Parmi les techniques usuelles de fouille de données, peu sont celles capables de tirer avantage de la complémentarité des dimensions pour des données sous forme de tableaux à plusieurs dimensions. A l'inverse les techniques de décomposition tensorielle recherchent spécifiquement les processus sous-jacents aux données, qui permettent d'expliquer les données dans toutes les dimensions. Les travaux rapportés dans ce manuscrit traitent de l'amélioration de l'interprétation des résultats de la décomposition tensorielle canonique polyadique par l'ajout de connaissances externes au modèle de décomposition, qui est par définition un modèle aveugle n'utilisant pas la connaissance du problème physique sous-jacent aux données. Les deux premiers chapitres de ce manuscrit présentent respectivement les aspects mathématiques et appliqués des méthodes de décomposition tensorielle. Dans le troisième chapitre, les multiples facettes des décompositions sous contraintes sont explorées à travers un formalisme unifié. Les thématiques abordées comprennent les algorithmes de décomposition, la compression de tenseurs et la décomposition tensorielle basée sur les dictionnaires. Le quatrième et dernier chapitre présente le problème de la modélisation d'une variabilité intra-sujet et inter-sujet au sein d'un modèle de décomposition contraint. L'état de l'art en la matière est tout d'abord présenté comme un cas particulier d'un modèle flexible de couplage de décomposition développé par la suite. Le chapitre se termine par une discussion sur la réduction de dimension et quelques problèmes ouverts dans le contexte de modélisation de variabilité sujet. / Among commonly used data mining techniques, few are those which are able to take advantage of the multiway structure of data in the form of a multiway array. In contrast, tensor decomposition techniques specifically look intricate processes underlying the data, where each of these processes can be used to describe all ways of the data array. The work reported in the following pages aims at incorporating various external knowledge into the tensor canonical polyadic decomposition, which is usually understood as a blind model. The first two chapters of this manuscript introduce tensor decomposition techniques making use respectively of a mathematical and application framework. In the third chapter, the many faces of constrained decompositions are explored, including a unifying framework for constrained decomposition, some decomposition algorithms, compression and dictionary-based tensor decomposition. The fourth chapter discusses the inclusion of subject variability modeling when multiple arrays of data are available stemming from one or multiple subjects sharing similarities. State of the art techniques are studied and expressed as particular cases of a more general flexible coupling model later introduced. The chapter ends on a discussion on dimensionality reduction when subject variability is involved, as well a some open problems.

Although much emphasis has been given to the analysis of continuous forest conversion in tropical regions, our understanding in detecting, mapping and interpreting the spatial pattern of woodland deforestation and degradation is still limited. This thesis focuses on two factors contributing to this limitation: uncertainties in retrieving woodland change from remote sensing imagery, and the complex processes that may cause woodland deforestation and degradation. Firstly, I investigate approaches to minimising uncertainty in ALOS PALSAR-derived biomass maps by modifying a widely used processing chain, with the aim of provide recommendations for producing radar-based biomass maps with reduced uncertainty. Secondly, to further improve the retrieval of woody biomass from ALOS PALSAR imagery, the semi-empirical Water Cloud Model (WCM) is introduced to account for backscattering from soil. In wooded areas with low canopy (such as the miombo woodland which dominates the study area) the effect from soil moisture on the received backscattered signal is critical. Thirdly, based on the biomass maps retrieved from the refined radar-remote-sensing-based methodology discussed above, the influence of driving variables of the woodland deforestation and degradation, and how they alter the spatial patterns of these two processes, are analysed. The threshold for defining woodland deforestation and degradation in terms of biomass loss intensity is generated through integration of radar-based biomass loss maps, an optical forest cover change map and fieldwork investigation. Multi-linear model simulations of the spatial variation of deforestation and degradation events were constructed at a district and 1 km resolution respectively to rank the relative importance of driving variables. Results suggest that biomass-backscatter relationships based on plots of approximately 1 ha, and processed with high resolution DEMs, are needed for low uncertainty biomass maps using ALOS PALSAR data. Although plots sizes of 0.1 - 0.5 ha lead to large uncertainties, aggregating 0.1 ha plots into larger calibration sites shows some promise even in hilly terrain, potentially opening up the use of common forest inventory data to calibrate remote-sensing-based biomass retrieval models. Such relationships appear to hold across the miombo woodland ecoregion, which implies that there is a consistent relationship at least in the miombo woodland. From this I infer that random error, different processing methods and fitting techniques, and data from small plots are the source of the differences in the savanna biomass-backscatter relationships seen in the literature. The interpreted WCM presented in this study for L-band backscatter at HV polarisation improves biomass retrieval for areas with a biomass value less than 15 tC/ha (or 0.025 m2/m2 in backscatter). Use of the WCM also results in better quality regional biomass mosaics. This is because the WCM helped to improve the correlation of biomass estimation for overlay areas by reducing bias between adjacent paths, especially the bias introduced by changes in soil moisture conditions between different acquisition dates for different paths. Result shows that active and combined soil moisture datasets (from the Climate Change Initiative Soil Moisture Dataset) can be used as effective soil moisture proxies in the WCM for biomass retrieval. This quantitative analysis on the driving variables of woodland deforestation and degradation suggests that large uncertainty exists in modelling the occurrence of deforestation and degradation, especially at a 1 km scale. The spatial patterns of woodland deforestation and degradation differ in terms of shape, size, intensity, and location. Agriculture-related driving variables account for most of the explained variance in deforestation, whereas for degradation, distance to settlements also plays an important role. Deforestation happens regardless of the original biomass levels, while degradation is likely to happen at high biomass areas. The sizes of degradation events are significantly smaller than those of deforestation events, with 90% of deforestation events sharing boundaries with degradation events. This thesis concludes by outlining the importance and difficulties in integrating 'distal' (underlying) drivers in modelling the spatial dynamics of deforestation and degradation. Further work on the causal connection between deforestation and degradation is also needed. The processing chain and biomass retrieval models presented in this study could be used to support monitoring and analysis of biomass change elsewhere in the tropics, and should be compatible with data derived from ALOS-2 and the future SAOCOM and BIOMASS satellite missions.