2023/01/15 by Angela Andreella, Andreella, Angela, Riccardo De Santis +5 · 3 citations
Computer Science · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Morphological variations and asymmetry
paper · pdf · doi:10.48550/arxiv.2301.06164
openalex publication_date 2023/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The statistical shape analysis called Procrustes analysis minimizes the 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.