Comments and CorrectionsConvergence Analysis on Trace Ratio Linear Discriminant Analysis Algorithms.

Linear discriminant analysis (LDA) may yield an inexact solution by transforming a trace ratio problem into a corresponding ratio trace problem. Most recently, optimal dimensionality LDA (ODLDA) and trace ratio LDA (TRLDA) have been developed to overcome this problem. As one of the greatest contributions, the two methods design efficient iterative algorithms to derive an optimal solution. However, the theoretical evidence for the convergence of these algorithms has not yet been provided, which renders the theory of ODLDA and TRLDA incomplete. In this correspondence, we present some rigorously theoretical insight into the convergence of the iterative algorithms. To be specific, we first demonstrate the existence of lower bounds for the objective functions in both ODLDA and TRLDA, and then establish proofs that the objective functions are monotonically decreasing under the iterative frameworks. Based on the findings, we disclose the convergence of the iterative algorithms finally.

Modelling the effects of topographic heterogeneity on distribution of Nitraria tangutorum Bobr. species in deserts using LiDAR-data.

Microclimate ecology is attracting renewed attention because of its fundamental importance in understanding how organisms respond to climate change. Many hot issues can be investigated in desert ecosystems, including the relationship between species distribution and environmental gradients (e.g., elevation, slope, topographic convergence index, and solar insolation). Species Distribution Models (SDMs) can be used to understand these relationships. We used data acquired from the important desert plant Nitraria tangutorum Bobr. communities and desert topographic factors extracted from LiDAR (Light Detection and Ranging) data of one square kilometer in the inner Mongolia region of China to develop SDMs. We evaluated the performance of SDMs developed with a variety of both the parametric and nonparametric algorithms (Bioclimatic Modelling (BIOCLIM), Domain, Mahalanobi, Generalized Linear Model, Generalized Additive Model, Random Forest (RF), and Support Vector Machine). The area under the receiver operating characteristic curve was used to evaluate these algorithms. The SDMs developed with RF showed the best performance based on the area under curve (0.7733). We also produced the Nitraria tangutorum Bobr. distribution maps with the best SDM and suitable habitat area of the Domain model. Based on the suitability map, we conclude that Nitraria tangutorum Bobr. is more suited to southern part with 0-20 degree slopes at an elevation of approximately 1010 m. This is the first attempt of modelling the effects of topographic heterogeneity on the desert species distribution on a small scale. The presented SDMs can have important applications for predicting species distribution and will be useful for preparing conservation and management strategies for desert ecosystems on a small scale.

Video Moment Retrieval With Noisy Labels.

Video moment retrieval (VMR) aims to localize the target moment in an untrimmed video according to the given nature language query. The existing algorithms typically rely on clean annotations to train their models. However, making annotations by human labors may introduce much noise. Thus, the video moment retrieval models will not be well trained in practice. In this article, we present a simple yet effective video moment retrieval framework via bottom-up schema, which is in end-to-end manners and robust to noisy label training. Specifically, we extract the multimodal features by syntactic graph convolutional networks and multihead attention layers, which are fused by the cross gates and the bilinear approach. Then, the feature pyramid networks are constructed to encode plentiful scene relationships and capture high semantics. Furthermore, to mitigate the effects of noisy annotations, we devise the multilevel losses characterized by two levels: a frame-level loss that improves noise tolerance and an instance-level loss that reduces adverse effects of negative instances. For the frame level, we adopt the Gaussian smoothing to regard noisy labels as soft labels through the partial fitting. For the instance level, we exploit a pair of structurally identical models to let them teach each other during iterations. This leads to our proposed robust video moment retrieval model, which experimentally and significantly outperforms the state-of-the-art approaches on standard public datasets ActivityCaption and textually annotated cooking scene (TACoS). We also evaluate the proposed approach on the different manual annotation noises to further demonstrate the effectiveness of our model.

Integrating spaceborne LiDAR and Sentinel-2 images to estimate forest aboveground biomass in Northern China.

BACKGROUND: Fast and accurate forest aboveground biomass (AGB) estimation and mapping is the basic work of forest management and ecosystem dynamic investigation, which is of great significance to evaluate forest quality, resource assessment, and carbon cycle and management. The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2), as one of the latest launched spaceborne light detection and ranging (LiDAR) sensors, can penetrate the forest canopy and has the potential to obtain accurate forest vertical structure parameters on a large scale. However, the along-track segments of canopy height provided by ICESat-2 cannot be used to obtain comprehensive AGB spatial distribution. To make up for the deficiency of spaceborne LiDAR, the Sentinel-2 images provided by google earth engine (GEE) were used as the medium to integrate with ICESat-2 for continuous AGB mapping in our study. Ensemble learning can summarize the advantages of estimation models and achieve better estimation results. A stacking algorithm consisting of four non-parametric base models which are the backpropagation (BP) neural network, k-nearest neighbor (kNN), support vector machine (SVM), and random forest (RF) was proposed for AGB modeling and estimating in Saihanba forest farm, northern China. RESULTS: The results show that stacking achieved the best AGB estimation accuracy among the models, with an R2 of 0.71 and a root mean square error (RMSE) of 45.67 Mg/ha. The stacking resulted in the lowest estimation error with the decreases of RMSE by 22.6%, 27.7%, 23.4%, and 19.0% compared with those from the BP, kNN, SVM, and RF, respectively. CONCLUSION: Compared with using Sentinel-2 alone, the estimation errors of all models have been significantly reduced after adding the LiDAR variables of ICESat-2 in AGB estimation. The research demonstrated that ICESat-2 has the potential to improve the accuracy of AGB estimation and provides a reference for dynamic forest resources management and monitoring.

Learning Robust Discriminant Subspace Based on Joint L2,ₚ- and L2,ₛ-Norm Distance Metrics.

Recently, there are many works on discriminant analysis, which promote the robustness of models against outliers by using L1- or L2,1-norm as the distance metric. However, both of their robustness and discriminant power are limited. In this article, we present a new robust discriminant subspace (RDS) learning method for feature extraction, with an objective function formulated in a different form. To guarantee the subspace to be robust and discriminative, we measure the within-class distances based on [Formula: see text]-norm and use [Formula: see text]-norm to measure the between-class distances. This also makes our method include rotational invariance. Since the proposed model involves both [Formula: see text]-norm maximization and [Formula: see text]-norm minimization, it is very challenging to solve. To address this problem, we present an efficient nongreedy iterative algorithm. Besides, motivated by trace ratio criterion, a mechanism of automatically balancing the contributions of different terms in our objective is found. RDS is very flexible, as it can be extended to other existing feature extraction techniques. An in-depth theoretical analysis of the algorithm's convergence is presented in this article. Experiments are conducted on several typical databases for image classification, and the promising results indicate the effectiveness of RDS.

Multiview Learning With Robust Double-Sided Twin SVM.

Multiview learning (MVL), which enhances the learners' performance by coordinating complementarity and consistency among different views, has attracted much attention. The multiview generalized eigenvalue proximal support vector machine (MvGSVM) is a recently proposed effective binary classification method, which introduces the concept of MVL into the classical generalized eigenvalue proximal support vector machine (GEPSVM). However, this approach cannot guarantee good classification performance and robustness yet. In this article, we develop multiview robust double-sided twin SVM (MvRDTSVM) with SVM-type problems, which introduces a set of double-sided constraints into the proposed model to promote classification performance. To improve the robustness of MvRDTSVM against outliers, we take L1-norm as the distance metric. Also, a fast version of MvRDTSVM (called MvFRDTSVM) is further presented. The reformulated problems are complex, and solving them are very challenging. As one of the main contributions of this article, we design two effective iterative algorithms to optimize the proposed nonconvex problems and then conduct theoretical analysis on the algorithms. The experimental results verify the effectiveness of our proposed methods.

Improved multi-view GEPSVM via Inter-View Difference Maximization and Intra-view Agreement Minimization.

Multiview Generalized Eigenvalue Proximal Support Vector Machine (MvGEPSVM) is an effective method for multiview data classification proposed recently. However, it ignores discriminations between different views and the agreement of the same view. Moreover, there is no robustness guarantee. In this paper, we propose an improved multiview GEPSVM (IMvGEPSVM) method, which adds a multi-view regularization that can connect different views of the same class and simultaneously considers the maximization of the samples from different classes in heterogeneous views for promoting discriminations. This makes the classification more effective. In addition, L1-norm rather than squared L2-norm is employed to calculate the distances from each of the sample points to the hyperplane so as to reduce the effect of outliers in the proposed model. To solve the resulting objective, an efficient iterative algorithm is presented. Theoretically, we conduct the proof of the algorithm's convergence. Experimental results show the effectiveness of the proposed method.

Nonpeaked Discriminant Analysis for Data Representation.

Of late, there are many studies on the robust discriminant analysis, which adopt L1-norm as the distance metric, but their results are not robust enough to gain universal acceptance. To overcome this problem, the authors of this article present a nonpeaked discriminant analysis (NPDA) technique, in which cutting L1-norm is adopted as the distance metric. As this kind of norm can better eliminate heavy outliers in learning models, the proposed algorithm is expected to be stronger in performing feature extraction tasks for data representation than the existing robust discriminant analysis techniques, which are based on the L1-norm distance metric. The authors also present a comprehensive analysis to show that cutting L1-norm distance can be computed equally well, using the difference between two special convex functions. Against this background, an efficient iterative algorithm is designed for the optimization of the proposed objective. Theoretical proofs on the convergence of the algorithm are also presented. Theoretical insights and effectiveness of the proposed method are validated by experimental tests on several real data sets.

Robust auto-weighted projective low-rank and sparse recovery for visual representation.

Most existing low-rank and sparse representation models cannot preserve the local manifold structures of samples adaptively, or separate the locality preservation from the coding process, which may result in the decreased performance. In this paper, we propose an inductive Robust Auto-weighted Low-Rank and Sparse Representation (RALSR) framework by joint feature embedding for the salient feature extraction of high-dimensional data. Technically, the model of our RALSR seamlessly integrates the joint low-rank and sparse recovery with robust salient feature extraction. Specifically, RALSR integrates the adaptive locality preserving weighting, joint low-rank/sparse representation and the robustness-promoting representation into a unified model. For accurate similarity measure, RALSR computes the adaptive weights by minimizing the joint reconstruction errors over the recovered clean data and salient features simultaneously, where L1-norm is also applied to ensure the sparse properties of learnt weights. The joint minimization can also potentially enable the weight matrix to have the power to remove noise and unfavorable features by reconstruction adaptively. The underlying projection is encoded by a joint low-rank and sparse regularization, which can ensure it to be powerful for salient feature extraction. Thus, the calculated low-rank sparse features of high-dimensional data would be more accurate for the subsequent classification. Visual and numerical comparison results demonstrate the effectiveness of our RALSR for data representation and classification.

Flexible non-greedy discriminant subspace feature extraction.

Recently, L1-norm-based non-greedy linear discriminant analysis (NLDA-L1) for feature extraction has been shown to be effective for dimensionality reduction, which obtains projection vectors by a non-greedy algorithm. However, it usually acquires unsatisfactory performances due to the utilization of L1-norm distance measurement. Therefore, in this brief paper, we propose a flexible non-greedy discriminant subspace feature extraction method, which is an extension of NLDA-L1 by maximizing the ratio of Lp-norm inter-class dispersion to intra-class dispersion. Besides, we put forward a powerful iterative algorithm to solve the resulted objective function and also conduct theoretical analysis on the algorithm. Finally, experimental results on image databases show the effectiveness of our method.

Robust capped L1-norm twin support vector machine.

Twin support vector machine (TWSVM) is a classical and effective classifier for binary classification. However, its robustness cannot be guaranteed due to the utilization of squared L2-norm distance that can usually exaggerate the influence of outliers. In this paper, we propose a new robust capped L1-norm twin support vector machine (CTWSVM), which sustains the advantages of TWSVM and promotes the robustness in solving a binary classification problem with outliers. The solution of the proposed method can be achieved by optimizing a pair of capped L1-norm related problems using a newly-designed effective iterative algorithm. Also, we present some theoretical analysis on existence of local optimum and convergence of the algorithm. Extensive experiments on an artificial dataset and several UCI datasets demonstrate the robustness and feasibility of our proposed CTWSVM.

Development of novel EST-SSR markers for Phyllanthus emblica (Phyllanthaceae) and cross-amplification in two related species.

PREMISE OF THE STUDY: A novel set of EST-SSR markers was developed for Phyllanthus emblica (Phyllanthaceae) to investigate the genetic structure and gene flow, identify novel genes of interest, and develop markers for assisted breeding. METHODS AND RESULTS: Based on the transcriptome data of P. emblica, 83 EST-SSR primer pairs were designed; 52 primer pairs were successfully amplified, with 20 showing polymorphisms in 90 individuals from three populations of P. emblica. The number of alleles per locus varied from 11 to 44. The observed and expected levels of heterozygosity for the 20 loci ranged from 0.240 to 0.868 and 0.754 to 0.933, respectively. Cross-species amplification was successful for all 20 loci in each of the two related species, P. reticulatus and Leptopus chinensis. CONCLUSIONS: These markers will be valuable for studying the population genetics and for mining genes of P. emblica, and may be useful for studies of related species.

Lp- and Ls-Norm Distance Based Robust Linear Discriminant Analysis.

Recently, L1-norm distance measure based Linear Discriminant Analysis (LDA) techniques have been shown to be robust against outliers. However, these methods have no guarantee of obtaining a satisfactory-enough performance due to the insufficient robustness of L1-norm measure. To mitigate this problem, inspired by recent works on Lp-norm based learning, this paper proposes a new discriminant method, called Lp- and Ls-Norm Distance Based Robust Linear Discriminant Analysis (FLDA-Lsp). The proposed method achieves robustness by replacing the L2-norm within- and between-class distances in conventional LDA with Lp- and Ls-norm ones. By specifying the values of p and s, many of previous efforts can be naturally expressed by our objective. The requirement of simultaneously maximizing and minimizing a number of Lp- and Ls-norm terms results in a difficulty to the optimization of the formulated objective. As one of the important contributions of this paper, we design an efficient iterative algorithm to address this problem, and also conduct some insightful analysis on the existence of local minimum and the convergence of the proposed algorithm. Theoretical insights of our method are further supported by promising experimental results on several images databases.

Study on Reproductive Biology of Rhododendron longipedicellatum: A Newly Discovered and Special Threatened Plant Surviving in Limestone Habitat in Southeast Yunnan, China.

Rhododendron longipedicellatum is a narrow endemic species and a subject of urgent demand in the domestic market and overseas. Its fascinating shapes, brilliantly gilvous flowers, and unusual flowering time endow this species with extremely high ornamental value. However, only five wild populations of R. longipedicellatum surviving in limestone habitat have been found through elaborate field investigation, and the number of the populations decreases further or is even confronted with risk of extinction due to the damage of human activities. To enhance the protection and utilization of R. longipedicellatum, this study systematically investigated several important aspects of reproductive biology, including floral syndrome, pollen viability and stigma receptivity, petal color reflectance, breeding system, and pollination biology. The results demonstrated that arched styles not only create obvious herkogamy that avoide self-pollination, but also effectively reduce rain damage to the intrinsic characteristics of the stigma surface secretions, promoting the female fitness of R. longipedicellatum in poor weather. Pollen viability maintained a high level over the flowering period. The reflectance spectrum of petals had two peaks at wavelengths of 360 and 580 nm. Tests of OCI, P/O and artificial pollination all indicated that R. longipedicellatum was self-compatible and that the breeding system was mixed mating. Geitonogamy mediated by Bombus braccatus was the primary pollination route in the natural environment, which suggested that the breeding system of R. longipedicellatum might be evolving from selfing to outcrossing. The pollination vector of R. longipedicellatum was very specific, in that only B. braccatus was confirmed to deliver pollen to the stigmas. Visitation frequency was influenced by the activity rhythms and resource requirements of the different castes (i.e., sex). B. braccatus workers were the most effective pollinators because of higher visitation frequency and more effective contribution to fruit production, whereas the presence of B. braccatus males might enhance pollen flow within the population to a certain extent. Finally, these findings not only provided a reliable theoretical basis for hybridization breeding of R. longipedicellatum as parents, but also laid a solid foundation for further molecular biology studies to more broadly reveal the mechanisms of its endangerment in the future.

How trees allocate carbon for optimal growth: insight from a game-theoretic model.

How trees allocate photosynthetic products to primary height growth and secondary radial growth reflects their capacity to best use environmental resources. Despite substantial efforts to explore tree height-diameter relationship empirically and through theoretical modeling, our understanding of the biological mechanisms that govern this phenomenon is still limited. By thinking of stem woody biomass production as an ecological system of apical and lateral growth components, we implement game theory to model and discern how these two components cooperate symbiotically with each other or compete for resources to determine the size of a tree stem. This resulting allometry game theory is further embedded within a genetic mapping and association paradigm, allowing the genetic loci mediating the carbon allocation of stemwood growth to be characterized and mapped throughout the genome. Allometry game theory was validated by analyzing a mapping data of stem height and diameter growth over perennial seasons in a poplar tree. Several key quantitative trait loci were found to interpret the process and pattern of stemwood growth through regulating the ecological interactions of stem apical and lateral growth. The application of allometry game theory enables the prediction of the situations in which the cooperation, competition or altruism is an optimal decision of a tree to fully use the environmental resources it owns.

Soil respiration and its environmental response varies by day/night and by growing/dormant season in a subalpine forest.

Comparisons of soil respiration (RS) and its components of heterotrophic (RH) and rhizospheric (RR) respiration during daytime and nighttime, growing (GS) and dormant season (DS), have not being well studied and documented. In this study, we compared RS, RH, RR, and their responses to soil temperature (T5) and moisture (θ5) in daytime vs. nighttime and GS vs. DS in a subalpine forest in 2011. In GS, nighttime RS and RH rates were 30.5 ± 4.4% (mean ± SE) and 30.2 ± 6.5% lower than in daytime, while in DS, they were 35.5 ± 5.5% and 37.3 ± 8.5% lower, respectively. DS RS and RH accounted for 27.3 ± 2.5% and 27.6 ± 2.6% of GS RS and RH, respectively. The temperature sensitivities (Q10) of RS and RH were higher in nighttime than daytime, and in DS than GS, while they all decreased with increase of T5. Soil C fluxes were more responsive to θ5 in nighttime than daytime, and in DS than GS. Our results suggest that the DS and nighttime RS play an important role in regulating carbon cycle and its response to climate change in alpine forests, and therefore, they should be taken into consideration in order to make accurate predictions of RS and ecosystem carbon cycle under climate change scenarios.

Multilevel Nonlinear Mixed-Effect Crown Ratio Models for Individual Trees of Mongolian Oak (Quercus mongolica) in Northeast China.

In this study, an individual tree crown ratio (CR) model was developed with a data set from a total of 3134 Mongolian oak (Quercus mongolica) trees within 112 sample plots allocated in Wangqing Forest Bureau of northeast China. Because of high correlation among the observations taken from the same sampling plots, the random effects at levels of both blocks defined as stands that have different site conditions and plots were taken into account to develop a nested two-level nonlinear mixed-effect model. Various stand and tree characteristics were assessed to explore their contributions to improvement of model prediction. Diameter at breast height, plot dominant tree height and plot dominant tree diameter were found to be significant predictors. Exponential model with plot dominant tree height as a predictor had a stronger ability to account for the heteroskedasticity. When random effects were modeled at block level alone, the correlations among the residuals remained significant. These correlations were successfully reduced when random effects were modeled at both block and plot levels. The random effects from the interaction of blocks and sample plots on tree CR were substantially large. The model that took into account both the block effect and the interaction of blocks and sample plots had higher prediction accuracy than the one with the block effect and population average considered alone. Introducing stand density into the model through dummy variables could further improve its prediction. This implied that the developed method for developing tree CR models of Mongolian oak is promising and can be applied to similar studies for other tree species.