PerTurbo manifold learning algorithm for weakly labelled hyperspectral image classification

International audienceHyperspectral data analysis has been given a growing attention due to the scientific challenges it raises and the wide set of applications that can benefit from it. Classification of hyperspectral images has been identified as one of the hottest topics in this context, and has been mainly addressed by discriminative methods such as SVM. In this paper, we argue that generative methods, and especially those based on manifold representation of classes in the hyperspectral space, are relevant alternatives to SVM. To illustrate our point, we focus on the recently published PerTurbo algorithm and benchmark against SVM this generative manifold learning algorithm in the context of hyperspectral image classification. This choice is motivated by the fact that PerTurbo is fitted with numerous interesting properties, such as low sensitivity to dimensionality curse, high accuracy in weakly labelled images classification context (few training samples), straightforward extension to on-line setting, and interpretability for the practitioner. The promising results call for an up-to-date interest toward generative algorithms for hyperspectral image classification

Variational blue noise sampling

Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including nonphotorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces. © 1995-2012 IEEE.published_or_final_versio

SAGA: Sparse And Geometry-Aware non-negative matrix factorization through non-linear local embedding

International audienceThis paper presents a new non-negative matrix factorization technique which (1) allows the decomposition of the original data on multiple latent factors accounting for the geometrical structure of the manifold embedding the data; (2) provides an optimal representation with a controllable level of sparsity; (3) has an overall linear complexity allowing handling in tractable time large and high dimensional datasets. It operates by coding the data with respect to local neighbors with non-linear weights. This locality is obtained as a consequence of the simultaneous sparsity and convexity constraints. Our method is demonstrated over several experiments, including a feature extraction and classification task, where it achieves better performances than the state-of-the-art factorization methods, with a shorter computational time