Data were acquired from four healthy subjects with normal or corrected-to-normal vision (three male, age range: 24–34 years). Three subjects were authors (S1–S3). Experiments were conducted with the written consent of each subject and in accordance with the safety guidelines for fMRI research, as approved by the University Committee on Activities Involving Human Subjects at New York University. Each subject participated in at least three scanning sessions: one session to obtain a set of high-resolution anatomical volumes, one session for standard retinotopic mapping (single-wedge angular-position and expanding-ring eccentricity), and one double-wedge, angular-position retinotopic mapping session for comparison to orientation maps. Three subjects (S1, S2, and S3) participated in the main orientation mapping experiment with annular stimulus. Three subjects (S1, S2, and S3) participated in the blurred-edge orientation mapping control experiment. Three subjects (S1, S2, and S4) participated in the full-field sinusoidal orientation mapping control experiment. Two subjects (S1 and S3) participated in the square-wave orientation mapping control experiment. Two subjects (S1 and S3) participated in a second double-wedge angular-position retinotopic mapping session. One subject (S1) participated in a repeat of the main orientation mapping experiment with annular stimuli. One subject (S2) participated in an event-related orientation mapping experiment.
Stimuli were generated using MATLAB
(MathWorks) and MGL
(available at http://justingardner.net/mgl
) on a Macintosh computer. Stimuli were displayed via an LCD projector onto a back-projection screen in the bore of the magnet. Subjects were supine and viewed the projected stimuli through an angled mirror (maximum eccentricity of 12 deg of visual angle).
Orientation mapping experiments
The stimulus was a large oriented sinusoidal grating (spatial frequency 0.5 cycles per deg) presented within a 5 deg peripheral annulus (inner radius of 4.5 deg, outer radius of 9.5 deg). Both the inner and outer edges of the annulus were blurred with a 1 deg raised cosine transition (centered on the inner and outer edges) from 100% to 0% contrast. The spatial phase of the grating was randomized every 250 ms from a predefined set of 16 phases uniformly distributed between 0 and 2π. Regions outside the annulus were a uniform gray, equal to the mean luminance of the gratings (526 cd/m2). The orientation of the grating cycled through sixteen evenly spaced angles between 0 and 180° (1.5 s per orientation). The stimulus completed ten and a half cycles in each run. Each cycle was 24 s long. Subjects completed 14–18 runs in each scanning session. The stimuli cycled clockwise in half of the runs and counter-clockwise in the other half.
Orientation mapping control experiments
The first control experiment tested whether the orientation map was due to a potential confound related to the visible edge of the stimulus. The stimulus consisted of the same annular oriented sinusoidal grating as in the main experiment except that the stimulus edge was blurred over a much larger extent so that there was no visible edge. Both edges were blurred with a raised cosine transition region (from 100% to 0% contrast). The transition region was 5 deg for the inner edge (extending from 2 deg to 7 deg eccentricity) and 5 deg for the outer edge (extending from 7 deg to 12 deg), such that the stimulus was 0% contrast at 2 deg, 100% contrast at 7 deg, and 0% contrast at the outermost edge of the screen (12 deg eccentricity). The grating thus achieved 100% contrast only at a single eccentricity (7 deg), and the region of blurring (5 deg) was more than two times the spatial period of the sinusoid (2 deg).
The second control experiment tested whether the map varied as a function of eccentricity by using a stimulus that included the central part of the visual field (9 deg annulus, inner radius 0.5 deg, outer radius 9.5 deg). The stimulus was otherwise identical to that in the main experiment. The third control experiment tested whether the map generalized to the stimulus parameters used in other fMRI studies (Kamitani and Tong, 2005
; Swisher et al., 2010
). The stimulus was a square-wave grating (rather than sinusoidal) with a higher spatial frequency of 1.4 cycles per deg (matched to the stimulus used by Kamitani and Tong, 2005
). This stimulus also included the central part of the visual field (9 deg annulus, inner radius 0.5 deg, outer radius 9.5 deg).
In a fourth control experiment, we measured orientation responses using an event-related protocol. The stimulus was a contrast-reversing oriented sinusoidal grating (spatial frequency 1 cycles per deg, temporal frequency 1.33 cycles per deg), presented within a 7.5 deg annulus (inner radius of 0.5 deg, outer radius of 8 deg). Stimuli were presented at 6 different orientations (0, 30, 60, 90, 120 and 150°) in randomized order. Each stimulus presentation was 1.5 s in duration, interleaved with interstimulus intervals (ISIs) that ranged from 3 to 6 s, in steps of 1.5 s. All 6 orientations were presented 8 times in each run, along with 8 blank trials. Standard methods were used to estimate the hemodynamic impulse response function (HIRF) and estimate a response amplitude to each orientation, separately for each voxel (see Brouwer and Heeger, 2009 for a description of a similar analysis). To estimate the preferred orientation of each voxel, we created 6 unit vectors with angles equally distributed between 0 and 2π. These 6 vectors were multiplied by the 6 response amplitudes to each presented orientation, and averaged to a single vector. The direction of the resulting vector represented the preferred orientation in radians (between 0 and 2π). Multiplying by 180/2π converted the preferred orientation to degrees (between 0 and 180°).
Angular-position mapping experiments
For angular-position mapping, the stimulus was a black and white high-contrast radial checkerboard pattern presented within a pair of wedges on opposite sides of fixation. Each wedge occupied 45° of angular position, and the wedges were restricted to a 5 deg peripheral annulus (inner radius 4.5 deg, outer radius 9.5 deg). No blurring was applied to the edges of the wedges. We used two wedges to equate the phase-range of the orientation and angular-position maps; in both cases, one full cycle covered 180° of the stimulus variable (angular position or orientation). The angular position of the wedges rotated through sixteen evenly spaced angular positions between 0 and 180° (1.5 s per angular position). Each radial strip of the checkerboard pattern within the wedge moved randomly inward or outward on each stimulus frame at a speed of 2 deg/s, giving rise to vivid motion boundaries between adjacent strips. Regions outside the wedges were a uniform gray, equal to the mean luminance of the checkerboard patterns within the wedges. As in the orientation mapping experiments the stimulus completed ten and a half cycles in each run, each cycle was 24 s long, subjects completed 14–18 runs in each session, and the stimuli cycled clockwise in half of the runs and counter-clockwise in the other half.
Observers performed a demanding two-back detection task continuously throughout each run to maintain a consistent behavioral state, encourage stable fixation, and divert attention from the peripheral stimulus. A continuous sequence of digits (0 to 9) was displayed at fixation, changing every 400 ms. The observer's task was to indicate, by means of a button press, whether the current digit matched the digit from two steps earlier.
MRI data were acquired on a Siemens (Erlangen, Germany) 3T Allegra head-only scanner using a head coil (NM-011; NOVA
Medical, Wakefield, MA) for transmitting and a eight-channel phased array surface coil (NOVA
Medical) for receiving. Functional scans were acquired with gradient recalled echo-planar imaging to measure blood oxygen level-dependent (BOLD) changes in image intensity (Ogawa et al., 1990
). Functional imaging was conducted with 24 slices oriented perpendicular to the calcarine sulcus and positioned with the most posterior slice at the occipital pole (1500 ms repetition time; 30 ms echo time; 72° flip angle; 2×2×2 mm voxel size; 104×80 voxel grid). A T1-weighted magnetization-prepared rapid gradient echo anatomical volume (MPRAGE) was acquired in each scanning session with the same slice prescriptions as the functional images (1530 ms repetition time; 3.8 ms echo time; 8° flip angle; 1×1×2.5 mm voxel size; 256×160 voxel grid). A high-resolution anatomical volume, acquired in a separate session, was the average of three MPRAGE
scans that were aligned to one another and averaged (2500 ms repetition time; 3.93 ms echo time; 8° flip angle; 1×1×1 mm voxel size; 256×256 voxel grid). This high resolution anatomical scan was used for both registration across scanning sessions and for gray matter segmentation and cortical flattening.
In one orientation mapping session, we measured gaze positions during the fMRI experiment. The eye tracker (EyeLink 1000, SR Research Ltd., Ottawa, ON, Canada) infrared camera was placed in the bore, recording the pupil centroid and corneal reflection. Raw gaze positions were calibrated and converted to degrees of visual angle (Stampe, 1993
). Preprocessing involved only blink removal: all samples during, and shortly (100 ms) preceding and following blinks were excluded from analysis. Eye position data were divided into segments corresponding to each stimulus orientation. Within each of these segments, average gaze position was computed over each period of stable fixation (defined as periods in which gaze velocity was less than 22 deg/s and gaze drift was less than 1 deg). The angular positions of averaged gaze positions were rotated so that their range matched the range of stimulus orientations. Finally, circular correlation, Eq. (5)
, was used to evaluate whether gaze position angular position varied as a function of stimulus orientation (Supplementary Fig. 1
Defining retinotopic regions of interest (ROIs)
Each subject participated in a standard retinotopic mapping experiment, explained in great detail elsewhere (Larsson and Heeger, 2006
; Gardner et al., 2008
). Standard traveling wave methods were used to identify meridian representations corresponding to the borders between retinotopically organized visual areas V1 and V2. For each subject, we defined an annular sub-region of area V1, including voxels responding preferentially to stimuli between 5 deg and 10 deg. These ROIs were defined with data that were statistically independent of those from the main experiment (i.e., measured in a separate scanning session). The annular V1 ROI was used in the correlation analyses shown in and in the classification analyses shown in . We also defined a rectangular ROI to examine the effect of filtering on classification (see below, Spatial filtering
). This ROI was the minimum rectangular volume that included the entire annular V1 ROI. Because the cortical surface is folded, this volume necessarily included additional voxels in the fovea and far-periphery of V1, along with voxels from other visual areas (e.g., V2) and other tissue types (e.g., white matter). This rectangular ROI was used only for the classification analysis shown in .
Figure 3 Orientation map matches angular-position map. A, Circular correlation between orientation and angular-position maps. Preferred orientation is plotted against preferred angular position. Each dot corresponds to a voxel from an annular region of interest (more ...)
Figure 5 Orientation map is necessary and sufficient for classification. A, Sufficiency. Gray symbols, the angular-position measurements were used to assign each voxel to one of a fixed number of angular-position bins, each corresponding to a different range of (more ...)
Figure 6 Decoding accuracy for both orientation and angular position decreases with low-pass filtering (i.e. spatial smoothing) and increasing with high-pass filtering. A, Decoding accuracy for orientation using unfiltered data (“None”) and for (more ...)
The anatomical volume acquired in each scanning session was aligned to the high resolution anatomical volume of the same subject's brain, using a robust image registration algorithm (Nestares and Heeger, 2000
). Data from the first half cycle (8 frames) of each functional run were discarded to minimize the effect of transient magnetic saturation and allow the hemodynamic response to reach steady state. Head movement within and across scans was compensated using standard procedures (Nestares and Heeger, 2000
). The time-series from each voxel was divided by its mean to convert from arbitrary intensity units to percent modulation and high-pass filtered (cutoff = 0.01 Hz) to remove low-frequency noise and drift (Smith et al., 1999
). Data acquired with different stimulus rotation directions (clockwise or counter-clockwise) were combined to estimate the response phase independent of the lag caused by the hemodynamic delay. Time series data from each scan were shifted back in time by 3 frames. The time series for the counter-clockwise runs were then time-reversed. Averaging clockwise and time-reversed counter-clockwise runs cancelled the residual hemodynamic lag (Engel et al., 1997
; Kalatsky and Stryker, 2003
Maps of orientation and angular-position preference
The average time series of each voxel was fit with a sinusoid with period matched to the period of stimulus rotations (24 s). The phase of the best-fitting sinusoid indicated the angular-position (or orientation) preference of the voxel. The responses of most voxels were very well fit by a sinusoidal model, and there was no evidence for systematic deviation from a sinusoid (e.g., multiple peaks in the responses) for either angular position or orientation. If there was any such non-sinusoidal component in the responses for some voxels, the phase value would not on its own sufficiently capture that voxel's orientation/angular-position preference in the maps; the classification analysis (described below) considered the full time series of responses to each stimulus, not just the phase.
We visualized orientation (and angular-position) preference on computationally flattened representations of each subject's occipital lobe. The signal-to-noise ratio of the responses was quantified as the coherence between the time series and the best-fitting sinusoid, separately for each voxel (Engel et al., 1997
). For each subject, the orientation maps were thresholded by displaying only voxels exceeding a coherence of 0.3. The coherence threshold for the angular-position maps was higher to reflect the five-fold larger signal amplitude (). Coherence is the ratio of the Fourier power (squared amplitude) at the signal frequency (S
) to the sum of power across all frequencies, including both the signal frequency and non-signal, i.e., noise frequencies (N
represents the coherence threshold. If the signal increases by a factor of m
and the noise remains constant, the threshold should be increased correspondingly so that the probability of exceeding the threshold is unchanged. To do so, we used Eq. (1)
to derive a new coherence threshold y
that accounted for a signal amplitude that was larger by a factor of m
. First, rewrite Eq. (1)
so that signal amplitude appears alone on one side:
If the signal amplitude is scaled by a factor of m
but the noise is unchanged, we seek a new threshold y
such that the probability of the signal exceeding the threshold remains the same. Without making any assumptions about the distribution of S
, the following equality holds
if the new threshold y
In our case, the threshold for orientation preference was 0.3 and the signal amplitude for angular position was five times higher than for orientation, so we used a threshold of 0.68 for the angular-position maps, computed using Eq. (4)
= 0.3 and m
Circular correlation was used to characterize the similarity between orientation and angular-position maps (Jammalamadaka and Gupta, 1999). For each voxel, phase values from orientation (o
) and angular-position (p
) mapping were modeled as being equal up to a phase shift:
The circular correlation coefficient rc
indexes voxels, n
is the number of voxels, (^) indicates the circular mean of all phase values for the corresponding measurement (either orientation or angular position), and R
) gives the concentration of the angular difference (or sum):
is the magnitude of a complex number. When two angular variables are related by Eq. (5)
, their difference will be tightly concentrated around Δθ
, so R
) will be close to n
) will be close to 0. If the relationship is of opposite sign, the reverse will be true. Thus, the relative magnitude of the two terms in the numerator of Eq. (6)
determines the degree of correlation (positive or negative), and the denominator serves to normalize the coefficient. The value of rc
ranges from −1 to 1, and the closer it is to 1, the greater the extent to which Eq. (5)
explains the relationship between o
(Jammalamadaka and Gupta, 1999). From hereon, we refer to circular correlation simply as “correlation.” For all experiments, correlations were computed using Eq. (6)
on a subset of voxels from an independently-defined annular region of interest within V1 (see above, Defining retinotopic regions of interest
). The phase values computed from the time series data for the two measurements (orientation and angular position) spanned the range 0 to 2π. These values were used to compute correlation in Eq. (5)
. But in , these values were scaled to match the actual stimulus orientations (and angular positions) tested, which ranged from 0 to π (or 0 to 180°, in degrees). A randomization test was used to assess the statistical significance of the correlations. Orientation and angular-position phase values were shuffled (i.e., randomly reassigned to different voxels) to simulate the null hypothesis that the two maps are unrelated, and correlations were recomputed. The process was repeated 10,000 times to obtain a null distribution of correlation values. A p-value was then computed as the proportion of samples in the null distribution that were less than the observed value.
An additional analysis was used to characterize the phase shift between the two maps. Specifically, the best-fitting value of the parameter Δθ
in the model from Eq. (5)
was found by minimizing:
indexes voxels and n
is the total number of voxels. This corresponds to the norm of the difference between two complex numbers, and is analogous to least squares but for circular variables. Differentiating Eq. (8)
and setting equal to 0 yields the following estimate of Δθ
Phase shift was computed using Eq. (9)
on the same independently-defined subset of voxels from the annular region of interest within V1 used in the correlation analysis.
A final analysis was used to characterize the correspondence between orientation and angular-position preference on a voxel-by-voxel basis. This analysis assessed how well the angular-position map explained the response time courses of individual voxels in the main orientation experiment. For each voxel, we randomly divided the orientation runs into “fitting” and “testing” halves. The fitting data was used to compute the amplitude and phase of the best-fitting sinusoid. We then computed the correlation between that sinusoid and the averaged time series from the testing half. This correlation value indicated the reliability of orientation preference across halves of the data within a session. In the second stage of the analysis, we used the fitting data to estimate only the best-fitting amplitude of a sinusoid having phase equal to that voxel's phase in the independently-measured angular-position experiment. We then computed the correlation between this sinusoid and the time series from the test data. This correlation value indicated how well the angular-position preference predicted the responses in the main orientation mapping experiment. We report the median correlation across voxels for the two versions of the analysis. To ensure that these correlations were not artifacts of the fitting, we repeated the fitting procedure using a random phase for each voxel to construct a null distribution. Correlations for both orientation and angular-position preference well exceeded the 95th percentile of this null distribution.
In multivariate classification analysis of fMRI data, each condition is represented by a set of points in a multi-dimensional space, where each point corresponds to a repeated measurement and where the dimensionality is equal to the number of voxels. Accurate decoding is possible when the responses corresponding to different conditions form distinct clusters within this high-dimensional space. We took the average of all 10 cycles in each run as providing measurements of the responses to each of the 16 orientations (or angular positions). Thus, the 16 time points of the cycle-averaged run were the “categories” to be classified. Before averaging, the counter-clockwise runs were reversed and time-shifted to match the clockwise runs (as described in Preprocessing). The cycle-averaged time courses were stacked across runs, forming an m × n matrix, with m being the number of voxels in the V1 region of interest and n being the number of repeated measurements in the session (n ranged from 224 to 288: 1 cycle-averaged time course per run × 16 orientations × between 14 and 18 runs per session).
Decoding was performed with a maximum likelihood classifier, using the MATLAB function “classify” with the option “diagLinear.” The maximum likelihood classifier optimally separated responses to each of the 16 orientations (or angular positions) if the response variability in each voxel was normally distributed and statistically independent across voxels. Because the number of voxels, m, was large relative to the number of repeated measurements, n, the computed covariance matrix would have been a poor estimate of the true covariance. This would have made the performance of the classifier unstable, as it relied on inversion of this covariance matrix. We therefore ignored covariances between voxels and modeled the responses as being statistically independent across voxels. Although noise in nearby voxels was likely correlated, the independence assumption was conservative; including accurate estimates of the covariances, if available, would have improved the decoding accuracies.
Decoding accuracy was computed using split-halves cross-validation. The m × n data matrix was randomly partitioned along the n dimension (repeated measurements) into training and testing sets, each containing an equal number of runs. Data in the training and testing sets were drawn from different runs in the same session and were thus statistically independent. The training set was used to estimate the parameters (multivariate means and variances) of the maximum-likelihood classifier. The testing set was then used for decoding. Decoding accuracy was determined as the proportion of the 16 test examples that the classifier was able to correctly assign to one of the 16 orientations (or angular positions). Recall that the 16 different test examples corresponded to the 16 time points of the cycle-averaged run, each of which yielded a particular pattern of voxel responses. The data were repartitioned into testing and training halves and decoding accuracy was recalculated. The median of many repeated cross-validations provided a stable estimate of decoding accuracy. A non-parametric permutation test was used to determine the significance of decoding accuracy. Specifically, we constructed a distribution of accuracies expected under the null hypothesis that there is no relationship between the presented orientation and the corresponding time point of the cycle-averaged run. To generate this null distribution, each cycle-averaged run in the training and testing data was phase-randomized and accuracy was recalculated. Phase-randomizing preserved the temporal autocorrelation (and power spectrum) of the responses, but still randomized the relationship between time points and orientations. Repeating this randomization 10,000 times yielded a distribution of accuracies expected under the null hypothesis. Accuracies computed using the unrandomized training data were then considered statistically significant when decoding accuracy was higher than the 95th percentile of the null distribution (P < 0.05, one-tailed permutation test). We used unaveraged () and unfiltered () data to compute the null distributions.
Sufficiency: angular-position based averaging
This analysis determined whether the coarse-scale topographic map of orientation was sufficient for orientation decoding. Statistically independent angular-position measurements were used to assign each voxel to one of a fixed set of bins, each corresponding to a different range (bin width) of angular positions. We then averaged the time series from the orientation experiment of all voxels within each bin to yield a small number of “super-voxels,” and repeated orientation classification. This procedure was performed for bins of different widths (ranging from 0.26° to 60°). For comparison, we also did the same amount of averaging while assigning voxels to bins randomly rather than based on the angular-position map.
Necessity: angular-position removal
This analysis determined whether the coarse-scale topographic map was necessary for orientation decoding. The angular-position map was “removed” from the orientation mapping data as follows. First, for each voxel, we computed the phase of the sinusoid that best fit the time series, averaged across all runs of the angular-position mapping experiment. These phase values were used to project the corresponding sinusoids out of the time series measured during orientation mapping. Specifically, let y
be the time series measured during orientation mapping, and let x
be a sinusoid with frequency equal to the stimulus frequency during orientation mapping and phase equal to the best-fitting phase from the angular-position mapping experiment. We computed a residual time series r
Removal by projection ensured that the residual time series r
was orthogonal to the removed component x
. Finally, classification analysis was performed on the residual time series, as described above.
A confidence interval was determined for the residual decoding accuracy after map removal, according to the hypothesis that the residual decoding depended only on imperfections (e.g., due to measurement noise and registration across experiments) in our ability to completely remove the map. Two subjects repeated the double-wedge angular-position mapping experiment. For these subjects, the first angular-position mapping experiment was used to remove the map from the second angular-position mapping experiment. Classification analysis was performed on data from the second angular-position mapping experiment before and after removing the map. The classification of angular position was identical to the classification of orientation, except that the 16 time points corresponded to different angular positions rather than different orientations. Signal-to-noise ratio was much higher for angular-position than for orientation measurements. Gaussian noise was added to the second angular-position dataset (from which the map was removed) so that baseline decoding accuracy (before map removal) was the same as for orientation mapping. Specifically, noise was added to the cycle-averaged time series of each run, the amplitude of which was slightly different for each of the two subjects (standard deviation of 6 for one subject, 6.5 for the other). Resampling was used to obtain a confidence interval for decoding accuracy. On each resampling, a new sample of noise was added to the data, and runs were randomly repartitioned into training and testing halves. Repeating this 10,000 times yielded a distribution of decoding accuracy. The median, 16th and 84th percentiles of this distribution are reported (, gray horizontal lines, percentiles were averaged across the two subjects). Orientation decoding accuracy (after map removal) fell within this confidence interval. The noise amplitude was set to match baseline decoding accuracy between the two data sets before map removal, but our conclusions depend on the fact that the decoding accuracies were indistinguishable after map removal.
The projection analysis could degrade decoding accuracy even if the phase-to-be-removed was randomly chosen. This could occur if, by chance for some voxels, the phase-to-be-removed matched the voxel's orientation preference. An additional test was performed to ensure that the degradation in classification was specifically due to removing the map. Specifically, the orientation and angular-position phase values were shuffled (i.e., randomly reassigned to different voxels) to project out sinusoids with random phase. Pairings were reshuffled 10,000 times to yield a distribution of decoding acccuracies, and the median is reported (, random component removed).
fMRI time series data were spatially filtered using a volumetric filtering procedure. The procedure was similar to the approach used in related studies (Op de Beeck, 2010
; Swisher et al., 2010
). After motion correction, each frame of the time series was filtered separably in each of its three dimensions. A one-dimensional filter was constructed by multiplying the inverse Fourier transform of an ideal lowpass filter by a Hamming window in the spatial domain. In the Fourier domain, this filter that has a nearly flat passband followed by a transition region (centered on the specified frequency cutoff) and a stopband with minimal ripple. The filter achieves better frequency isolation than a Gaussian filter while minimizing artifacts due to ringing. For consistency with previous reports (Swisher et al., 2010
), we report the size of each lowpass filter as the full-width half-maximum (in the spatial domain) of a Gaussian that achieves half power at the same frequency cutoff (in the Fourier domain). Filtering was performed on a fixed rectangular region of interest that was cropped from the full volume to avoid artifacts associated with extracting the data from ROIs after filtering (Kamitani and Sawahata, 2010
). Filtering was performed in the spatial domain, separably along each dimension, using reflective boundary handing. For each filter size, low-pass filtering was performed by filtering the data with the corresponding filter, and high-pass filtering was performed by subtracting the results of low-pass filtering from the unfiltered data. Many different versions of the analysis (e.g., sharp-cutoff “ideal” filter, non-rectangular region of interest) yielded a qualitatively similar result: classification monotonically decreased with low-pass filtering and increased with high-pass filtering, for both orientation and angular position. Like Swisher et al. (2010)
, we also found qualitatively similar results when performing filtering on the surface (instead of in the volume).
The response amplitudes in the angular-position mapping sessions were five times larger than the response amplitudes in the orientation mapping sessions (). The higher signal-to-noise ratio in the angular-position measurements resulted in near-perfect decoding accuracy with any kind of spatial filtering, which we interpreted as a ceiling effect. To avoid the ceiling effect, only a single cycle of angular-position data was included in the analysis, rather than the average of all ten cycles. In each iteration of the cross-validation procedure, a single cycle of the angular-position data was randomly selected for each run. This approximately compensated for the difference in the signal-to-noise ratio between the two datasets, and avoided a ceiling effect without directly modifying the time series data.
Two different procedures were adopted to reduce the signal-to-noise of angular-position measurements. In the projection analysis (see Necessity, above), the goal was to precisely equate baseline classification accuracy, and this was best accomplished by adding noise to the time series. In the spatial filtering analysis, we simply wanted to avoid a ceiling effect, thus we used the simplest procedure that modified the data the least, i.e. using only a single cycle of the time series per run.