LASS: a simple assignment model with Laplacian smoothing

TL;DR

This paper introduces LASS, a quadratic programming model for soft assignment of items to categories using similarity matrices, with applications in semi-supervised and multi-label learning.

Contribution

It presents a simple, effective quadratic programming approach with Laplacian smoothing for multi-category assignment, extending semi-supervised learning.

Findings

Predicts reasonable assignments with limited similarity data

Handles multi-category and hierarchical category structures

Provides a training algorithm based on ADMM

Abstract

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity matrix, which encourages similar items to have similar assignments. We propose a simple quadratic programming model that captures this intuition. We give necessary conditions for its solution to be unique, define an out-of-sample mapping, and derive a simple, effective training algorithm based on the alternating direction method of multipliers. The model predicts reasonable assignments from even a few similarity values, and can be seen as a generalization of semisupervised learning. It is particularly useful when items naturally belong to multiple categories, as for example when annotating documents with keywords or pictures with tags, with partially tagged items, or when the categories have complex interrelations (e.g. hierarchical) that are unknown.