# Relevance Feedback with Latent Variables in Riemann spaces

## TL;DR

This paper introduces two novel relevance feedback methods using Riemannian geometry in semantic query spaces, employing Gaussian and latent semantic models, and provides a new evaluation methodology for comparison.

## Contribution

It develops and evaluates two new relevance feedback techniques based on Riemannian metrics and probabilistic models, with a novel experimental evaluation approach.

## Key findings

- Gaussian-based relevance feedback improves retrieval accuracy.
- Latent semantic variable model enhances relevance estimation.
- New evaluation methodology offers unbiased comparison of feedback methods.

## Abstract

In this paper we develop and evaluate two methods for relevance feedback based on endowing a suitable "semantic query space" with a Riemann metric derived from the probability distribution of the positive samples of the feedback. The first method uses a Gaussian distribution to model the data, while the second uses a more complex Latent Semantic variable model. A mixed (discrete-continuous) version of the Expectation-Maximization algorithm is developed for this model. We motivate the need for the semantic query space by analyzing in some depth three well-known relevance feedback methods, and we develop a new experimental methodology to evaluate these methods and compare their performance in a neutral way, that is, without making assumptions on the system in which they will be embedded.