Procrustes Analysis for High-Dimensional Data

Andreella, Angela; Finos, Livio

doi:10.1007/s11336-022-09859-5

Cited by 8 publications

(9 citation statements)

References 37 publications

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“…In the previous example, we empirically proved the nonuniqueness of hyperalignment and GPA. For a formal proof, see Andreella & Finos ( 2022 ). This result means that we have a different representation of the aligned images and related results in the brain space for each set of transformations.…”

Section: Resultsmentioning

confidence: 99%

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Enhanced hyperalignment via spatial prior information

Andreella

Finos

Lindquist

2022

Human Brain Mapping

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Functional alignment between subjects is an important assumption of functional magnetic resonance imaging (fMRI) group-level analysis. However, it is often violated in practice, even after alignment to a standard anatomical template. Hyperalignment, based on sequential Procrustes orthogonal transformations, has been proposed as a method of aligning shared functional information into a common high-dimensional space and thereby improving inter-subject analysis. Though successful, current hyperalignment algorithms have a number of shortcomings, including difficulties interpreting the transformations, a lack of uniqueness of the procedure, and difficulties performing whole-brain analysis. To resolve these issues, we propose the ProMises (Procrustes von Mises-Fisher) model. We reformulate functional alignment as a statistical model and impose a prior distribution on the orthogonal parameters (the von Mises-Fisher distribution). This allows for the embedding of anatomical information into the estimation procedure by penalizing the contribution of spatially distant voxels when creating the shared functional high-dimensional space. Importantly, the transformations, aligned images, and related results are all unique. In addition, the proposed method allows for efficient whole-brain functional alignment. In simulations and application to data from four fMRI studies we find that ProMises improves inter-subject classification in terms of between-subject accuracy and interpretability compared to standard hyperalignment algorithms.

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Section: Resultsmentioning

confidence: 99%

“…The algorithms describing the ProMises model estimation process and its Efficient version are reported in Appendix 1. For further details and proofs about the ProMises model and its efficient version, please see Andreella and Finos ( 2022 ).…”

Section: Methodsmentioning

confidence: 99%

Enhanced hyperalignment via spatial prior information

Andreella

Finos

Lindquist

2022

Human Brain Mapping

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“…In other words, the model simply reflects the assumption underlining hyperalignment, namely that neural activity in different brains are noisy rotations of a common space (Haxby et al, 2011). In this paper, we assume Σ v = I v , where I v is the identity matrix of size v. The extension to an arbitrary type of variance matrix Σ v and incorporation of its estimation into the ProMises model is discussed in Andreella and Finos (2022).…”

Section: Modelmentioning

confidence: 99%

“…The algorithms describing the ProMises model estimation process and its Efficient version are reported in A. For further details and proofs about the ProMises model and its efficient version, please see Andreella and Finos (2022).…”

Section: Efficient Promises Modelmentioning

confidence: 99%

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Enhanced hyperalignment via spatial prior information

Andreella¹,

Finos²,

Lindquist³

2022

Preprint

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Functional alignment between subjects is an important assumption of functional magnetic resonance imaging (fMRI) group-level analysis. However, it is often violated in practice, even after alignment to a standard anatomical template. Hyperalignment, based on sequential Procrustes orthogonal transformations, has been proposed as a method of aligning shared functional information into a common high-dimensional space and thereby improving inter-subject analysis. Though successful, current hyperalignment algorithms have a number of shortcomings, including difficulties interpreting the transformations, a lack of uniqueness of the procedure, and difficulties performing whole-brain analysis.To resolve these issues, we propose the ProMises (Procrustes von Mises-Fisher) model. We reformulate functional alignment as a statistical model and impose a prior distribution on the orthogonal parameters (the von Mises-Fisher distribution). This allows for the embedding of anatomical information into the estimation procedure by penalizing the contribution of spatially distant voxels when creating the shared functional high-dimensional space. Importantly, the transformations, aligned images, and related results are all unique. In addition, the proposed method allows for efficient whole-brain functional alignment. In simulations and application to data from four fMRI studies we find that ProMises improves inter-subject classification in terms of between-subject accuracy and interpretability compared to standard hyperalignment algorithms.

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Procrustes-based distances for exploring between-matrices similarity

et al. 2023

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The statistical shape analysis called Procrustes analysis minimizes the Frobenius distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This manuscript presents two types of distances derived from Procrustes analysis for exploring between-matrices similarity. The first one focuses on the residuals from the Procrustes analysis, i.e., the residual-based distance metric. In contrast, the second one exploits the fitted orthogonal matrices, i.e., the rotational-based distance metric. Thanks to these distances, similarity-based techniques such as the multidimensional scaling method can be applied to visualize and explore patterns and similarities among observations. The proposed distances result in being helpful in functional magnetic resonance imaging (fMRI) data analysis. The brain activation measured over space and time can be represented by a matrix. The proposed distances applied to a sample of subjects—i.e., matrices—revealed groups of individuals sharing patterns of neural brain activation. Finally, the proposed method is useful in several contexts when the aim is to analyze the similarity between high-dimensional matrices affected by functional misalignment.

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Procrustes Analysis for High-Dimensional Data

Cited by 8 publications

References 37 publications

Enhanced hyperalignment via spatial prior information

Enhanced hyperalignment via spatial prior information

Enhanced hyperalignment via spatial prior information

Procrustes-based distances for exploring between-matrices similarity

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