Feature Selection for Linear SVM with Provable Guarantees

We give two provably accurate feature-selection techniques for the linear SVM. The algorithms run in deterministic and randomized time respectively. Our algorithms can be used in an unsupervised or supervised setting. The supervised approach is based on sampling features from support vectors. We prove that the margin in the feature space is preserved to within $\epsilon$-relative error of the margin in the full feature space in the worst-case. In the unsupervised setting, we also provide worst-case guarantees of the radius of the minimum enclosing ball, thereby ensuring comparable generalization as in the full feature space and resolving an open problem posed in Dasgupta et al. We present extensive experiments on real-world datasets to support our theory and to demonstrate that our method is competitive and often better than prior state-of-the-art, for which there are no known provable guarantees.Comment: Appearing in Proceedings of 18th AISTATS, JMLR W&CP, vol 38, 201

CanopyShotNoise - An individual-based tree canopy modelling framework for projecting remote-sensing data and ecological sensitivity analysis

Very few spatially explicit tree models have so far been constructed with a view to project remote-sensing data directly. To fill this gap, we introduced the prototype of the CanopyShotNoise model, an individual-based model specifically designed for projecting airborne laser scanning (ALS) data. Given the nature of ALS data, the model focuses on the dynamics of individual-tree canopies in forest ecosystems, that is, spatial tree interaction and resulting growth, birth and death processes. In this study, CanopyShotNoise was used to analyse the long-term effects of the processes crown plasticity (C) and superorganism formation (S) on spatial tree canopy patterns that are likely to play an important role in ongoing climate change. We designed a replicated computer experiment involving the four scenarios C0S0, C1S0, C0S1 and C1S1 where 0 and 1 imply that the preceding process was switched off and on, respectively. We hypothesized that C and S are antagonistic processes, specifically that C would lead to increasing regularity of tree locations and S would result in clustering. Our simulation results confirmed that in the long run intertree distances decreased and canopy gap size increased when superorganisms were encouraged to form. At the same time, the overlap and packing of tree crowns increased. The long-term effect of crown plasticity increased the regularity of tree locations; however, this effect was much weaker than that of superorganism formation. As a result, gap patterns remained more or less unaffected by crown plasticity. In scenario C1S1, both processes interestingly interacted in such a way that crown plasticity even increased the effect of superorganism formation. Our simulation results are likely to prove helpful in recognizing patterns of facilitation with ongoing climate change

Analysing gap dynamics in forest canopies with landscape metrics based on multi-temporal airborne laser scanning surveys - A pilot study

For a long time gaps or openings in the forest canopy have been of considerable interest to forest ecologists and to forest managers. In the context of disturbances induced by climate change, canopy gap dynamics are of particular interest, since they can indicate imminent damage to forest resources and irreversible trends such as forest decline. Here, statistical significance is crucial for establishing whether any imminent large-scale threat to the sustainability of forest resources exists. In order to be able to assess significance, we applied the Boolean model, a null or reference model from random set statistics. The Boolean model served as a theoretical benchmark for testing the significance of the observed trends in forest canopy gap dynamics. As a pilot study we analysed airborne laser scan (ALS) data collected in the Krycklan catchment area (Northern Sweden) in 2006 and 2015. The data were analysed using eight different landscape metrics. Despite the moderate resolution of our ALS data the landscape metrics have proved to be useful tools for monitoring canopy gap dynamics of forest ecosystems. The Boolean model has been successful in ascertaining statistical significance and the model parameters indi-cated important trends. In the Krycklan catchment area, there was no significant trend of canopy gap dynamics indicating any harmful development between 2006 and 2015. On the contrary, we found evidence for gaps closing in and gap locations becoming more random whilst the canopy cover increased between the two survey years

Evaluating the potential of ALS data to increase the efficiency of aboveground biomass estimates in tropical peat–swamp forests

Estimates of aboveground biomass (AGB) in forests are critically required by many actors including forest managers, forest services and policy makers. Because the AGB of a forest cannot be observed directly, models need to be employed. Allometric models that predict the AGB of a single tree as a function of diameter at breast height (DBH) are commonly used in forest inventories that use a probability selection scheme to estimate total AGB. However, for forest areas with limited accessibility, implementing such a field-based survey can be challenging. In such cases, models that use remotely sensed information may support the biomass assessment if useful predictor variables are available and statistically sound estimators can be derived. Airborne laser scanning (ALS) has become a prominent auxiliary data source for forest biomass assessments and is even considered to be one of the most promising technologies for AGB assessments in forests. In this study, we combined ALS and forest inventory data from a logged-over tropical peat swamp forest in Central Kalimantan, Indonesia to estimate total AGB. Our objective was to compare the precision of AGB estimates from two approaches: (i) from a field-based inventory only and, (ii) from an ALS-assisted approach where ALS and field inventory data were combined. We were particularly interested in analyzing whether the precision of AGB estimates can be improved by integrating ALS data under the particular conditions. For the inventory, we used a standard approach based on a systematic square sample grid. For building a biomass-link model that relates the field based AGB estimates to ALS derived metrics, we used a parametric nonlinear model. From the field-based approach, the estimated mean AGB was 241.38 Mgha −1 with a standard error of 11.17 Mgha −1 (SE% = 4.63%). Using the ALS-assisted approach, we estimated a similar mean AGB of 245.08 Mgha −1 with a slightly smaller standard error of 10.57 Mgha −1 (SE% = 4.30%). Altogether, this is an improvement of precision of estimation, even though the biomass-link model we found showed a large Root Mean Square Error (RMSE) of 47.43 Mgha −1 . We conclude that ALS data can support the estimation of AGB in logged-over tropical peat swamp forests even if the model quality is relatively low. A modest increase in precision of estimation (from 4.6% to 4.3%), as we found it in our study area, will be welcomed by all forest inventory planners as long as ALS data and analysis expertise are available at low or no cost. Otherwise, it gives rise to a challenging economic question, namely whether the cost of the acquisition of ALS data is reasonable in light of the actual increase in precisionWe are grateful to the Galician Government and European Social Fund (Official Journal of Galicia DOG n 52, 17 March 2014, p. 11343, exp: POS-A/2013/049) for financing the postdoctoral research stays of Eduardo González-Ferreiro at different institutionsS

The Horizontal Distribution of Branch Biomass in European Beech: A Model Based on Measurements and TLS Based Proxies

Forest biomass is currently among the most important and most researched target variables in forest monitoring. The common approach of observing individual tree biomass in forest inventory is to assign the total tree biomass to the dimensionless point of the tree position. However, the tree biomass, in particular in the crown, is horizontally distributed above the crown projection area. This horizontal distribution of individual tree biomass (HBD) has not attracted much attention—but if quantified, it can improve biomass estimation and help to better represent the spatial distribution of forest fuel. In this study, we derive a first empirical model of the branch HBD for individual trees of European beech (Fagus sylvatica L.). We destructively measured 23 beech trees to derive an empirical model for the branch HBD. We then applied Terrestrial Laser Scanning (TLS) to a subset of 17 trees to test a simple point cloud metric predicting the branch HBD. We observed similarities between a branch HBD and commonly applied taper functions, which inspired our HBD model formulations. The models performed well in representing the HBD both for the measured biomass, and the TLS-based metric. Our models may be used as first approximations to the HBD of individual trees—while our methodological approach may extend to trees of different sizes and speciesThis research was funded by the Forest Research Institute of the German Federal State of Rheinland-Pfalz (FAWF) in Trippstadt. We also thank the Marie Sklodowska-Curie Action fellow QUAFORD and the Ramón y Cajal Tenure Track awarded to C.P.-CS

Understanding forest health with Remote sensing-Part II-A review of approaches and data models

Stress in forest ecosystems (FES) occurs as a result of land-use intensification, disturbances, resource limitations or unsustainable management, causing changes in forest health (FH) at various scales from the local to the global scale. Reactions to such stress depend on the phylogeny of forest species or communities and the characteristics of their impacting drivers and processes. There are many approaches to monitor indicators of FH using in-situ forest inventory and experimental studies, but they are generally limited to sample points or small areas, as well as being time- and labour-inte

Correction to: A Range of Earth Observation Techniques for Assessing Plant Diversity

The original version of this book was inadvertently published with an incorrect affiliation