# Fisher Vectors Derived from Hybrid Gaussian-Laplacian Mixture Models for Image Annotation

arXiv: https://arxiv.org/abs/1411.7399 · HTML: https://mlsanity.com/paper/1411.7399/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2014.

## Built on by (most cited first, 16 of 16)

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- [Describing Sets of Images with Textual-PCA](https://mlsanity.com/paper/2210.12112/) (2022)
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## Abstract (arXiv)

In the traditional object recognition pipeline, descriptors are densely sampled over an image, pooled into a high dimensional non-linear representation and then passed to a classifier. In recent years, Fisher Vectors have proven empirically to be the leading representation for a large variety of applications. The Fisher Vector is typically taken as the gradients of the log-likelihood of descriptors, with respect to the parameters of a Gaussian Mixture Model (GMM). Motivated by the assumption that different distributions should be applied for different datasets, we present two other Mixture Models and derive their Expectation-Maximization and Fisher Vector expressions. The first is a Laplacian Mixture Model (LMM), which is based on the Laplacian distribution. The second Mixture Model presented is a Hybrid Gaussian-Laplacian Mixture Model (HGLMM) which is based on a weighted geometric mean of the Gaussian and Laplacian distribution. An interesting property of the Expectation-Maximization algorithm for the latter is that in the maximization step, each dimension in each component is chosen to be either a Gaussian or a Laplacian. Finally, by using the new Fisher Vectors derived from HGLMMs, we achieve state-of-the-art results for both the image annotation and the image search by a sentence tasks.