Levels of details for Gaussian mixture models

Abstract. Mixtures of Gaussians are a crucial statistical modeling tool at the heart of many challenging applications in computer vision and machine learning. In this paper, we first describe a novel and efficient algorithm for simplifying Gaussian mixture models using a generalization of the celebrated k-means quantization algorithm tailored to relative entropy. Our method is shown to compare experimentally favourably well with the state-of-the-art both in terms of time and quality performances. Second, we propose a practical enhanced approach providing a hierarchical representation of the simplified GMM while automatically computing the optimal number of Gaussians in the simplified mixture. Application to clustering-based image segmentation is reported. 1 Introduction and prior work A mixture model is a powerful framework to estimate the probability density function of a random variable. For instance, the Gaussian mixture models (GMMs for short) – also known as mixture of Gaussians (MoGs) – have bee

Achievements and Challenges in Improving Temperate perennail Forage legumes

International audienceThe expected move towards more sustainable crop-livestock systems implies wider cultivation of perennial forage legumes. Alfalfa (Medicago sativa subsp. sativa) is the main perennial legume in most temperate regions, especially where farm systems rely largely on forage conservation. White clover (Trifolium repens) and red clover (Trifolium pratense) are dominant in specific regions and farm systems. Although breeding progress for disease and insect resistance has been achieved, these crops have shown lower rates of genetic gain for yield than major grain crops, owing to lower breeding investment, longer selection cycles, impossibility to capitalize on harvest index, outbreeding mating systems associated with severe inbreeding depression, and high interaction of genotypes with cropping conditions and crop utilizations. Increasing yield, persistence, adaptation to stressful conditions (drought; salinity; grazing) and compatibility with companion grasses are major breeding targets. We expect genetic gain for yield and other complex traits to accelerate due to progress in genetic resource utilization, genomics resource development, integration of marker-assisted selection with breeding strategies, and trait engineering. The richness in adaptive genes of landraces and natural populations can be fully exploited through an ecological understanding of plant adaptive responses and improved breeding strategies. Useful genetic variation from secondary and tertiary gene pools of Medicago and Trifolium is being increasingly accessed. Genome sequencing projects in alfalfa and white clover will enrich physical, linkage and trait maps. Genome sequences will underpin fine mapping of useful loci and subsequent allele mining, leveraging the synteny of these crops with M. truncatula. Low-cost genome-wide markers generated through genotyping-by-sequencing will make genomic selection for adaptation and forage yield possible for these crops. Genetic markers will also be used for dissecting quantitative traits and developing toolboxes of functional markers for stress tolerance and other traits. Under current regulatory policies, transgenic approaches are likely to be limited to a few breakthrough traits. The key challenge for future applications of genomics technologies is their seamless integration with breeding system logistics and breeding schemes