Iterative Multiplicative Filters for Data Labeling

TL;DR

The paper introduces an efficient iterative multiplicative filtering algorithm for data label assignment, suitable for supervised data partitioning, with proven convergence and successful application to manifold-valued image segmentation.

Contribution

It presents a novel multiplicative filtering method for label assignment, with a convergence analysis and practical effectiveness demonstrated on manifold-valued images.

Findings

Algorithm is fast and yields high-quality label assignments.

Convergence is guaranteed under boundedness conditions.

Effective in segmenting manifold-valued images.

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.