Optimal Tagging with Markov Chain Optimization

TL;DR

This paper introduces a principled approach to optimal tagging by modeling user navigation as a Markov chain, formulating it as an NP-hard subset optimization problem, and providing an efficient greedy approximation with demonstrated effectiveness on real datasets.

Contribution

It formulates the optimal tagging problem using Markov chain modeling and offers a simple greedy algorithm with provable approximation guarantees.

Findings

Greedy algorithm achieves (1-1/e)-approximation for the NP-hard problem.

The method outperforms baseline approaches on three real datasets.

Efficient implementation of the greedy step enhances practical applicability.

Abstract

Many information systems use tags and keywords to describe and annotate content. These allow for efficient organization and categorization of items, as well as facilitate relevant search queries. As such, the selected set of tags for an item can have a considerable effect on the volume of traffic that eventually reaches an item. In settings where tags are chosen by an item's creator, who in turn is interested in maximizing traffic, a principled approach for choosing tags can prove valuable. In this paper we introduce the problem of optimal tagging, where the task is to choose a subset of tags for a new item such that the probability of a browsing user reaching that item is maximized. We formulate the problem by modeling traffic using a Markov chain, and asking how transitions in this chain should be modified to maximize traffic into a certain state of interest. The resulting optimization problem involves maximizing a certain function over subsets, under a cardinality constraint. We show that the optimization problem is NP-hard, but nonetheless has a simple (1-1/e)-approximation via a simple greedy algorithm. Furthermore, the structure of the problem allows for an efficient implementation of the greedy step.To demonstrate the effectiveness of our method, we perform experiments on three tagging datasets, and show that the greedy algorithm outperforms other baselines.