more similar, and so are its neighboring vec-tors. The size of this neighborhood decreases as the number of iterations increases. Upon conver-gence of the algorithm, the original data vectors are mapped on the grid such that vectors that are similar in their properties are placed at topographically nearby nodes (Kohonen, 2001). In the

28

A.2.4 : Methods - Analysis

present study, the map was two-dimensional (10 by 10 nodes) and the 16 original vectors were mapped onto it to form geometrically meaningful clusters. For illustration purposes, the U-MAT al-gorithm was implemented on the organized map (Ultsch, 1993). This alal-gorithmcolours the organ-ized map using a grey scale, such that the actual similarity between the high-dimensional vectors (concepts) that are represented by the nodes in the two-dimensional map is reflected by colour dens-ity: Darker demarcation space reflects larger high-dimensional distance between the adjacent nodes.

The input to the SOM consisted of the same data vectors as for the unsupervised hierarchical clus-tering. The computation of the SOM is a stochastic process; several runs of the algorithm with the identical input may result in slightly different output. To account for this, the algorithm was applied four times to each input data set and based on visual inspection the ‘best’ map was selected.

A.2.4.6 Statistical analysis

The General Linear Model (GLM) as implemented in the SAS System for Windows (SAS Institute Inc., Cary, NC ) was used to perform statistical analysis. Versions 6.12 and 8.02 were used.

Statistical analyses were performed on time windows of 40 ms from 90 to 450 ms after stimulus on-set to follow the time course of categorization. For each window, statistical comparisons were car-ried out by repeated measurement analysis of variance (ANOVA).

Tests were performed independently on different transformations of the data: a) the ‘raw” neuro-magnetic fields, b) the MNE (after the previous subtraction of the overall grand average) and c) the z’-transformed correlation coefficients. Sensors (or dipole locations for the MNE) were grouped into regional means prior to analysis as illustrated in Figure A-4.

Based on findings presented in the introduction of this thesis and published reviews (Grill-Spector, 2003), category-related differences were expected in occipital and temporal brain areas and the ar-eas 1,2,3,4,5,6,9,10,11,12,15 and 16 (Figure A-4) were included in statistical tests.

A.2.4 : Methods - Analysis

The within-factors CATEGORY or OBJECT tested for differences between the stimuli. Tests for differences in the topographical distribution were performed with the within-factors HEMISPHERE (right [areas 1,2,5,6,11,12], left [areas 3,4,9,10,15,16]), GRADIENT (central [areas 2,3,6,9,12,15], posterior [areas 1,4,5,10,11,16]) and DEPTH (3 levels in dorso-ventral direction: dorsal [areas 1,2,3,4], medial [areas 5,6,9,10], ventral [areas 11,12,15,16]). To control for Type I errors associat-ed with inhomogeneity of variance, the degrees of freassociat-edom (df) were decreasassociat-ed using the Green-house-Geisser epsilon (ε) for all repeated measures with more than one df (Greenhouse & Geisser, 1959). Corrected P-values are reported.

Hierarchical clustering and SOM were performed on the group data and are therefore interpreted based on visual inspection.