Decomposition of vegetation cover into woody and herbaceous components using AVHRR NDVI time series

A method is developed to separate Normalised Difference Vegetation Index (NDVI) time series data into contributions from woody (perennial) and herbaceous (annual) vegetation, and thereby to infer their separate leaf area indices and cover fractions. The method is formally consistent with fundamental linearity requirements for such a decomposition, and is capable of rejecting contaminated NDVI data. In this study, estimates of annual averaged woody cover and monthly averaged herbaceous cover over Australia are determined using Pathfinder AVHRR Land series (PAL) Global Area Coverage (GAC) Advanced Very High Resolution Radiometer (AVHRR) NDVI data from 1981 to 1994, together with ground-based measurements of leaf area index (LAI) and foliage projective cover (FPC).     

Estimating spatio-temporal patterns of agricultural productivity in fragmented landscapes using AVHRR NDVI time series

The characteristics of Normalized Difference Vegetation Index (NDVI) time series can be disaggregated into a set of quantitative metrics that may be used to derive information about vegetation phenology and land cover. In this paper, we examine the patterns observed in metrics calculated for a time series of 8 years over the southwest of Western Australia—an important crop and animal production area of Australia. Four analytical approaches were used; calculation of temporal mean and standard deviation layers for selected metrics showing significant spatial variability; classification based on temporal and spatial patterns of key NDVI metrics; metrics were analyzed for eight areas typical of climatic and production systems across the agricultural zone; and relationships between total production and productivity measured by dry sheep equivalents were developed with time integrated NDVI (TINDVI). Two metrics showed clear spatial patterns; the season duration based on the smooth curve produced seven zones based on increasing length of growing season; and TINDVI provided a set of classes characterized by differences in overall magnitude of response, and differences in response in particular years. Frequency histograms of TINDVI could be grouped on the basis of a simple shape classification: tall and narrow with high, medium or low mean indicating most land is responsive agricultural cover with uniform seasonal conditions; broad and short indicating that land is of mixed cover type or seasonal conditions are not spatially uniform. TINDVI showed a relationship to agricultural productivity that is dependent on the extent to which crop or total agricultural production was directly reduced by rainfall deficiency. TINDVI proved most sensitive to crop productivity for Statistical Local Areas (SLAs) having rainfall less than 600 mm, and in years when rainfall and crop production were highly correlated. It is concluded that metrics from standardized NDVI time series could be routinely and transparently used for retrospective assessment of seasonal conditions and changes in vegetation responses and cover.     

A curve fitting procedure to derive inter-annual phenologies from time series of noisy satellite NDVI data

Annual, inter-annual and long-term trends in time series derived from remote sensing can be used to distinguish between natural land cover variability and land cover change. However, the utility of using NDVI-derived phenology to detect change is often limited by poor quality data resulting from atmospheric and other effects. Here, we present a curve fitting methodology useful for time series of remotely sensed data that is minimally affected by atmospheric and sensor effects and requires neither spatial nor temporal averaging. A two-step technique is employed: first, a harmonic approach models the average annual phenology; second, a spline-based approach models inter-annual phenology. The principal attributes of the time series (e.g., amplitude, timing of onset of greenness, intrinsic smoothness or roughness) are captured while the effects of data drop-outs and gaps are minimized. A recursive, least squares approach captures the upper envelope of NDVI values by upweighting data values above an average annual curve. We test this methodology on several land cover types in the western U.S., and find that onset of greenness in an average year varied by less than 8 days within land cover types, indicating that the curve fit is consistent within similar systems. Between 1990 and 2002, temporal variability in onset of greenness was between 17 and 35 days depending on the land cover type, indicating that the inter-annual curve fit captures substantial inter-annual variability. Employing this curve fitting procedure enhances our ability to measure inter-annual phenology and could lead to better understanding of local and regional land cover trends.     

A hybrid modular neural network architecture with fuzzy Sugeno integration for time series forecasting

We describe in this paper the application of a modular neural network architecture to the problem of simulating and predicting the dynamic behavior of complex economic time series. We use several neural network models and training algorithms to compare the results and decide at the end, which one is best for this application. We also compare the simulation results with the traditional approach of using a statistical model. In this case, we use real time series of prices of consumer goods to test our models. Real prices of tomato in the U.S. show complex fluctuations in time and are very complicated to predict with traditional statistical approaches. For this reason, we have chosen a neural network approach to simulate and predict the evolution of these prices in the U.S. market.     

Univariate modeling and forecasting of monthly energy demand time series using abductive and neural networks

Neural networks have been widely used for short-term, and to a lesser degree medium and long-term, demand forecasting. In the majority of cases for the latter two applications, multivariate modeling was adopted, where the demand time series is related to other weather, socio-economic and demographic time series. Disadvantages of this approach include the fact that influential exogenous factors are difficult to determine, and accurate data for them may not be readily available. This paper uses univariate modeling of the monthly demand time series based only on data for 6 years to forecast the demand for the seventh year. Both neural and abductive networks were used for modeling, and their performance was compared. A simple technique is described for removing the upward growth trend prior to modeling the demand time series to avoid problems associated with extrapolating beyond the data range used for training. Two modeling approaches were investigated and compared: iteratively using a single next-month forecaster, and employing 12 dedicated models to forecast the 12 individual months directly. Results indicate better performance by the first approach, with mean percentage error (MAPE) of the order of 3% for abductive networks. Performance is superior to naı¨ve forecasts based on persistence and seasonality, and is better than results quoted in the literature for several similar applications using multivariate abductive modeling, multiple regression, and univariate ARIMA analysis. Automatic selection of only the most relevant model inputs by the abductive learning algorithm provides better insight into the modeled process and allows constructing simpler neural network models with reduced data dimensionality and improved forecasting performance.     

Selection of significant input variables for time series forecasting

Appropriate selection of inputs for time series forecasting models is important because it not only has the potential to improve performance of forecasting models, but also helps reducing cost in data collection. This paper presents an investigation of selection performance of three input selection techniques, which include two model-free techniques, partial linear correlation (PLC) and partial mutual information (PMI) and a model-based technique based on genetic programming (GP). Four hypothetical datasets and two real datasets were used to demonstrate the performance of the three techniques. The results suggested that the model-free PLC technique due to its computational simplicity and the model-based GP technique due to its ability to detect non-linear relationships (demonstrated by its relatively good performance on a hypothetical complex non-linear dataset) are recommended for the input selection task. Candidate inputs which are selected by both these recommended techniques should be considered as significant inputs.     

A spatio-temporal decomposition based deep neural network for time series forecasting

Spatio-temporal problems arise in a broad range of applications, such as climate science and transportation systems. These problems are challenging because of unique spatial, short-term and long-term patterns, as well as the curse of dimensionality. In this paper, we propose a deep learning framework for spatio-temporal forecasting problems. We explicitly design the neural network architecture for capturing various types of spatial and temporal patterns, and the model is robust to missing data. In a preprocessing step, a time series decomposition method is applied to separately feed short-term, long-term and spatial patterns into different components of the neural network. A fuzzy clustering method finds clusters of neighboring time series residuals, as these contain short-term spatial patterns. The first component of the neural network consists of multi-kernel convolutional layers which are designed to extract short-term features from clusters of time series data. Each convolutional kernel receives a single cluster of input time series. The output of convolutional layers is concatenated by trends and followed by convolutional-LSTM layers to capture long-term spatial patterns. To have a robust forecasting model when faced with missing data, a pretrained denoising autoencoder reconstructs the model’s output in a fine-tuning step. In experimental results, we evaluate the performance of the proposed model for the traffic flow prediction. The results show that the proposed model outperforms baseline and state-of-the-art neural network models.     

Reducing error in neural network time series forecasting

Neural network time series forecasting error comprises autocorrelation error, due to an imperfect model, and random noise, inherent in the data. Both problems are addressed here, the first using a two stage training, growth-network neuron: the autocorrelation error (ACE) neuron. The second is considered as a post-processing noise filtering problem. These techniques are applied in forecasting the sunspot time series, with comparison of stochastic, BFGS and conjugate gradient solvers.     

Image data compression using autoregressive time series models

A two-dimensional image model is formulated using a seasonal autoregressive time series. With appropriate use of initial conditions, the method of least squares is used to obtain estimates of the model parameters. The model is then used to regenerate the original image. Results obtained indicate this method could be used to code textures for low bit rates or be used in an application of generating compressed background scenes. A differential pulse code modulation (DPCM) scheme is also demonstrated as a means of archival storage of images along with a new quantization technique for DPCM. This quantization technique is compared with standard quantization methods.     

Recursive prediction for long term time series forecasting using advanced models

There exists a wide range of paradigms, and a high number of different methodologies that are applied to the problem of time series prediction. Most of them are presented as a modified function approximation problem using input/output data, in which the input data are expanded using values of the series at previous steps. Thus, the model obtained normally predicts the value of the series at a time (t+h) using previous time steps (t-τ₁),(t-τ₂),…,(t-τ_n). Nevertheless, learning a model for long term time series prediction might be seen as a more complicated task, since it might use its own outputs as inputs for long term prediction (recursive prediction). This paper presents the utility of two different methodologies, the TaSe fuzzy TSK model and the least-squares SVMs, to solve the problem of long term time series prediction using recursive prediction. This work also introduces some techniques that upgrade the performance of those advanced one-step-ahead models (and in general of any one-step-ahead model), where they are used recursively for long term time series prediction.     

Vegetation dynamics from NDVI time series analysis using the wavelet transform

A multi-resolution analysis (MRA) based on the wavelet transform (WT) has been implemented to study NDVI time series. These series, which are non-stationary and present short-term, seasonal and long-term variations, can be decomposed using this MRA as a sum of series associated with different temporal scales. The main focus of the paper is to check the potential of this MRA to capture and describe both intra- and inter-annual changes in the data, i.e., to discuss the ability of the proposed procedure to monitor vegetation dynamics at regional scale. Our approach concentrates on what wavelet analysis can tell us about a NDVI time series. On the one hand, the intra-annual series, linked to the seasonality, has been used to estimate different key features related to the vegetation phenology, which depend on the vegetation cover type. On the other hand, the inter-annual series has been used to identify the trend, which is related to land-cover changes, and a Mann-Kendall test has been applied to confirm the significance of the observed trends. NDVI images from the MEDOKADS (Mediterranean Extended Daily One-km AVHRR Data Set) imagery series over Spain are processed according to a per-pixel strategy for this study. Results show that the wavelet analysis provides relevant information about vegetation dynamics at regional scale, such as the mean and minimum NDVI value, the amplitude of the phenological cycle, the timing of the maximum NDVI and the magnitude of the land-cover change. The latter, in combination with precipitation data, has been used to interpret the observed land-cover changes and identify those subtle changes associated to land degradation.     

间歇性时间序列的可预测性评估及联合预测方法

在高端制造企业的运维业务中,配件需求随机发生,且伴随有大量的零需求阶段,同时,对应的配件需求数据量小,且呈现出间歇性和块状分布的特点,导致现有时间序列预测方法难以有效预测配件需求走势。为解决该问题,提出了一种间歇性时间序列的可预测性评估及联合预测方法。首先,提出了一种新的间歇相似度指标,通过统计两条序列中“0”元素出现的频次和位置,并结合最大信息系数和平均需求间隔等度量指标,有效评估了序列的趋势信息和波动规律,并实现了对间歇性序列可预测性的量化;其次,基于该指标,构建了一个间歇相似度层次聚类方法来自适应地筛选相似性高、可预测性强的序列,剔除极度稀疏、无法预测的序列;此外,探索利用序列间的结构化信息,并构建多输出支持向量回归（M-SVR）模型,从而实现小样本下的间歇性序列联合预测;最后,分别在两个公开数据集（UCI礼品零售数据集和华为电脑配件数据集）和某大型制造企业实际配件售后数据集上进行实验。实验结果表明,相比多个典型的时间序列预测方法,所提方法可有效挖掘各类间歇性序列的可预测性,提高小样本间歇性序列的预测精度,从而为制造企业配件需求预测提供了一种新的解决方案。     

Combining medium and coarse spatial resolution satellite data to improve the estimation of sub-pixel NDVI time series

The potential of multitemporal coarse spatial resolution remotely sensed images for vegetation monitoring is reduced in fragmented landscapes, where most of the pixels are composed of a mixture of different surfaces. Several approaches have been proposed for the estimation of reflectance or NDVI values of the different land-cover classes included in a low resolution mixed pixel. In this paper, we propose a novel approach for the estimation of sub-pixel NDVI values from multitemporal coarse resolution satellite data. Sub-pixel NDVIs for the different land-cover classes are calculated by solving a weighted linear system of equations for each pixel of a coarse resolution image, exploiting information about within-pixel fractional cover derived from a high resolution land-use map. The weights assigned to the different pixels of the image for the estimation of sub-pixel NDVIs of a target pixel i are calculated taking into account both the spatial distance between each pixel and the target and their spectral dissimilarity estimated on medium-resolution remote-sensing images acquired in different periods of the year. The algorithm was applied to daily and 16-day composite MODIS NDVI images, using Landsat-5 TM images for calculation of weights and accuracy evaluation.Results showed that application of the algorithm provided good estimates of sub-pixel NDVIs even for poorly represented land-cover classes (i.e., with a low total cover in the test area). No significant accuracy differences were found between results obtained on daily and composite MODIS images. The main advantage of the proposed technique with respect to others is that the inclusion of the spectral term in weight calculation allows an accurate estimate of sub-pixel NDVI time series even for land-cover classes characterized by large and rapid spatial variations in their spectral properties.     

Short-term time series forecasting based on the identification of skeleton algebraic sequences

A new short-term time series forecasting method based on the identification of skeleton algebraic sequences is proposed in this paper. The concept of the rank of the Hankel matrix is exploited to detect a base fragment of the time series. Particle swarm optimization and evolutionary algorithms are then used to remove the noise and identify the skeleton algebraic sequence. Numerical experiments with an artificially generated and a real-world time series are used to illustrate the functionality of the proposed method.     

A neural network ensemble method with jittered training data for time series forecasting

Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing decision makers in many areas. Combining multiple models can be an effective way to improve forecasting performance. Recently, considerable research has been taken in neural network ensembles. Most of the work, however, is devoted to the classification type of problems. As time series problems are often more difficult to model due to issues such as autocorrelation and single realization at any particular time point, more research is needed in this area.In this paper, we propose a jittered ensemble method for time series forecasting and test its effectiveness with both simulated and real time series. The central idea of the jittered ensemble is adding noises to the input data and thus augments the original training data set to form models based on different but related training samples. Our results show that the proposed method is able to consistently outperform the single modeling approach with a variety of time series processes. We also find that relatively small ensemble sizes of 5 and 10 are quite effective in forecasting performance improvement.     

A hybrid optimized error correction system for time series forecasting

Time series forecasting is a challenging task in machine learning. Real world time series are often composed by linear and nonlinear structures which need to be mapped by some forecasting method. Linear methods such as autoregressive integrated moving average (ARIMA) and nonlinear methods such as artificial neural networks (ANNs) could be employed to handle such problems, however model misspecification hinders the forecasting process producing inaccurate models. Hybrid models based on error forecasting and combination can reduce the misspecification of single models and improve the accuracy of the system. This work proposes a hybrid system that is composed of three parts: a) linear modeling of the time series, b) nonlinear modeling of the error series, and c) combination of the forecasts using three distinct approaches. The system performs a search for the best parameters of the linear and nonlinear components, and of the combination approaches. Particle swarm optimization is used to find suitable architecture and weights. Experiments show that the proposed technique achieved promising results in time series forecasting.     

Automatic time series analysis for electric load forecasting via support vector regression

In this work, a strategy for automatic lag selection in time series analysis is proposed. The method extends the ideas of feature selection with support vector regression, a powerful machine learning tool that can identify nonlinear patterns effectively thanks to the introduction of a kernel function. The proposed approach follows a backward variable elimination procedure based on gradient descent optimisation, iteratively adjusting the widths of an anisotropic Gaussian kernel. Experiments on four electricity demand forecasting datasets demonstrate the virtues of the proposed approach in terms of predictive performance and correct identification of relevant lags and seasonal patterns, compared to well-known strategies for time series analysis designed for energy load forecasting and state-of-the-art strategies for automatic model selection.     

A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition

Multi-step ahead forecasting is still an open challenge in time series forecasting. Several approaches that deal with this complex problem have been proposed in the literature but an extensive comparison on a large number of tasks is still missing. This paper aims to fill this gap by reviewing existing strategies for multi-step ahead forecasting and comparing them in theoretical and practical terms. To attain such an objective, we performed a large scale comparison of these different strategies using a large experimental benchmark (namely the 111 series from the NN5 forecasting competition). In addition, we considered the effects of deseasonalization, input variable selection, and forecast combination on these strategies and on multi-step ahead forecasting at large. The following three findings appear to be consistently supported by the experimental results: Multiple-Output strategies are the best performing approaches, deseasonalization leads to uniformly improved forecast accuracy, and input selection is more effective when performed in conjunction with deseasonalization.     

A method to convert AVHRR Normalized Difference Vegetation Index time series to a standard viewing and illumination geometry

The bi-directional reflectance distribution function (BRDF) alters the seasonal and inter-annual variations exhibited in Advanced Very High Resolution Radiometer (AVHRR) Normalized Difference Vegetation Index (NDVI) data and this hampers the detection and, consequently, the interpretation of temporal variations in land-surface vegetation. The magnitude and sign of bi-directional effects in commonly used AVHRR data sets depend on land-surface properties, atmospheric composition and the type of atmospheric correction that is applied to the data. We develop an approach to estimate BRDF effects in AVHRR NDVI time series using the Moderate Resolution Imaging Spectrometer (MODIS) BRDF kernels and subsequently adjust NDVI time series to a standard illumination and viewing geometry. The approach is tested on NDVI time series that are simulated for representative AVHRR viewing and illumination geometry. These time series are simulated with a canopy radiative transfer model coupled to an atmospheric radiative transfer model for four different land cover types—tropical forest, boreal forest, temperate forest and grassland - and five different atmospheric conditions - turbid and clear top-of-atmosphere, turbid and clear top-of-atmosphere with a correction for ozone absorption and Rayleigh scattering applied (Pathfinder AVHRR Land data) and ground-observations (fully corrected for atmospheric effects). The simulations indicate that the timing of key phenological stages, such as start and end of growing season and time of maximum greenness, is affected by BRDF effects. Moreover, BRDF effects vary with latitude and season and increase over the time of operation of subsequent NOAA satellites because of orbital drift. Application of the MODIS kernels on simulated NVDI data results in a 50% to 85% reduction of BRDF effects. When applied to the global 18-year global Normalized Difference Vegetation Index (NDVI) Pathfinder data we find BRDF effects similar in magnitude to those in the simulations. Our analysis of the global data shows that BRDF effects are especially large in high latitudes; here we find that in at least 20% of the data BRDF errors are too large for accurate detection of seasonal and interannual variability. These large BRDF errors tend to compensate, however, when averaged over latitude.