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Okay, I've merged and integrated the original proposal and the revision into one comprehensive document. All changes and additions from the revision have been incorporated.

Full RSA Proposal: "Multi-Dimensional Signed Representational Voxel Encoding (MS-ReVE) with Flow Mapping"

Abstract: This proposal outlines a comprehensive Representational Similarity Analysis (RSA) framework, "Multi-Dimensional Signed Representational Voxel Encoding (MS-ReVE)," designed to compute interpretable, signed voxel-wise contributions to multi-class neural representations. MS-ReVE extends standard RSA by: 1) defining model-relevant contrasts; 2) using multiple-regression RSA on cross-validated, noise-normalized condition means to determine the strength of these contrasts within local searchlights; 3) projecting condition means onto contrast axes to derive signed voxel contributions; and 4) combining these elements to produce robust voxel-weight maps. The framework incorporates advanced features including voxel reliability weighting, voxel-specific RDM reconstruction scores, mapping of interaction effects, and rigorous basis robustness checks. Crucially, MS-ReVE culminates in "Representational Flow Mapping" (RFM), a novel technique to visualize and quantify how these multi-contrast representations transform across the cortical surface (with volumetric extensions possible), revealing large-scale organizational principles and information processing dynamics. A complementary "Representational Cross-Talk" analysis further probes the spatial co-localization of different representational dimensions.

1. Introduction & Rationale:

Representational Similarity Analysis (RSA) has proven invaluable for linking brain activity to computational models and psychological theories. However, traditional RSA often yields searchlight-level summary statistics (e.g., RDM correlations) or classifier-based voxel weights that can be hard to interpret directly in terms of underlying neural coding, especially for designs with more than two conditions. There is a pressing need for methods that:

  • Provide signed voxel weights indicating how individual voxels contribute to specific, theoretically meaningful representational dimensions (contrasts).
  • Scale robustly beyond two experimental conditions.
  • Are firmly anchored in RSA theory (distance-based, second-moment statistics) rather than relying solely on classification.
  • Offer insights into the spatial organization and transformation of these representations across the brain.

MS-ReVE addresses these needs by integrating regression-RSA with voxel-level projections, enhanced with reliability measures, interaction analyses, and a novel flow-mapping visualization approach.

2. Research Questions & Hypotheses (Example-driven):

This framework can address a wide range of questions, such as:

  1. Which specific representational dimensions (e.g., animacy, object size, task rule) are encoded in a given brain region?
  2. How do individual voxels contribute (positively or negatively) to the encoding of these distinct dimensions?
  3. Are there voxels that reliably contribute to specific dimensions, and how does this reliability vary spatially?
  4. How well does a voxel's multi-contrast contribution profile explain the local empirical representational geometry?
  5. Are there conjunctive codes, where voxels respond to interactions between representational dimensions?
  6. How sensitive are these voxel-level interpretations to the precise definition of theoretical contrasts?
  7. What is the large-scale spatial organization of these multi-dimensional representations across the cortex (e.g., gradients, boundaries)?
  8. How do these representations transform (e.g., rotate, scale, differentiate, integrate) along cortical pathways?

3. Methodology & Implementation Plan:

A. Preprocessing & Experimental Design:

  1. Data Acquisition: Standard fMRI data acquisition.
  2. Preprocessing: Standard fMRI preprocessing (motion correction, slice-time correction, spatial normalization/surface projection, temporal filtering). Crucially, include noise normalization/whitening of voxel time-series, typically using the residuals from a first-level GLM, to ensure that pattern analyses are not dominated by voxels with high noise variance.
  3. Experimental Design: Assumes a K-condition experimental design where K ≥ 2 (multi-way case emphasized), though the framework naturally includes the binary case.

B. Contrast Matrix Definition (C):

  1. A Priori Contrasts: Define a K x Q contrast matrix C, where each of the Q columns c_q represents a theoretically meaningful comparison or feature dimension (e.g., faces - houses, tools - animals, abstract - concrete).
    • Contrasts should be centered (sum of elements in each c_q is zero).
    • Ideally, contrasts should be made orthonormal (CᵀC = I) for independent β weights.
  2. Data-Driven Contrasts (Alternative/Complementary):
    • Construct a model RDM based on theoretical predictions.
    • Apply classical Multidimensional Scaling (MDS) to the model RDM.
    • Use the first Q MDS embedding dimensions as columns in C.
    • This provides a data-driven way to define orthogonal axes capturing the model's primary representational structure.

C. Searchlight RSA Core Engine (Iterate across searchlights):

  1. Cross-Validated Condition Means (Û):
    • Within each searchlight (sphere of voxels V):
    • Estimate condition-specific activation patterns (μ_k) for each of the K conditions using a cross-validation scheme (e.g., leave-one-run-out, split-half). Employ methods like crossnobis to obtain unbiased estimates of pattern distinctness.
    • This results in a K x V matrix Û of cross-validated, noise-normalized condition means.
  2. Empirical Second-Moment Matrix (Ĝ):
    • Calculate the unbiased empirical second-moment matrix: Ĝ = ÛÛᵀ. This K x K matrix fully determines all Mahalanobis distances between conditions within the searchlight.
  3. Multiple-Regression RSA:
    • Vectorize the lower (or upper) triangle of Ĝ to form the dependent variable y.
    • For each contrast c_q in C, form a predictor RDM R_q = c_q c_qᵀ. Vectorize the lower triangle of each R_q to form columns of the design matrix X.
    • Fit the multiple linear regression: y = Xβ + ε.
    • The resulting β_q coefficients indicate how strongly the geometry implied by contrast c_q is present in the local empirical geometry Ĝ.
    • Regularization (Optional): If Q is large or contrasts are correlated, use ridge regression (β_ridge = (XᵀX + λI)⁻¹Xᵀy) or elastic-net. Hyperparameters (λ, and α for elastic-net) should be chosen via nested cross-validation within the searchlight training data to avoid bias.
  4. Signed Voxel Contributions (Δ_q):
    • For each contrast c_q, project the cross-validated condition means Û onto it: Δ_q = Ûᵀc_q. This yields a V-dimensional vector where each element Δ_{q,v} represents voxel v's signed contribution to contrast q.
    • Store both:
      • Raw Δ_q: Preserves magnitude, reflecting effect size of the contrast in voxel activity.
      • Normalized ~Δ_q = Δ_q / ||Δ_q||: Captures direction only.

D. Voxel-Level Refinements & Metrics (within each searchlight):

  1. Voxel Reliability Weighting (ρ_q,v):
    • For each Δ_{q,v} estimate, compute its stability across cross-validation folds.
    • Define ρ_{q,v} = 1 - Var_folds(Δ_{q,v}^{(fold)}) / (Var_folds(Δ_{q,v}^{(fold)}) + σ²_noise,q,v).
    • σ²_noise,q,v (expected variance of Δ_{q,v} under the null) is estimated from within-condition residual variances and contrast weights: σ²_noise,q,v = (1/S) Σ_s Σ_k (w_qk² / n_k^(s)) * σ_k,v²^(s).
    • Alternatively, use ρ_{q,v} = 1 / (1 + SE(Δ_{q,v})^2) or similar based on Walther et al. (2016).
  2. Voxel-Specific RDM Reconstruction Score (r_v):
    • For each voxel v, construct a predicted RDM based only on its signed contrast profile: Ĝ^(v) = C * diag(β_1Δ_{1,v}, ..., β_QΔ_{Q,v}) * Cᵀ (using raw Δ).
    • Calculate r_v = corr(vec_lower(Ĝ^(v)), vec_lower(Ĝ_empirical)) as a measure of how crucial voxel v's multi-contrast profile is for reconstructing the local empirical RDM.

E. Generating Voxel-Weight Maps:

  1. Contrast-Specific Maps (Set of Q maps):
    • M_{q,v} = β_q * Δ_{q,v} (magnitude-preserved signed contribution).
    • ~M_{q,v} = β_q * ~Δ_{q,v} (direction-only, scaled by RSA fit).
    • M_{q,v}_reliab = ρ_{q,v} * β_q * Δ_{q,v} (reliability-weighted).
  2. Single Composite Map (optional):
    • w_v = Σ_q (β_q * ~Δ_{q,v}) (or use reliability-weighted terms). Represents the net pull of voxel v in the overall representational space. Note: If C is not orthogonal, the interpretation of w_v is less straightforward as contributions are summed across potentially non-independent axes.

F. Extending to Interaction Effects:

  1. Define Interaction Contrasts: Create new columns in C by taking element-wise products of main effect contrast columns (c_{pq} = c_p ⊙ c_q).
  2. Orthogonalize Expanded Matrix: Orthogonalize the expanded contrast matrix C_exp = [C_main | C_interaction] (e.g., using QR decomposition or Gram-Schmidt) to ensure interpretability of interaction βs as unique contributions. Note: Orthogonalization procedures may arbitrarily flip the sign of contrast vectors; after orthogonalization, consider aligning the sign of each derived column (e.g., interaction terms) with its primary parent component or based on its correlation with the raw Δ projection for consistent interpretation.
  3. Re-run C.3 and C.4: Fit multiple-regression RSA with C_exp to get β_{pq} and compute interaction voxel contributions Δ_{pq,v} = Ûᵀc̃_{pq} (where c̃_{pq} is the orthogonalized interaction contrast).

G. Aggregation & Statistical Inference:

  1. Searchlight Aggregation: Average the voxel weights (M_{q,v}, w_v, r_v, etc.) each voxel receives from all searchlights containing it. An RSA-weighted average (weighting by β_q or searchlight R²) can also be used.
  2. Permutation Testing: For voxel-wise significance testing, shuffle condition labels consistently across cross-validation folds, recompute the entire pipeline (from Û onwards) many times to build null distributions for β_q, M_{q,v}, w_v, r_v, etc. Apply appropriate cluster-correction methods. Note on memory: Storing all intermediate Δ values across permutations can be memory-intensive. Consider strategies like streaming permutations (recomputing Δ on the fly within the permutation loop) or writing intermediate searchlight results to disk if RAM is limited.

H. Representational Flow Mapping (RFM):

  1. Surface Projection: Project voxel-wise multi-contrast loading vectors m_v = [β_1Δ_{1,v}, ..., β_QΔ_{Q,v}] (or reliability-weighted versions) to the nearest vertices on a cortical surface model (e.g., subject's midthickness surface). This creates Q scalar maps f_q(i) on the surface.
  2. Tangential Gradient Estimation: For each surface map f_q(i), compute its 2D tangential gradient ∇_T f_q(i) at each vertex i, typically using filters approximating Gaussian derivatives to ensure robustness to high-frequency noise.
  3. Local PCA for Principal Flow:
    • In a moving geodesic window on the surface:
    • Stack all Q gradient vectors ∇_T f_q(i) from all vertices within the window into a large matrix (effectively (|WindowVertices|*Q) rows x 2 columns).
    • Perform PCA on this matrix's 2x2 covariance to find the principal flow direction e₁ (a 2D unit vector) and its associated eigenvalue λ₁.
  4. Streamline Visualization:
    • Draw streamlines (e.g., using Line Integral Convolution) along e₁.
    • Color streamlines by the contrast q whose gradient ∇_T f_q(i) aligns best with e₁ (i.e., argmax_q |<∇_T f_q(i), e₁>|), with sign indicating increase/decrease.
    • Modulate streamline opacity/thickness by λ₁ (flow strength) and/or underlying ρ_q,v.
  5. Analysis of Transformation Along Flow Lines:
    • Sample m(s) (the Q-dimensional vector of βΔ values) along streamlines.
    • Calculate directional derivatives (dm/ds) to assess rate and dimensionality of change (via SVD).
    • Compare m(s) and m(s+Δs) to quantify representational rotation (angle change) and scaling (norm change).
    • Visualize these transformations (e.g., map rotation rate to streamline hue).
    • Use permutation testing for significance of flow properties.
  6. Volumetric Extension (Optional): While surface-based RFM is often preferred for visualizing cortical organization, the core logic can be extended to 3D volume space by computing 3D gradients and performing PCA on the resulting 3x3 covariance matrix within volumetric searchlights. Visualization is more challenging but may be relevant for subcortical structures.

I. Robustness & Validation:

  1. Basis Robustness Checks:
    • Re-run key analyses (e.g., generating M_{q,v} maps) with an alternative, plausible contrast matrix C' (e.g., MDS-derived if initially theory-driven, or vice-versa).
    • Correlate the resulting voxel maps. Low correlations suggest basis-dependent interpretations.
    • Use diagnostics: Compare searchlight R² for different bases; Canonical Correlation Analysis (CCA) between C and C'; assess R² gain when using [C | C']; compare with non-linear/kernel RSA to probe model mismatch.

4. Data Analysis & Interpretation Strategy:

  • β_q maps (from searchlight regression): Indicate regions where the geometry predicted by contrast q is prevalent.
  • M_{q,v} maps: Reveal how individual voxels contribute (sign and magnitude) to each specific contrast q.
  • M_{q,v}_reliab maps: Highlight robust voxel contributions.
  • w_v composite map: Shows the net directional "pull" of voxels in the combined representational space.
  • r_v maps: Identify voxels whose multi-contrast tuning is critical for the local empirical geometry.
  • Interaction maps (β_{pq}Δ_{pq,v}): Uncover voxels involved in conjunctive coding.
  • RFM visualizations: Provide insights into the large-scale topological organization, functional boundaries, and representational transformations across cortex. Analysis of λ₁, rotation, and scaling along flow lines will characterize the nature of these transformations.
  • Representational Cross-Talk Analysis:
    • Compute the voxel-wise correlation between pairs of reliability-weighted contrast maps (M_{q,v}_reliab and M_{p,v}_reliab) across voxels within relevant brain regions or the whole brain/surface.
    • High positive correlations suggest shared neural populations contribute similarly to both contrasts.
    • High negative correlations suggest competitive coding or opponent populations.
    • Visualizing these correlation patterns (e.g., as a matrix or projecting strong correlations onto the brain) complements RFM by showing where different representational dimensions spatially co-localize or segregate.
  • Group-Level Inference: For analyzing results across participants, individual participant maps (M_q,v, r_v, RFM-derived metrics, etc.) should be aligned to a common space (e.g., MNI volume space or a surface template like fsaverage). Standard group-level statistical approaches (e.g., mixed-effects models, t-tests on aggregated maps with appropriate permutation-based correction) can then be applied.

5. Expected Outcomes & Significance:

MS-ReVE will provide an unprecedentedly rich and interpretable view of distributed neural representations. Expected outcomes include:

  • Detailed, signed voxel-level maps of multi-dimensional neural codes.
  • Identification of robust and reliable voxel contributions.
  • Discovery of conjunctive coding patterns.
  • A quantitative understanding of how representations are organized and transform across cortical areas, linking local computations to large-scale network dynamics.
  • This framework will significantly advance our ability to test nuanced theories of neural representation and bridge the gap between computational models and brain activity.

6. Potential Challenges & Mitigations:

  • Computational Cost: Searchlight analyses, permutation testing, and RFM can be computationally intensive. Mitigation: Efficient coding, parallel processing, optimized algorithms.
  • Interpretation Complexity: The wealth of generated maps requires careful interpretation. Mitigation: Clear guidelines, targeted research questions, development of standardized reporting.
  • Choice of Contrasts: Results can be sensitive to C. Mitigation: Explicit reporting of C, basis robustness checks, use of both theory-driven and data-driven contrasts.
  • Multiple Comparisons: Extensive voxel-wise testing. Mitigation: Rigorous permutation-based cluster correction methods.
  • Memory Usage: Especially during permutation testing. Mitigation: Streaming computations, disk caching, efficient data structures (as noted in 3.G.2).

7. Implementation Plan (Conceptual - Language/Platform Agnostic):

The implementation will be modular:

  1. Module 1: Core RSA Engine:
    • Input: Preprocessed fMRI data, condition labels, contrast matrix C, searchlight definitions.
    • Functions for: Cross-validated mean estimation, Ĝ computation, multiple-regression RSA (with optional regularization), Δ_q calculation.
    • Output: β_q values per searchlight, raw Δ_q and ~Δ_q vectors per searchlight.
  2. Module 2: Voxel-Level Metrics & Map Generation:
    • Input: Outputs from Module 1.
    • Functions for: Reliability (ρ_q,v) calculation, RDM reconstruction (r_v), map generation (M_q,v, w_v), searchlight aggregation.
  3. Module 3: Interaction Analysis:
    • Functions for: Generating interaction contrasts, orthogonalizing C_exp, integrating with Module 1 & 2 for interaction maps.
  4. Module 4: Statistical Inference & Aggregation:
    • Functions for: Permutation testing framework (including memory management considerations), cluster correction, group-level analysis preparation and execution.
  5. Module 5: Representational Flow Mapping (RFM):
    • Input: Aggregated β_qΔ_{q,v} maps, cortical surface model (and/or volumetric data).
    • Functions for: Surface projection (if applicable), gradient calculation (with smoothing options), local PCA (for surface or volume), streamline generation, transformation analysis along streamlines.
    • Visualization tools (interfacing with existing surface/volume visualization libraries).
  6. Module 6: Cross-Talk & Diagnostics:
    • Functions for: Basis robustness checks (CCA, R² comparisons), Representational Cross-Talk computation and visualization.

This modular design will facilitate development, testing, and future extensions. Each module will encapsulate specific mathematical operations and data transformations.

Okay, this is a very comprehensive summary of the rMVPA codebase. It clearly lays out the object-oriented structure, key functionalities, and dependencies. This is an excellent foundation for thinking about how to integrate the G-ReCa Phase 0 (and subsequently Phase 1) plan.

Based on this summary and our G-ReCa Phase 0 proposal, here's how we can conceptualize the integration and identify next steps.

Conceptual Integration of G-ReCa Phase 0 with rMVPA:

The core idea is to leverage rMVPA's existing capabilities for data handling, design specification, and potentially some pre-processing, and then build new modules or extend existing ones to perform the G-ReCa specific steps: MS-ReVE output generation, PCA pre-reduction, PPCA/lightweight manifold learning, ID estimation, and validation.

Proposed Workflow & rMVPA Integration Points:

  1. Data Preparation (Leveraging rMVPA):

    • Dataset Creation (mvpa_dataset, mvpa_surface_dataset): Use rMVPA to load and structure the fMRI data (volume or surface). This handles train/test splits if needed for initial pattern estimation.
    • Design Specification (mvpa_design): Define the experimental conditions, blocking variables for cross-validation, etc., using rMVPA's design objects.

  2. MS-ReVE Output Generation (New Module/Extension):

    • This is the most significant new piece. We need a way to generate the m_v vectors ([β₁Δ₁,v, ..., β_QΔ₁,v]).
    • Step 2a: Cross-Validated Condition Means (Û):
      • rMVPA's mvpa_model with a simple "model" (e.g., just averaging betas from a first-level GLM within each condition and cross-validation fold) could be adapted.
      • Alternatively, a new function might be needed that takes an mvpa_dataset and mvpa_design (with cv_spec) and returns the K x V matrix Û (cross-validated condition means for each voxel/vertex V).
    • Step 2b: Contrast Definition (C): This would be user-defined outside rMVPA as a K x Q matrix.
    • Step 2c: Regression RSA (β_q):
      • This could potentially leverage rsa_model if adapted, or be a custom function. The rsa_model currently seems focused on RDM-to-RDM regression. We need to regress vec_lower(ÛÛᵀ) onto vec_lower(c_q c_qᵀ) for Q contrasts. This might require a new mvpa_mod_spec or a custom process_roi function for a searchlight approach if β_q are to be searchlight-specific. For a whole-brain m_v, β_q might be derived globally.
      • Decision Point: Are β_q global or searchlight-specific for constructing m_v? The G-ReCa proposal implied searchlight aggregation, so β_q would be local.
    • Step 2d: Voxel Contributions (Δ_q = Ûᵀc_q): This is a matrix multiplication.
    • Step 2e: Construct m_v: Combine local β_q and Δ_q for each voxel.
    • Output: A NeuroVec or NeuroSurfaceVector object containing the m_v vectors.

  3. Dimensionality Pre-Reduction (PCA - New or Util):

    • Input: The m_v NeuroVec/NeuroSurfaceVector.
    • rMVPA doesn't seem to have a dedicated top-level PCA function for this purpose, though pcadist implies PCA capability. A utility function using stats::prcomp or a more scalable randomized PCA (e.g., from irlba or rsvd packages) would be needed.
    • Output: PCA-reduced m_v matrix (N_voxels x ~256 components).

  4. Phase 0 Manifold Learning (PPCA - New Module):

    • Input: PCA-reduced m_v matrix.
    • Implement PPCA (e.g., using EM algorithm, or leveraging existing R packages like pcaMethods::ppca if suitable and its uncertainty outputs are accessible).
    • Output: Latent coordinates z, posterior covariance Cov(z|m_v).

  5. Intrinsic Dimensionality Estimation (New or Util):

    • Input: PCA-reduced m_v (or PPCA-whitened data).
    • Implement/wrap TwoNN and Levina-Bickel MLE (e.g., using R packages like intrinsicDimension or custom code).
    • Use scree plot from PPCA likelihoods.
    • Output: ID estimates, plot.

  6. Validation (Leveraging rMVPA Utilities where possible, plus New):

    • Reconstruction MSE: Calculated from PPCA.
    • Trustworthiness/Continuity: Use scikit-learn via reticulate, or find/implement R equivalents. rMVPA doesn't seem to have these directly.
    • External Gradient Correlations: Standard R functions (cor).
    • Leave-One-Subject-Out: This requires iterating the PPCA fitting and prediction steps.

  7. Output Storage & Visualization:

    • Store z and uncertainty maps as NeuroVec/NeuroSurfaceVector for easy visualization with neuroim2/neurosurf tools.
    • Report generation (Markdown/Jupyter via R Markdown/knitr).

Key rMVPA Objects that Might be Extended or Reused:

  • mvpa_model_spec: Could we define a g_reca_phase0_model_spec that encapsulates the PPCA step and its parameters?
  • run_custom_regional / run_custom_searchlight: These are very promising. The core MS-ReVE output generation (steps 2a-2e) could potentially be wrapped in a custom_func for either ROI or searchlight application. The run_searchlight machinery would handle the iteration and provide sl_data (voxel patterns within a sphere) to our custom function.
  • NeuroVec / NeuroSurfaceVector (nvec, nsvec): These will be the primary data containers for m_v, z, and uncertainty maps.

Concrete Proposal for Initial Integration Steps (Focusing on MS-ReVE Output Generation):

Project: grecamvpa - G-ReCa Integration with rMVPA (Phase 0 Focus)

Module 1: MS-ReVE Output Generation

  • msreve_design (New S3/S4 class):

    • Slots:
      • mvpa_design: The underlying mvpa_des object for condition/block info.
      • contrast_matrix: The user-defined K x Q matrix C.
      • beta_estimation_method: char (e.g., "global_rsa", "searchlight_rsa").
    • Purpose: Encapsulates all necessary inputs for MS-ReVE.

  • compute_crossvalidated_means (fun):

    • Input: mvpa_dataset (ds), mvpa_design (des), cv_spec (cv).
    • Process: Iterates through cv_spec folds. For each fold:
      • Identifies training data for that fold.
      • Estimates condition means (μ_k) for all K conditions using the training data (e.g., simple averaging of voxel activities per condition, or betas from a simple GLM fit on training data).
      • Stores these means, associated with the test fold conditions.
    • Output: A list structure or array containing Û (the K x V matrix of cross-validated condition means, where each row k is the mean for condition k estimated from data not including trials of condition k from the current test fold/run).

  • run_msreve_searchlight (fun wrapping run_custom_searchlight):

    • Input: mvpa_dataset (ds), msreve_design (msreve_des), radius (num), cv_spec (cv).
    • Internal custom_func (process_msreve_sphere):
      1. Receives sl_data (data for current searchlight sphere) and sl_info.
      2. Calls compute_crossvalidated_means on sl_data using the provided msreve_des$mvpa_design and cv_spec to get local Û_sl.
      3. Computes local Ĝ_sl = Û_sl Û_slᵀ.
      4. Performs multiple regression RSA using msreve_des$contrast_matrix (C) to get local β_q_sl vector (length Q).
      5. Computes local Δ_q_sl = Û_slᵀ c_q for each contrast q.
      6. Constructs the local m_v_sl vector for the center voxel of the sphere: m_v_center = [β_1_sl * Δ_1_center_sl, ..., β_Q_sl * Δ_Q_center_sl]. (Need to decide if Δ_q is for the whole sphere or just center voxel for m_v). The proposal implies Δ_q is a V-dim vector, so β_q * Δ_q would be too. For m_v which is Q-dim per voxel, we'd use m_v[q] = β_q_sl * Δ_{q,center_voxel_sl}.
      7. Returns this Q-dimensional m_v_sl vector for the center voxel.
    • Output: A NeuroVec or NeuroSurfaceVector where each voxel/vertex value is its Q-dimensional m_v vector (this implies the output is actually a Q-channel NeuroVec/NeuroSurfaceVector).

Module 2: PPCA & ID Estimation (Can be more standalone R functions initially)

  • Functions for PCA pre-reduction.
  • Function for PPCA (EM algorithm or wrapper).
  • Functions for TwoNN, Levina-Bickel MLE.

Module 3: Validation (Standalone R functions)

  • Functions for Trustworthiness/Continuity (possibly via reticulate).
  • Functions for correlation with external maps.

Phased Implementation Plan for grecamvpa (Phase 0):

  1. Develop compute_crossvalidated_means: This is foundational. Test thoroughly.
  2. Develop msreve_design object.
  3. Develop the process_msreve_sphere custom function:
    • First, implement the regression RSA and Δ_q calculation.
    • Then, integrate with compute_crossvalidated_means.
    • Carefully define how m_v is constructed from local β_q and Δ_q.
  4. Wrap process_msreve_sphere in run_msreve_searchlight using run_custom_searchlight: This generates the primary m_v maps.
  5. Implement PCA pre-reduction for m_v maps.
  6. Implement PPCA module.
  7. Implement ID estimation module.
  8. Implement validation metrics.
  9. End-to-end pipeline test and report generation.

This approach leverages rMVPA's strengths in data handling and searchlight iteration, while building the new MS-ReVE and manifold learning components in a modular way. The run_custom_searchlight function seems like a key enabler.