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Deep Air Learning: Interpolation, Prediction, and Feature Analysis of Fine-grained Air Quality
Zhongang Qi, Tianchun Wang, Guojie Song, Weisong Hu, Xi Li, Zhongfei, Zhang
TL;DR
Fine-grained air-quality interpolation, prediction, and feature analysis are commonly handled by separate models despite sparse and incomplete monitoring data. DAL unifies these tasks in one deep network by embedding feature selection and spatio-temporal semi-supervised learning. Experiments on real Beijing data report that DAL performs well against peer methods across the three tasks.
Problem
Fine-grained air-quality interpolation, prediction, and feature analysis are important but existing work generally solves them separately, while labeled monitoring data are insufficient and incomplete.
Method
DAL embeds feature selection and spatio-temporal semi-supervised learning in different deep-network layers to unify interpolation, prediction, feature selection, and analysis.
Results
DAL performs well compared with peer methods in extensive evaluations on real Beijing datasets across interpolation, prediction, and fine-grained air-quality feature analysis.
Takeaways & Limitations
The unified model uses unlabeled spatio-temporal information for interpolation and prediction while revealing relevant features associated with air-quality variation.
Takeaways & Limitations
For interpolation alone, DAL provides only moderate improvement over simple models, although integrating interpolation with prediction adds almost no computation complexity.
Abstract
from arXiv · showhide
The interpolation, prediction, and feature analysis of fine-gained air quality are three important topics in the area of urban air computing. The solutions to these topics can provide extremely useful information to support air pollution control, and consequently generate great societal and technical impacts. Most of the existing work solves the three problems separately by different models. In this paper, we propose a general and effective approach to solve the three problems in one model called the Deep Air Learning (DAL). The main idea of DAL lies in embedding feature selection and semi-supervised learning in different layers of the deep learning network. The proposed approach utilizes the information pertaining to the unlabeled spatio-temporal data to improve the performance of the interpolation and the prediction, and performs feature selection and association analysis to reveal the main relevant features to the variation of the air quality. We evaluate our approach with extensive experiments based on real data sources obtained in Beijing, China. Experiments show that DAL is superior to the peer models from the recent literature when solving the topics of interpolation, prediction, and feature analysis of fine-gained air quality.
1 INTRODUCTION
Fine-grained air-quality computing must address interpolation, prediction, and feature analysis despite sparse, incomplete monitoring data and diverse spatio-temporal observations. DAL unifies these tasks by combining feature selection and spatio-temporal semi-supervised learning in one deep network.
- 1 INTRODUCTION: Interpolation, prediction, and feature analysis provide information for addressing sparse monitoring coverage, pollution risks, and relevant air-quality factors.Interpolation addresses limited and uneven station distributions; prediction supports protection from air pollution; feature analysis identifies relevant variation factors.
- 1 INTRODUCTION: Urban air-quality data are constrained by insufficient monitoring stations, incomplete historical labels, and varied data types.Stations are expensive to build and maintain, while device maintenance and failures create missing historical outputs.
- 1 INTRODUCTION: Nearby observations in space and time tend to be more alike than distant observations, providing structure for completing missing historical labels.Figure 1 contrasts observations across locations and time, while the text identifies spatial-temporal proximity as a statistical characteristic.
- 1 INTRODUCTION: DAL introduces an extra sparse neural-network layer to select relevant input features and support analysis of black-box predictions.The sparse layer is designed for feature selection, while the resulting analysis reveals feature importance and relevant factors linked to air-quality variation.
- 1 INTRODUCTION: DAL unifies interpolation, prediction, feature selection, and feature analysis in one deep-learning model using unlabeled spatio-temporal data.The approach embeds feature selection and semi-supervised learning in different network layers.
- 1 INTRODUCTION: The paper reports that DAL outperforms peer models on interpolation, prediction, and fine-grained air-quality feature analysis.The evaluation uses extensive experiments on real Beijing data sources.
2 RELATED WORK
Related work spans air-pollution control, semi-supervised learning, and feature selection. DAL draws on methods from these areas while exploiting spatial-temporal proximity and unlabeled data for air-quality interpolation.
- Air pollution control: Prior air-pollution-control research applies data mining to air-quality interpolation, prediction, and feature analysis.The cited literature includes spatio-temporal interpolation, co-training-based fine-grained air-quality inference, and related approaches.
- Semi-supervised learning: Semi-supervised learning trains with a small amount of labeled data and a large amount of unlabeled data.Existing approaches include self-training, co-training, geometric-structure modeling, and joint embedding with unlabeled data.
- Semi-supervised learning: For spatio-temporal data, nearby observations tend to resemble one another more than observations separated in space or time.DAL uses this characteristic in semi-supervised learning to exploit the data geometry for interpolation.
- Feature selection: Feature-selection research includes filter, wrapper, embedded, and neural-network approaches for removing irrelevant attributes.Related embedded methods include L1-penalized lasso and grouped L1-penalized methods.
3 MODEL FORMULATION
DAL is a multiple-output deep network that embeds feature selection and spatio-temporal semi-supervised learning into different layers to address air-quality interpolation and prediction while supporting feature analysis.
- 3 MODEL FORMULATION: DAL uses a general multiple-output classifier to treat interpolation and prediction as classification problems with different outputs.The method describes both tasks as outputs of one deep learning network.
- 3.1 Data Representations and Symbols: The data representation assigns each instance a K-dimensional feature descriptor and an O-dimensional target label, with neural-network layers parameterized by weights and biases.The notation distinguishes input features, target outputs, activations, and layer-wise parameter matrices.
- 3.2 Feature Selection in Neural Network: The grouped L1 input-layer penalty selects complete feature groups, while L2 regularization on later layers helps avoid over-fitting.Grouped regularization treats all parameters associated with one feature as a natural group rather than selecting individual parameters.
- 3.2 Feature Selection in Neural Network: DAL performs feature selection with an extra sparse layer placed between the input layer and the second neural-network layer.The extra layer has the same number of nodes as the input layer and uses one connection per input feature through a diagonal weight matrix.
- 3.2 Feature Selection in Neural Network: The feature-selection objective combines training loss with sparsity constraints based on the average activation of nodes in the extra sparse layer.The formulation uses Kullback-Leibler divergence between the target sparsity and average node activations.
- 3.3 Spatio-temporal Semi-supervised Learning in Neural Network: Spatio-temporal semi-supervised learning regularizes predictions for nearby observations, using spatial and temporal neighborhoods across labeled and unlabeled data.The method relies on the tendency of observations close in space and time to be more alike.
- 3.3 Spatio-temporal Semi-supervised Learning in Neural Network: For interpolation, DAL predicts labels at the current time; for prediction, it predicts labels at a future time, while the same mechanism supports both tasks.The output-layer semi-supervised component is used both to achieve interpolation and to improve prediction performance.
- 3.4 Deep Air Learning: DAL combines input-layer feature selection with output-layer spatio-temporal semi-supervised learning and can pretrain deep-model weights using abundant unlabeled spatial and temporal data.Feature effects are then used in association analysis; larger positive effects indicate greater relevance to the target.
4 EXPERIMENTS
Experiments on Beijing air-quality data evaluate DAL for interpolation, prediction, feature selection, and feature analysis. DAL uses labeled and unlabeled spatio-temporal data, selects features through a sparse layer, and outperforms most compared methods while revealing relevant pollution factors.
- Data and Parameter Setting: The experiments use 3km×3km meteorological data, six hourly pollutant concentrations from 35 Beijing stations, and 35 labeled versus 3420 unlabeled grids.The grid task interpolates current PM2.5 for unlabeled locations and predicts subsequent PM2.5 concentrations for labeled and unlabeled locations.
- Feature Selection: DAL selects fewer features as λ1 increases, while its sparse-layer activations remove minor features with only a small prediction-accuracy decline.At λ1 = 3, mean activations ranged from 8.5906e−140 to 1, and features with very small activation were removed.
- Interpolation and Prediction: DAL outperforms Logistic Regression, L1-regularized variants, Neural Network, Autoencoder, LapReg, and ARIMA for interpolation and prediction, while RNN is slightly better only for interpolation.RNN performs much worse than DAL as the prediction horizon increases because it ignores spatial information and abundant unlabeled data.
- Discussion: For interpolation alone, DAL’s improvement over simple models is moderate, although its unified design performs interpolation and prediction synchronously without extra interpolation time.Adding one output dimension integrates the two tasks with almost no increase in prediction-model computation complexity.
- Spatio-temporal Semi-supervised Learning: Increasing α or β decreases testing RMSE, with the larger decline for β indicating stronger temporal than spatial semi-supervised effects in these experiments.Here α controls spatial-neighborhood constraints and β controls temporal-neighborhood constraints.
- Feature Analysis: The most relevant PM2.5 features are PM2.5, CO, PM10, northern wind strength, and temperature, while barometric pressure and humidity are most irrelevant.The feature analysis is reported as consistent with winter haze intuitions and identifies relevant and irrelevant factors from the available data.
- Pollution-source Analysis: DAL interpolation depicts haze spreading from southern to northern Beijing, suggesting southern pollution sources consistent with heavy industry in Hebei.The analysis concerns a December haze event within Beijing’s Fifth Ring Road.
5 CONCLUSION
The conclusion presents DAL as one model for fine-grained air-quality interpolation, prediction, feature selection, and analysis. It combines spatio-temporal semi-supervised learning with input-layer feature selection and association analysis.
- DAL unifies interpolation, prediction, feature selection, and feature analysis of fine-grained air quality in one model.
- Spatio-temporal semi-supervised learning uses unlabeled data and spatio-temporal structure to improve interpolation and prediction.
- DAL’s input-layer feature-selection method removes redundant or irrelevant features, while association analysis identifies their importance.