Spatial multi-attention conditional neural processes.

Spatial prediction tasks are challenging when observed samples are sparse and prediction samples are abundant. Gaussian processes (GPs) are commonly used in spatial prediction tasks and have the advantage of measuring the uncertainty of the interpolation result. However, as the sample size increases, GPs suffer from significant overhead. Standard neural networks (NNs) provide a powerful and scalable solution for modeling spatial data, but they often overfit small sample data. Based on conditional neural processes (CNPs), which combine the advantages of GPs and NNs, we propose a new framework called Spatial Multi-Attention Conditional Neural Processes (SMACNPs) for spatial small sample prediction tasks. SMACNPs are a modular model that can predict targets by employing different attention mechanisms to extract relevant information from different forms of sample data. The task representation is inferred by measuring the spatial correlation contained in different sample points and the relationship contained in attribute variables, respectively. The distribution of the target variable is predicted by GPs parameterized by NNs. SMACNPs allow us to obtain accurate predictions of the target value while quantifying the prediction uncertainty. Experiments on spatial prediction tasks on simulated and real-world datasets demonstrate that this framework flexibly incorporates spatial context and correlation into the model, achieving state-of-the-art results in spatial small sample prediction tasks in terms of both predictive performance and reliability. For example, on the California housing dataset, our method reduces MAE by 8% and MSE by 7% compared to the second-best method. In addition, a spatiotemporal prediction task to forecast traffic speed further confirms the effectiveness and generality of our method.

A novel method for identifying hotspots and forecasting air quality through an adaptive utilization of spatio-temporal information of multiple factors.

Air pollution exerts serious impacts on human health and sustainable development. The accurate forecasting of air quality can guide the formulation of mitigation strategies and reduce exposure to air pollution. It is beneficial to explicitly consider both spatial and temporal information of multiple factors, e.g., the meteorological data, in the forecasting of air pollutant concentrations. The temporal information of relevant factors collected at a location should be considered for forecasting. In addition, these factors recorded at other locations may also provide useful information. Existing methods utilizing the spatio-temporal information of these relevant factors are usually based on some very complicated frameworks. In this study, we propose a novel and simple spatial attention-based long short-term memory (SA-LSTM) that combines LSTM and a spatial attention mechanism to adaptively utilize the spatio-temporal information of multiple factors for forecasting air pollutant concentrations. Specifically, the SA-LSTM employs gated recurrent connections to extract temporal information of multiple factors at individual locations, and the spatial attention mechanism to spatially fuse the temporal information extracted at these locations. This method is effective and applicable to forecast any air pollutant concentrations when spatio-temporal information of relevant factors has to be utilized. To validate the effectiveness of the proposed SA-LSTM, we apply it to forecast the daily air quality in Hong Kong, a high density city with peculiar cityscapes, by using the air quality and meteorological data. Empirical results demonstrate that the proposed SA-LSTM outperforms the conventional models with respect to one-day forecast accuracy, especially for extreme values. Moreover, the attention weights learned by the SA-LSTM can identify hotspots of the air pollution process for reducing computational complexity of forecasting and provide a better understanding of the underlying mechanism of air pollution.

Robust clustering by pruning outliers.

In many applications of C-means clustering, the given data set often contains noisy points. These noisy points will affect the resulting clusters, especially if they are far away from the data points. In this paper, we develop a pruning approach for robust C-means clustering. This approach identifies and prunes the outliers based on the sizes and shapes of the clusters so that the resulting clusters are least affected by the outliers. The pruning approach is general, and it can improve the robustness of many existing C-means clustering methods. In particular, we apply the pruning approach to improve the robustness of hard C-means clustering, fuzzy C-means clustering, and deterministic-annealing C-means clustering. As a result, we obtain three clustering algorithms that are the robust versions of the existing ones. In addition, we integrate the pruning approach with the fuzzy approach and the possibilistic approach to design two new algorithms for robust C-means clustering. The numerical results demonstrate that the pruning approach can achieve good robustness.