Iterative Multiplicative Filters for Data Labeling

Abstract

Based on an idea in [4] we propose a new iterative multiplicative filtering algorithm for label assignment matrices which can be used for the supervised partitioning of data. Starting with a row-normalized matrix containing the averaged distances between prior features and the observed ones the method assigns in a very efficient way labels to the data. We interpret the algorithm as a gradient ascent method with respect to a certain function on the product manifold of positive numbers followed by a reprojection onto a subset of the probability simplex consisting of vectors whose components are bounded away from zero by a small constant. While such boundedness away from zero is necessary to avoid an arithmetic underflow, our convergence results imply that they are also necessary for theoretical reasons. Numerical examples show that the proposed simple and fast algorithm leads to very good results. In particular we apply the method for the partitioning of manifold-valued images.

References in corpus (2)

• Image Labeling by Assignment
• Entropic Wasserstein Gradient Flows

Cited by in corpus (6)

• Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint
• Geometric Numerical Integration of the Assignment Flow
• A Graph Framework for Manifold-valued Data
• Assignment Flows for Data Labeling on Graphs: Convergence and Stability
• Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment
• Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment