LASS: a simple assignment model with Laplacian smoothing
This addresses the problem of multi-category assignment, such as tagging documents or images, for scenarios with partially labeled data or unknown category interrelations, representing an incremental improvement.
The paper tackles the problem of learning soft assignments of items to categories using both item-category and item-item similarity matrices, proposing a quadratic programming model with a training algorithm based on ADMM. It shows the model predicts reasonable assignments from few similarity values and generalizes semisupervised learning.
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.