FineMorphs: Affine-diffeomorphic sequences for regression

2023/05/26 by Michele Lohr, Lohr, Michele, Laurent Younès +1
Computer Science · #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Medical Image Segmentation Techniques #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2305.17255

openalex publication_date 2023/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A multivariate regression model of affine and diffeomorphic transformation sequences - FineMorphs - is presented. Leveraging concepts from shape analysis, model states are optimally "reshaped" by diffeomorphisms generated by smooth vector fields during learning. Affine transformations and vector fields are optimized within an optimal control setting, and the model can naturally reduce (or increase) dimensionality and adapt to large datasets via suboptimal vector fields. An existence proof of solution and necessary conditions for optimality for the model are derived. Experimental results on real datasets from the UCI repository are presented, with favorable results in comparison with state-of-the-art in the literature and densely-connected neural networks in TensorFlow.

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