Nonlinear Metric Learning through Geodesic Interpolation within Lie Groups

2018/05/12 by Zhewei Wang, Wang, Zhewei, Bibo Shi +5
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Component (thermodynamics) #Computer science #Diffeomorphism #FOS: Computer and information sciences #Gait Recognition and Analysis #Geodesic #Human Pose and Action Recognition #Interpolation (computer graphics) #Lie group #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical analysis #Mathematics #Metric (unit) #Motion (physics) #Nonlinear system #Physics #Pure mathematics #Transformation (genetics) #Video Surveillance and Tracking Methods

paper · pdf · doi:10.48550/arxiv.1805.04784

openalex publication_date 2018/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we propose a nonlinear distance metric learning scheme based on the fusion of component linear metrics. Instead of merging displacements at each data point, our model calculates the velocities induced by the component transformations, via a geodesic interpolation on a Lie transfor- mation group. Such velocities are later summed up to produce a global transformation that is guaranteed to be diffeomorphic. Consequently, pair-wise distances computed this way conform to a smooth and spatially varying metric, which can greatly benefit k-NN classification. Experiments on synthetic and real datasets demonstrate the effectiveness of our model.

Citations

• A Survey on Metric Learning for Feature Vectors and Structured Data

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