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

Neighbor Embedding with Non-negative Matrix Factorization for image prediction

International audienceThe paper studies several non-negative matrix factorization methods with nearest neighbors constrained dictionaries for image prediction. The methods considered include the multiplicative update algorithm, the projected gradient algorithm, as well as the graph-regularized NMF solution which aims at taking into account the geometrical structure of the input data. The Intra prediction problem based on these NMF solutions amounts to a neighbor embedding problem. Both prediction and rate-distortion performances are then given in comparison with other neighbor embedding methods like locally linear embedding (LLE) and locally linear embedding with low dimensional neigborhood representation (LLE-LDNR)

Analyse de séries temporelles d’images à moyenne résolution spatiale : reconstruction de profils de LAI, démélangeage : application pour le suivi de la végétation sur des images MODIS

This PhD dissertation is concerned with time series analysis for medium spatial resolution (MSR) remote sensing images. The main advantage of MSR data is their high temporal rate which allows to monitor land use. However, two main problems arise with such data. First, because of cloud coverage and bad acquisition conditions, the resulting time series are often corrupted and not directly exploitable. Secondly, pixels in medium spatial resolution images are often “mixed” in the sense that the spectral response is a combination of the response of “pure” elements.These two problems are addressed in this PhD. First, we propose a data assimilation technique able to recover consistent time series of Leaf Area Index from corrupted MODIS sequences. To this end, a plant growth model, namely GreenLab, is used as a dynamical constraint. Second, we propose a new and efficient unmixing technique for time series. It is in particular based on the use of “elastic” kernels able to properly compare time series shifted in time or of various lengths.Experimental results are shown both on synthetic and real data and demonstrate the efficiency of the proposed methodologies.Cette thèse s’intéresse à l’analyse de séries temporelles d’images satellites à moyenne résolution spatiale. L’intérêt principal de telles données est leur haute répétitivité qui autorise des analyses de l’usage des sols. Cependant, deux problèmes principaux subsistent avec de telles données. En premier lieu, en raison de la couverture nuageuse, des mauvaises conditions d’acquisition, ..., ces données sont souvent très bruitées. Deuxièmement, les pixels associés à la moyenne résolution spatiale sont souvent “mixtes” dans la mesure où leur réponse spectrale est une combinaison de la réponse de plusieurs éléments “purs”. Ces deux problèmes sont abordés dans cette thèse. Premièrement, nous proposons une technique d’assimilation de données capable de recouvrer des séries temporelles cohérentes de LAI (Leaf Area Index) à partir de séquences d’images MODIS bruitées. Pour cela, le modèle de croissance de plantes GreenLab estutilisé. En second lieu, nous proposons une technique originale de démélangeage, qui s’appuie notamment sur des noyaux “élastiques” capables de gérer les spécificités des séries temporelles (séries de taille différentes, décalées dans le temps, ...)Les résultats expérimentaux, sur des données synthétiques et réelles, montrent de bonnes performances des méthodologies proposées