Voxel-Based Information Metric in fMRI

• Voxel-Based Information Metric is a quantitative approach that evaluates voxel informativeness in fMRI by computing the mutual information between BOLD responses and stimulus labels.
• It employs a wrapper-based selection strategy with simulated annealing to simultaneously optimize voxel selection thresholds and regularization parameters, ensuring robust classification performance.
• The method significantly reduces feature dimensionality while achieving high accuracy on benchmark datasets such as DS105 and DS107, demonstrating its practical applicability in neuroimaging.

A voxel-based information metric is a quantitative approach for evaluating the informativeness of individual voxels in functional neuroimaging, particularly within brain decoding paradigms using fMRI data. In the voxel selection framework described by (Hourani et al., 2021), the central principle is to assess each voxel according to the mutual information (MI) between its response and the stimulus label, thereby nominating those voxels most relevant for decoding task-relevant brain states. This metric forms the basis of a wrapper-based selection strategy, in which MI is embedded within a meta-heuristic (Simulated Annealing) optimization loop to jointly determine optimal selection thresholds and regularization parameters.

1. Mutual Information-Based Voxel Scoring

The primary criterion for voxel selection is the total mutual information between a voxel's BOLD response and the stimulus label. For voxel $v$, the discretized response $X_v$ and class label $Y \in \{1, ..., K\}$ are considered. The mutual information is calculated as: $$I(X_v; Y) = \sum_{x \in X_v} \sum_{y=1}^K p(x, y) \log \frac{p(x, y)}{p(x) p(y)}$$

A "summed-MI" scoring method is applied, where $Y$ is binarized one-versus-rest for each class $j$, yielding $Y_j \in \{0,1\}$ and corresponding

$$MI_j(v) = \sum_x \sum_{y_j\in\{0,1\}} p(x, y_j) \log \frac{p(x, y_j)}{p(x) p(y_j)}$$

The final voxel score is $S(v) = \sum_{j=1}^K MI_j(v)$, and only voxels with $S(v) \geq \alpha$ are retained, where $\alpha$ is a tunable threshold.

2. Empirical Estimation of Information Metrics

Following post-processing and discretization into $B$ bins, the empirical joint and marginal distributions are estimated via histograms over trial segments. For each voxel and class, the joint histogram $H_{v,j}[x, y_j]$ is constructed, with probabilities:

• $p(x, y_j) = H_{v,j}[x, y_j]/N$
• $p(x) = \sum_{y_j} p(x, y_j)$
• $p(y_j) = \sum_x p(x, y_j)$

These frequencies are used directly in the mutual information calculations above. This data-driven estimation offers robustness under histogram-based MI, contingent on the discretization choices.

3. Meta-Heuristic Parameter Search and Wrapper Integration

The mutual information metric is embedded within a Simulated Annealing (SA) wrapper to search for the optimal selection thresholds $(\alpha, \beta)$, where $\beta$ is a regularization-related hyperparameter. The search loop operates as follows:

• Initialize $(\alpha, \beta)$, set temperature $T$.
• Iteratively select voxels meeting current threshold, evaluate classification error using a leave-one-subject-out SVM cross-validation scheme.
• Propose local perturbations $(\alpha', \beta')$, accept or reject per the stochastic SA acceptance criterion.
• Cooling schedule $T \leftarrow \eta T$ guides the search towards convergence (typical settings: exponential cooling, $\eta \approx 0.95$, $M \approx 200$ iterations).

The final voxel set corresponds to the parameterization minimizing cross-validated error, supporting data-driven adaptivity and avoiding reliance on a priori fixed thresholds.

4. Preprocessing, Voxel Filtering, and Postprocessing

The framework integrates standardized neuroimaging methods at several stages:

• Preprocessing: Brain extraction (BET), motion correction (MCFLIRT), spatial smoothing (Gaussian FWHM 5mm), grand-mean scaling, high-pass filtering, registration to 2mm MNI152 space.
• Voxel Filtering: First-level GLM analysis with separate regressors per stimulus; intersection of class-specific $z$-stat maps with Harvard–Oxford Cortical Atlas ROIs, retaining the maximum $z$-score voxel per ROI/class.
• Postprocessing: Column-wise normalization, segmentation into trial blocks (9 or 7 TRs per trial depending on dataset), flattening to feature vectors, discretization into $B \approx 20$ bins, and scaling to $[0,1]$.

These steps precede the MI-based selection and ensure the input for the information metric exhibits both physiological plausibility and statistical tractability.

5. Classification Performance and Comparative Results

The method was evaluated on DS105 and DS107 from OpenfMRI (multi-class, multi-subject visual task datasets). Main inter-subject leave-one-out results were:

• DS105: Mean accuracy $92.4\%$ $(\sigma = 9.18\%)$
• DS107: Mean accuracy $92.0\%$ $(\sigma = 8.3\%)$

Comparison against alternative voxel selection and classification pipelines demonstrated substantial accuracy gains:

Method	Accuracy (DS105)	Accuracy (DS107)
Correlation+SVM [8]	18.3%	38.0%
Atlas ∩ GLM + SVM [29]	28.7%	68.5%
Graph-based embedded [39]	50.6%	89.7%
Anatomical Pattern Analysis [57]	59.2%	95.6%
MFWVS (MI–metaheuristic)	92.4%	92.0%

A two-way ANOVA on bootstrapped distributions confirmed significance at $p<0.001$ for DS105 improvements. The information-based selection consistently reduced the feature set from approximately 100,000 to $200$–$300$, and further to $100$–$200$ voxels post-MI thresholding, representing less than $1\%$ of the original dimensionality.

6. Limitations, Computational Aspects, and Extensions

The framework exhibits several limitations:

• Accurate voxel filtering requires valid GLM timing/onset files; missing data renders this step inoperable.
• Choice of threshold and meta-heuristic schedule parameters lacks closed-form guidance, necessitating empirical tuning.
• Histogram-based MI assumes discrete bins, potentially discarding fine-grained feature information.

Computational complexity for each $(\alpha, \beta)$ evaluation is $\mathcal{O}(K N B)$ for MI scoring, with total complexity dominated by repeated SVM training/testing in the SA loop ($\approx \mathcal{O}(M K (N B + \text{SVM}))$). The use of GLM and atlas pre-filtering reduces dimensionality and renders the wrapper approach feasible.

Extensions include continuous-MI estimators (e.g., Kraskov–Stögbauer–Grassberger) to obviate binning, alternative meta-heuristics (genetic algorithms, particle swarm), pairwise MI incorporation for redundancy reduction, dynamic MI analysis, or generalization to other modalities such as EEG/MEG or multimodal fusion with anatomical priors.

7. Context and Implications in Brain Decoding

Adoption of mutual information as a voxel-selection metric, coupled with meta-heuristic optimization, offers a principled reduction in fMRI feature set size with minimal loss—and in some cases, gain—in decoding accuracy. The integrated framework demonstrates scalable, statistically robust voxel selection and classification under realistic inter-subject cross-validation. This paradigm provides a benchmark for subsequent feature selection approaches in computational neuroimaging and supports efficient pipelines for brain-computer interface applications, as evidenced by the comparative and statistical outcomes on established open datasets (Hourani et al., 2021).