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Journal ArticleDOI: 10.1080/13658816.2020.1775836

Geographically and temporally neural network weighted regression for modeling spatiotemporal non-stationary relationships

04 Mar 2021-International Journal of Geographical Information Science (Taylor & Francis)-Vol. 35, Iss: 3, pp 582-608
Abstract: Geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR) are classic methods for estimating non-stationary relationships. Although these methods have be...

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Topics: Unit-weighted regression (54%)
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10 results found


Open accessJournal ArticleDOI: 10.3832/IFOR3705-014
Y. Sun, Z. Ao, W. Jia, Y. Chen  +1 more
Abstract: In natural forest ecosystems, there is often abundant down dead wood (DDW) due to wind disasters, which greatly changes the size and structure of forests. Accurately determining the DDW volume (DDWV) is crucial for sustaining forest management, predicting the dynamic changes in forest resources and assessing the risks of natural disasters or disturbances. However, existing models cannot accurately express the significant spatial nonstationarity or complexity in their spatial relationships. To this end, we established a geographically weighted deep neural network (GWDNN) model that constructs a spatially weighted neural network (SWNN) through geographic location data and builds a neural network through stand factors and remote sensing factors to improve the interpretability of the spatial model of DDWV. To verify the effectiveness of this method, using 2019 data from Liangshui National Nature Reserve, we compared model fit, predictive ability and residual spatial autocorrelation among the GWDNN model and four other spatial models: an ordinary least squares (OLS) model, a linear mixed model (LMM), a geographically weighted regression (GWR) model and a deep neural network (DNN) model. The experimental results show that the GWDNN model is far superior to the other four models according to various indicators; the coefficient of determination R2, root mean square error (RMSE), mean absolute error (MAE), Moran’s I and Z-statistic values of the GWDNN model were 0.95, 1.05, 0.77, -0.01 and -0.06, respectively. In addition, compared with the other models, the GWDNN model can more accurately depict local spatial variations and details of the DDWV in Liangshui National Nature Reserve.

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Topics: Spatial analysis (55%)

2 Citations


Journal ArticleDOI: 10.1080/13658816.2021.1965608
Arif Masrur1, Manzhu Yu1, Prasenjit Mitra2, Donna J. Peuquet1  +1 moreInstitutions (2)
Abstract: Machine learning (ML) interpretability has become increasingly crucial for identifying accurate and relevant structural relationships between spatial events and factors that explain them. Methodolo...

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Topics: Interpretability (61%)

2 Citations


Open accessJournal ArticleDOI: 10.5194/GMD-13-6149-2020
Xiang Que1, Xiaogang Ma1, Chao Ma1, Qiyu Chen2Institutions (2)
Abstract: . Local spatiotemporal non-stationarity occurs in various natural and socioeconomic processes. Many studies have attempted to introduce time as a new dimension into the geographically weighted regression model (GWR), but the actual results are sometimes not satisfied or even worse than the original GWR model. The core issue here is a mechanism for weighting effects of both temporal variation and spatial variation. In many geographical and temporal weighted regression models (GTWR), the concept of time distance has been inappropriately treated as time interval. Consequently, the combined effect of temporal and spatial variation is often inaccurate in the resulting spatiotemporal kernel function. This limitation restricts the configuration and performance of spatiotemporal weights in many existing GTWR models. To address this issue, we propose a new spatiotemporal weighted regression (STWR) model and the calibration method for it. A highlight of STWR is a new temporal kernel function, in which the method for temporal weighting is based on the degree of impact from each observed point to a regression point. The degree of impact, in turn, is based on the rate of value variation of the nearby observed point during the time interval. The updated spatiotemporal kernel function is based on a weighted combination of the temporal kernel with a commonly used spatial kernel (Gaussian or bi-square) by specifying a linear function of spatial bandwidth versus time. Three simulated datasets of spatiotemporal processes were used to test the performance of GWR, GTWR and STWR. Results show that STWR significantly improves the quality of fit and accuracy. Similar results were obtained by using real-world data for the precipitation hydrogen isotopes (δ2H) in Northeastern United States. The Leave-one-out cross-validation (LOOCV) test demonstrates that, comparing with GWR, the total prediction error of STWR is reduced by using recent observed points. Prediction surfaces of models in this case study show that STWR is more localized than GWR. Our research validates the ability of STWR to take full advantage of all the value variation of past observed points. We hope STWR can bring fresh ideas and new capabilities for analyzing and interpreting local spatiotemporal non-stationarity in many disciplines.

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2 Citations


Open accessJournal ArticleDOI: 10.3390/IJGI9110653
Abstract: Geographically weighted regression (GWR) introduces the distance weighted kernel function to examine the non-stationarity of geographical phenomena and improve the performance of global regression. However, GWR calibration becomes critical when using a serial computing mode to process large volumes of data. To address this problem, an improved approach based on the compute unified device architecture (CUDA) parallel architecture fast-parallel-GWR (FPGWR) is proposed in this paper to efficiently handle the computational demands of performing GWR over millions of data points. FPGWR is capable of decomposing the serial process into parallel atomic modules and optimizing the memory usage. To verify the computing capability of FPGWR, we designed simulation datasets and performed corresponding testing experiments. We also compared the performance of FPGWR and other GWR software packages using open datasets. The results show that the runtime of FPGWR is negatively correlated with the CUDA core number, and the calculation efficiency of FPGWR achieves a rate of thousands or even tens of thousands times faster than the traditional GWR algorithms. FPGWR provides an effective tool for exploring spatial heterogeneity for large-scale geographic data (geodata).

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Topics: CUDA (54%)

1 Citations


Journal ArticleDOI: 10.1007/S11269-021-02969-2
Abstract: Water quality experiments are difficult, costly, and time-consuming. Therefore, different modeling methods can be used as an alternative for these experiments. To achieve the research objective, geospatial artificial intelligence approaches such as the self-organizing map (SOM), artificial neural network (ANN), and co-active neuro-fuzzy inference system (CANFIS) were used to simulate groundwater quality in the Mazandaran plain in the north of Iran. Geographical information system (GIS) techniques were used as a pre-processer and post-processer. Data from 85 drinking water wells was used as secondary data and were separated into two splits of (a) 70 percent for training (60% for training and 10% for cross-validation), and (b) 30 percent for the test stage. The groundwater quality index (GWQI) and the effective water quality factors (distance from industries, groundwater depth, and transmissivity of aquifer formations) were implemented as output and input variables, respectively. Statistical indices (i.e., R squared (R-sqr) and the mean squared error (MSE)) were utilized to compare the performance of three methods. The results demonstrate the high performance of the three methods in groundwater quality simulation. However, in the test stage, CANFIS (R-sqr = 0.89) had a higher performance than the SOM (R-sqr = 0.8) and ANN (R-sqr = 0.73) methods. The tested CANFIS model was used to estimate GWQI values on the area of the plain. Finally, the groundwater quality was mapped in a GIS environment associated with CANFIS simulation. The results can be used to manage groundwater quality as well as support and contribute to the sustainable development goal (SDG)-6, SDG-11, and SDG-13.

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1 Citations


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43 results found


Journal ArticleDOI: 10.1038/NATURE14539
Yann LeCun1, Yann LeCun2, Yoshua Bengio3, Geoffrey E. Hinton4  +1 moreInstitutions (5)
28 May 2015-Nature
Abstract: Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.

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33,931 Citations


Open accessJournal Article
Abstract: Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.

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Topics: Overfitting (66%), Deep learning (62%), Convolutional neural network (61%) ... show more

27,534 Citations


Open accessBook
18 Nov 2016-
Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

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Topics: Feature learning (61%), Deep learning (59%), Approximate inference (51%) ... show more

26,972 Citations


Open accessPosted Content
Sergey Ioffe1, Christian Szegedy1Institutions (1)
11 Feb 2015-arXiv: Learning
Abstract: Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9% top-5 validation error (and 4.8% test error), exceeding the accuracy of human raters.

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17,151 Citations


Open accessJournal ArticleDOI: 10.1016/J.NEUNET.2014.09.003
Jürgen Schmidhuber1Institutions (1)
01 Jan 2015-Neural Networks
Abstract: In recent years, deep artificial neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarizes relevant work, much of it from the previous millennium. Shallow and Deep Learners are distinguished by the depth of their credit assignment paths, which are chains of possibly learnable, causal links between actions and effects. I review deep supervised learning (also recapitulating the history of backpropagation), unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.

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Topics: Deep learning (65%), Deep belief network (64%), Unsupervised learning (63%) ... show more

11,176 Citations


Performance
Metrics
No. of citations received by the Paper in previous years
YearCitations
20218
20202