Spatio-temporal patterns assisted deep learning model for PM 2.5 prediction (STEEP)

Abstract

Air pollution is an alarming problem in many cities and countries around the globe. The ability to forecast air pollutant levels plays a crucial role in implementing necessary prevention measures to curb its effects in advance. There are many statistical, machine learning, and deep learning models available to predict air pollutant values, but only a limited number of models take into account the spatio-temporal factors that influence pollution. In this study a novel Deep Learning model that is augmented with Spatio-Temporal Co-Occurrence Patterns (STEEP) is proposed. The deep learning model uses the Closed Spatio-Temporal Co-Occurrence Pattern mining (C-STCOP) algorithm to extract non-redundant/closed patterns and the Diffusion Convolution Recurrent Neural Network (DCRNN) for time series prediction. By constructing a graph based on the co-occurrence patterns obtained from C-STCOP, the proposed model effectively addresses the spatio-temporal association among monitoring stations. Furthermore, the sequence-to-sequence encoder-decoder architecture captures the temporal dependencies within the time series data. The STEEP model is evaluated using the Delhi air pollutants dataset and shows an average improvement of 8%–13% in RMSE, MAE and MAPE metric compared to the baseline models.

Keywords

spatio-temporal patterns deep learning time series prediction delhi air pollution

1. Introduction

The abrupt economic development, urbanization, and the increase in vehicle usage and energy consumption have led to a drastic rise in air pollution in India’s National capital, Delhi. Therefore, air pollution in Delhi is a colossal threat to the environment and human health. Air quality monitoring stations are available in and around Delhi to report the concentrations of pollutants on hourly basis. Air pollution is attributed to pollutants like PM_2.5, PM₁₀, O₃, CO, SO₂, NO₂, and NH₃. The particulate matter (PM_2.5 and PM₁₀) has become a severe issue in the Delhi megacity, requiring immediate mitigation efforts. Numerous epidemiological studies show that exposure to PM_2.5 causes serious health issues [1, 2, 3]. Short-term or acute exposure (24-hour concentration) to particulate matter causes breathing difficulty, eye irritation, etc. Long-term or chronic exposure (annual concentration) causes respiratory issues, reduced immunity levels, cardiovascular risk, etc. The derivates of particulate matter also cause harmful environmental effects like poor visibility, climate change, economic drawbacks, health hazards, reduced lifespan, indoor pollution, etc. The World Health Organisation (WHO) report in 2006 states that long-term exposures to PM_2.5 should be less than 10 $μ$ g/m³, and short-term exposures should be less than 25 $μ$ g/m³ [4]. The particulate matter suspended in the atmosphere causes severe health hazards to sensitive groups of people like children, the elderly, sick patients, etc. Therefore, forecasting air pollutants concentration is crucial to minimize the high concentration of air pollutants. By forecasting, the public can be warned to plan their activities or stay indoors. Forecasting air pollutants is also tedious as factors like geography, meteorology, population, traffic, etc, influence it. According to the National ambient air quality standards, the pollutants are categorized into six categories [5]. Table 1 depicts the air pollutants and their permissible hourly range. Table 2 shows the pollutant categories and the range for each type.

Table 1
Ambient air quality standard.

Pollutants Time-weighted average The concentration of ambient air

PM₁₀ ( $μ$ g/m³) 24 h 100

PM_2.5 ( $μ$ g/m³) 24 h 60

SO₂ ( $μ$ g/m³) 24 h 80

NO₂( $μ$ g/m³) 24 h 80

O₃ ( $μ$ g/m³) 8 h 100

CO (mg/m³) 8 h 02

NH₃ ( $μ$ g/m³) 24 h 400

Pollutants	Time-weighted average	The concentration of ambient air
PM₁₀ ( $μ$ g/m³)	24 h	100
PM_2.5 ( $μ$ g/m³)	24 h	60
SO₂ ( $μ$ g/m³)	24 h	80
NO₂( $μ$ g/m³)	24 h	80
O₃ ( $μ$ g/m³)	8 h	100
CO (mg/m³)	8 h	02
NH₃ ( $μ$ g/m³)	24 h	400

Table 2

National Air Quality Index (AQI) categorization.

	PM₁₀ 24 h	PM_2.5 24 h	SO₂ 24 h	NO₂ 24 h	O₃ 8 h	CO 8 h	NH₃ 24 h
AQI class	( $μ$ g/m³)	( $μ$ g/m³)	( $μ$ g/m³)	( $μ$ g/m³)	( $μ$ g/m³)	( $μ$ g/m³)	( $μ$ g/m³)
Good (0–50)	0–50	0–30	0–40	0–40	0–50	0–1	0–200
Satisfactory (51–100)	51–100	31–60	41–80	41–80	51–100	1.1–2	201–400
Moderately polluted (101–200)	101–250	61–90	81–380	81–180	101–168	2.1–10	401–800
Poor (201–300)	251–350	91–120	381–800	181–280	169–208	10–17	801–1200
Very poor (301–400)	351–430	121–250	801–1600	281–400	209–748	17–34	1200–1800
Severe (401–500)	$>$ 430	$>$ 250	$>$ 1600	$>$ 400	$>$ 748	$>$ 34	$>$ 1800

Numerous studies have been conducted using the observations collected from monitoring stations to predict air quality. These studies are generally denoted as time series forecasting. Auto-regressive moving average [6], Kalman filtering [7], regression method [8], and artificial neural network (ANN) [9] are some of the most famous techniques for time series prediction. But, only a limited number of existing studies address the spatial association among monitoring stations when predicting air pollution levels, where the spatial association is primarily attributed to the proximity or distance between the monitoring stations. And no existing work addresses the spatio-temporal association among the monitoring stations. Spatio-temporal association refers to the relationship or correlation between spatial and temporal factors within a time series dataset. It focuses on identifying patterns, co-occurrences, or associations between different locations or monitoring stations and analysing the simultaneous occurrence or behaviour of pollutants across space and time. Hence, a Spatio-Temporal Co-Occurrence Pattern assisted Deep Learning Model (STEEP) is proposed in this research. The deep learning model used here is Diffusion Convolution Recurrent Neural Network which takes the closed spatio-temporal patterns as input. The Spatio-temporal association among the stations is obtained by translating the non-redundant/ closed Spatio-temporal co-occurrence pattern mined using the C-STCOP approach. These patterns are converted to a matrix or constructed as a graph to be fed as knowledge to time series prediction. The sequence-to-sequence encoder-decoder architecture in Recurrent Neural Network (RNN) is used to capture the temporal dependency among time series data. Temporal dependency in time series prediction refers to the inherent relationship and influence of past observations on future values within a sequential dataset. The time series air pollutant and meteorological data, along with the C-STCOP patterns, is given as input to the STEEP model. The diffusion convolution process captures the spatio-temporal association among stations from the graph. The STEEP model then forecasts the air pollutants value for the next few hours (1, 6, 12, 18, 24 hours) at a location. Delhi air quality data is used to forecast the PM_2.5 data and evaluate the model. The experimental results show that the proposed method gives better results than the baseline approach.

The rest of the paper is organized as follows. Section 2 overviews the existing techniques available for time series prediction. Section 3 gives an insight into the data, study area, and data pre-processing steps. In Section 4, the Methodology of the proposed STEEP model is explained. The Experimental Setup, results, and discussion is presented in Sections 5 and 6, followed by the Conclusion in Section 7.

2. Literature review

Numerous research works exist on real-time air quality forecasting (RT-AQF) for short and long-term prediction [10, 11]. Typically, short-term predictions (1–5 days) are employed to notify the citizens about potentially hazardous pollution levels so that they can take preventative countermeasures. Long-term ( $>$ 1 year) predictions can offer variation trends of pollutants, which environmental health specialists frequently employ to study climatic change [12]. The short-term RT-AQF strategies are generally categorized as simple empirical methods, statistical measures, and physical measurement-based methodologies [10, 11]. Simple empirical methods are typically insufficient to solve the air quality prediction challenge since they provide results associated with historical data (e.g., temperature). Typically, physical methods require a solid understanding of air contaminants and data for assessing atmospheric, physical, and chemical phenomena. Unfortunately, the data are generally unavailable to the general audience, and it is hard to analyse the complex procedures. Consequently, statistical techniques and machine learning approaches are the most prominent ways to estimate air pollution levels [13, 14, 15, 16]. Auto-regressive integrated moving average (ARIMA) is a well-known time series analysis approach that has been effectively implemented in air quality prediction [6, 14, 15]. Other well-known time series prediction techniques include K-Nearest Neighbour (KNN), Support Vector Regression (SVR), and Gaussian Process [17]. Nevertheless, these time series models typically rely on the aspect of stationarity (i.e., the mean, variance, and autocorrelation structure do not change over time), which makes it inappropriate for real-time air quality data.

Artificial Neural Networks (ANN) are widely used for air quality predictions as they can accommodate the nonlinear temporal dependence among data. In [18], a multi-layer perceptron (MLP) and artificial neural network (ANN) model was applied to estimate daily maximum and mean Ozone and particulate matter (PM_2.5 and PM₁₀). It demonstrated that MLP surpassed the conventional multiple linear regression (MLR). In [9], the authors recommended constructing independent ANN models for every monitoring centre to predict the 24-hour moving average maximum value of PM_2.5. The research outcome demonstrated that the multi-layer neural network outperformed linear regression and the persistent baseline (i.e., assigning hourly values for the next day with the values from the current day). The approaches mentioned above demonstrate a comparatively superior performance of ANN for air quality prediction.

Hybrid methods for handling linear and nonlinear trends in air quality time series analysis have also been developed. In [19], the authors introduced a hybrid model that combines ARIMA and ANN to enhance the precision of forecasts for a region with inadequate meteorological and air quality inputs. The results indicate that the hybrid model outperforms the ARIMA and ANN models separately. Likewise, in [13], the authors suggested a hybrid method composed of an ARIMA and a nonlinear model. Unfortunately, these hybrid techniques do not include spatial association with other monitoring locations’ air quality data. Therefore, a hybrid method was developed to estimate air quality over the next 48 hours at every monitoring centre [16]. The hybrid model might account for temporal and spatial dependence in separate models (i.e., temporal predictor and spatial predictor) and integrate the two predictors using a regression tree.

Deep learning techniques offer considerable potential for time series prediction [20, 21, 22]. Deep recurrent neural network (RNN), which can model nonlinear temporal dependency, has produced impressive outcomes in sequence modelling as well as time series modelling [23], such as speech recognition [24] and traffic prediction [25]. In [26], a more sophisticated variant of RNN called the Diffusion Convolutional Recurrent Neural Network (DCRNN) model is introduced. This model combines diffusion convolution and RNN to effectively handle the spatial association among monitoring stations and the temporal dependency within time series. An extension of it is the Geo-context-based diffusion convolutional recurrent neural network (GC-DCRNN); this model finds the similarity of environment between the monitoring stations to construct a graph for addressing the spatial association among monitoring stations [27]. Later, a model incorporating the Graph convolution neural network and Long short-term memory (GC-LSTM) was proposed to perform time series prediction [28]. This model uses the geographic distance between the monitoring station to construct a graph for accommodating spatial association among the stations.

The Existing air quality prediction models do not consider spatial and temporal aspect of the data. But the spatio-temporal factor gives additional information about the monitoring location and improves the prediction accuracy. Therefore, a model that integrates the spatio-temporal characteristics along with the time series data fulfils this research gap. The proposed STEEP model uses the spatio-temporal co-occurrence patterns obtained from C-STCOP to construct a graph from which the spatio-temporal association among the monitoring stations can be extracted. This graph is fed as knowledge to the DCRNN model for performing time series forecasting. Also, the proposed model can forecast the PM_2.5 value for the next 24 hours across all stations simultaneously.

3. Data

This section gives a description of the study area, along with the data collection and cleaning process. The resulting dataset will be a pre-processed dataset ready to be used by the STEEP model for forecasting PM_2.5 values.

3.1. Study area

The study area is Delhi (India), the National Capital Region (NCR) of India (28.7041^∘ N, 77.1025^∘ E). The total land area of Delhi is 1,483 sq. km. Delhi has been experiencing the worst pollution level for the past few years. Though Delhi is an urban city with significant economic achievements, it continues to be one of the worst-polluted metropolitan cities in the world [1, 29, 30]. Despite the relocation of many industries, 30% of the capital’s population still suffers from respiratory diseases. The most influencing factor on air quality is wind speed and direction. That is the reason behind comparatively less air pollution in Chennai than in Delhi, even though Chennai has more industries. Delhi’s poor geography and meteorology also make things worse, as Delhi could be imagined as an inverted bowl that collects air pollution with only a narrow outlet to escape. Various air pollutants like CO, NH₃, PM_2.5, PM₁₀, etc., lead to air pollution. Among the numerous air pollutants, PM_2.5 is hazardous as exposure to this pollutant has led to the death of 54000 people in Delhi during 2020. Although Delhi experienced a temporary respite from air pollution due to the COVID-19 lockdown, air pollution seriously threatens public health and the economy [31]. In this work, short-term forecasting of PM_2.5 pollutants using the proposed STEEP model is done to forecast pollutant values effectively. The Spatio-temporal dependency among the stations is considered to predict the PM_2.5 concentration effectively.

There is a total of 36 monitoring stations in Delhi. The 27 air quality monitoring stations in and around NCR were considered for this analysis. Based on data availability, these stations were chosen. The distribution of monitoring stations is visualized in Figure 1.

Figure 1.

Delhi monitoring stations.

3.2. Air quality data

The air pollutants, namely PM₁₀, PM_2.5, NO₂, CO, Ozone, SO₂, NH₃, and the weather parameters, atmospheric temperature (AT), relative humidity (RH), wind direction (WD), and wind speed (WS) that are monitored on hourly and daily basis are available in the central pollution control board. The PM_2.5, AT, RH, and WS data from January 2019 to December 2020 are taken into consideration for this study. Table 3 gives the statistics of the data used for the analysis. From Table 3, it can also be observed that the PM_2.5, RH, and WS standard deviation for 2020 is less compared to 2019 due to covid lockdown. The nationwide lockdown temporarily impacted air pollution, but the effect wore out as the unlock phases began.

Table 3
Statistics of the dataset used.

Variable Unit Range 2019 Range 2020 Mean 2019 Mean 2020 St. dev. 2019 St. dev. 2020

PM_2.5 $μ$ g/m3 [3,716] [5,699] 108.73 92.93 89.38 81.90

AT ^∘C [0,60] [0,58] 25.18 25.21 8.57 8.97

RH % [0,100] [0,100] 58.41 60.64 26.73 19.29

WS m/s [0,15] [0,12] 1.20 1.04 1.14 0.86

Latitude ^∘ [28.4517, 28.84467] – – – –

Longitude ^∘ [77.1424, 77.09335] – – – –

Year NA [2019, 2020] – – – –

Month NA [1,12] – – – –

Day NA [1,31] – – – –

Variable	Unit	Range 2019	Range 2020	Mean 2019	Mean 2020	St. dev. 2019	St. dev. 2020
PM_2.5	$μ$ g/m3	[3,716]	[5,699]	108.73	92.93	89.38	81.90
AT	^∘C	[0,60]	[0,58]	25.18	25.21	8.57	8.97
RH	%	[0,100]	[0,100]	58.41	60.64	26.73	19.29
WS	m/s	[0,15]	[0,12]	1.20	1.04	1.14	0.86
Latitude	^∘	[28.4517, 28.84467]	–	–	–	–
Longitude	^∘	[77.1424, 77.09335]	–	–	–	–
Year	NA	[2019, 2020]	–	–	–	–
Month	NA	[1,12]	–	–	–	–
Day	NA	[1,31]	–	–	–	–

3.2.1. Data pre-processing

The raw data obtained from the Central Pollution control board (CPCB) [32] must be cleansed and pre-processed for analysis. The pre-processing steps required are given below.

Missing values: The missing values are filled using the linear interpolation method. Various interpolation methods are available, like nearest neighbour interpolation, regression-based interpolation, and cubic spline interpolation, to fill missing values. But the, linear interpolation was used because of its simplicity and success in the past [33, 34].

Remove duplicates: The duplicate entries are removed by setting the timestamp attribute as the primary index. There were no duplicate values observed in the dataset.

The cleansed hourly data for each pollutant will be given as the time series data input for STEEP. The pre-processed data will have the following attributes: timestamp, station name, and PM_2.5 concentration value. A sample of the cleaned data for five stations is given in Table 4.

Table 4
Cleansed PM_2.5 data.

Timestamp Alipur Anand vihar Ashok vihar Bawana DrKarni shooting range

01-01-2019 01:00 361.5 517.25 408.25 128 360

01-01-2019 02:00 348 531.25 466.75 138 312

01-01-2019 03:00 298 542 496 123 291

01-01-2019 04:00 276.5 547.50 467.25 125 287

01-01-2019 05:00 295 497 453.25 130 289

Timestamp	Alipur	Anand vihar	Ashok vihar	Bawana	DrKarni shooting range
01-01-2019 01:00	361.5	517.25	408.25	128	360
01-01-2019 02:00	348	531.25	466.75	138	312
01-01-2019 03:00	298	542	496	123	291
01-01-2019 04:00	276.5	547.50	467.25	125	287
01-01-2019 05:00	295	497	453.25	130	289

3.2.2. Event modelling

The daily time series data are modelled into events for finding C-STCOP patterns. The values are categorized as safe and unsafe based on the categories in Table 2. If the recorded PM_2.5 falls in the severe category, it is marked as unsafe, and for all other categories, it is marked safe. Stations experiencing dangerous level on a day was modelled into an event.

The PM_2.5 data after event modelling has the following attributes: timestamp, Event (station), Latitude, and Longitude. This data is used to find the Spatio-temporal co-occurrence pattern by the C-STCOP algorithm. Table 5 shows a sample of the pollution data modelled into events.

Table 5
Event modelling.

Timestamp Event Latitude Longitude

02-01-2019 00:00 Alipur 28.79792 77.12327

03-01-2019 00:00 Alipur 28.79792 77.12327

04-01-2019 00:00 Alipur 28.79792 77.12327

20-01-2019 00:00 Anand Vihar 28.69177 77.13061

21-01-2019 00:00 Anand Vihar 28.69177 77.13061

Timestamp	Event	Latitude	Longitude
02-01-2019 00:00	Alipur	28.79792	77.12327
03-01-2019 00:00	Alipur	28.79792	77.12327
04-01-2019 00:00	Alipur	28.79792	77.12327
20-01-2019 00:00	Anand Vihar	28.69177	77.13061
21-01-2019 00:00	Anand Vihar	28.69177	77.13061

3.3. Metrological data

The meteorology data, namely Wind Speed (WS), Wind direction (WD), Relative humidity (RH), atmospheric Temperature (AT), solar radiation (SR), and barometric pressure (BP), are monitored in each station. The weather parameters AT, RH, and WS were considered for this study. Data preprocessing steps, as explained in Section 3.2.1, are applied for weather data. Therefore, the weather data, PM_2.5 values, and Spatio-temporal patterns are input to the STCOP-DCRNN model.

4. Methodology

The goal is to do a short-term forecast of PM_2.5 values, given previously recorded data from $S$ Stations. A graph is constructed to render the Spatio-temporal dependency among monitoring stations. An undirected graph $G = (V, ε, M)$ is built where $V$ is a set of monitoring stations recording pollutants value $| V | = S$ , $ε$ is a set of edges and $M$ is the weighted adjacency matrix. The observations are denoted as graph signals $X \in R^{S \times F}$ , where $S$ is the number of nodes in the graph or monitoring stations considered, and $F$ is the total number of features for each node. $X$ is composed of two parts, the air quality readings $X_{R} \in R^{S \times F_{R}}$ and the additional features (i.e., metrological values in this case) $X_{A} \in R^{S \times F_{A}}$ . The total number of features $F = F_{R} + F_{A}$ . The graph signal at time $t$ is denoted as $X^{(t)}$ , the previous hours of the day are represented as $T^{'}$ i.e., the time between $(t + T^{'} - 1)$ to $(t)$ , the future or remaining hours of the day are denoted as $T$ .

\begin{aligned} [X^{(t - T^{'} + 1)}, \dots, X^{(t)}; G] \overset{h (\cdot)}{⟶} [X_{R}^{(t + 1)}, \dots, X_{R}^{(t + T)}] \end{aligned}

(1)

This model aims to learn a function $h (.)$ that maps $T^{'}$ (historical data) to future graph signals $T$ , given a graph $G$ .

Figure 2 represents the architecture of the proposed STEEP model. The PM_2.5 observations, meteorological values, and Spatio-temporal patterns are pre-processed and given as input to the model. The patterns are represented as an undirected graph (i.e., matrix M) and given as input, along with the pre-processed time series data in the input layer. The spatio-temporal dependencies in the data are captured in the spatio-temporal processing layer using Diffusion Convolution (DC) and Gated Recurrent Unit (GRU). The predicted PM_2.5 value is given in the output layer.

Figure 2.

STEEP architecture.

4.1. C-STCOP

The C-STCOP algorithm in Table 6 uses an Apriori-based candidate generation strategy to produce unique, closed patterns. The significance of closed and lossless ST patterns is quantified using the coupling co-efficient measure $(c o c o)$ and closed participation index $(c p i)$ . Listed below are some of the parameters that the C-STCOP algorithm relies on,

$l$ : represents the size of the co-occurrence pattern

$C_{l}$ : denotes the group of candidates of $s i z e l$ STCOP obtained from $s i z e (l - 1)$

$T_{l}$ : set of $l s i z e$ tab-instance

$P_{l}$ : represents the collection of frequently occurring non-redundant STCOP obtained from candidate STCOP of $s i z e l$

$P r e v_{S T C O P}$ : represents the complete collection of all non-redundant frequently occurring STCOP (all sizes)

$c P_{l}$ : denotes the group of prevalent patterns that the super patterns address.

Table 6
C-STCOP algorithm.

Algorithm: C-STCOP

Input: ST instances (In), ST events $(E)$ , Coupling co-efficient threshold ( $c o c o_{t h}$ ), Prevalence threshold ( ${p i}_{t h}$ ), Spatial buffer ( $D i s t - r$ ), Temporal buffer ( $Δ t$ ), $l = 1$ , $C_{1} = E$ , $P r e v_{S T C O P} = \emptyset, T_{1} = g e n_s i z e 1 (C_{1}, I, {p i}_{t h}), P_{l} = T_{1}$

Output: Set of Closed Spatio-temporal co-occurring patterns

1: $l =$ 1, $C_{1} = E$ , $P r e v_{S T C O P = \emptyset}$ ;

2: $T_{1} = g e n_size 1 (C_{1}, In, {pi}_{t h});$

3: $P_{l} = T_{1}$ ;

4: While $(P_{l} \neq \emptyset)$ do

5: $C_{(l + 1)} = g e n_candidate (P_{l})$ ;

6: $T_{(l + 1)} = g e n_t a b_i n s (c_{(l + 1)}, c o c o_{t h})$ ;

7: $P_{(l + 1)} = P r e v (C_{(l + 1)}, {pi}_{t h})$ ;

8: $c P_{l} = cpi (P_{(l + 1)}, P_{l})$ ;

9: $P r e v_{C - S T C O P} = (P r e v_{C - S T C O P} \cup P_{(l + 1)}) - c P_{l}$ ;

10: $l = l + 1;$

11: Return $P r e v_{C - S T C O P}$

12: End While

Algorithm: C-STCOP
	Input:	ST instances (In), ST events $(E)$ , Coupling co-efficient threshold ( $c o c o_{t h}$ ), Prevalence threshold ( ${p i}_{t h}$ ), Spatial buffer ( $D i s t - r$ ), Temporal buffer ( $Δ t$ ), $l = 1$ , $C_{1} = E$ , $P r e v_{S T C O P} = \emptyset, T_{1} = g e n_s i z e 1 (C_{1}, I, {p i}_{t h}), P_{l} = T_{1}$
	Output:	Set of Closed Spatio-temporal co-occurring patterns
1:	$l =$ 1, $C_{1} = E$ , $P r e v_{S T C O P = \emptyset}$ ;
2:	$T_{1} = g e n_size 1 (C_{1}, In, {pi}_{t h});$
3:	$P_{l} = T_{1}$ ;
4:	While $(P_{l} \neq \emptyset)$ do
5:		$C_{(l + 1)} = g e n_candidate (P_{l})$ ;
6:		$T_{(l + 1)} = g e n_t a b_i n s (c_{(l + 1)}, c o c o_{t h})$ ;
7:		$P_{(l + 1)} = P r e v (C_{(l + 1)}, {pi}_{t h})$ ;
8:		$c P_{l} = cpi (P_{(l + 1)}, P_{l})$ ;
9:		$P r e v_{C - S T C O P} = (P r e v_{C - S T C O P} \cup P_{(l + 1)}) - c P_{l}$ ;
10:		$l = l + 1;$
11:		Return $P r e v_{C - S T C O P}$
12:	End While

The prevalence of an individual event in the entire dataset is determined initially. If an event is not frequent with respect to the prevalence value, then patterns are not generated for those events. The candidate patterns are produced using an apriori approach if and only if $P_{l} \neq \emptyset$ . Patterns of frequency of $s i z e l$ are used to generate potential candidate patterns of $s i z e - l + 1$ . Instances of tables of $s i z e - l + 1$ are generated using the generate table instance function for each possible pattern. Candidates for patterns in a table are identified using a neighborhood function. Each pattern instance’s location and time stamp are recorded for calculating the pattern’s coco value. When evaluating a pattern, coco value must be greater than the threshold set by the user ( $c o c o_{t h}$ ). All frequent patterns are identified by eliminating the candidate patterns of $s i z e l + 1$ that have $pi < {pi}_{t h}$ . Along with these patterns, the $s i z e l$ frequent patterns are fed as input to the closed participation index function cpi. The non-redundant spatio-temporal frequent co-occurrence pattern kept in the $P r e v_{C - S T C O P}$ set are updated with the frequent patterns of $s i z e - l + 1$ i.e $P_{(l + 1)}$ . In addition, the $P_{l}$ patterns that are covered by the $P_{(l + 1)}$ super patterns are removed from the $P r e v_{C - S T C O P}$ set. With this process in place, we can eliminate redundancy in patterns instantly. The method is iterated over for each value of $s i z e - l$ , and the set of all non-redundant STCOP or C-STCOP is returned.

4.2. Graph construction

The spatiotemporal patterns obtained from C-STCOP is represented as an undirected graph $G = (V, ε, M)$ , where $V$ is a set of monitoring stations recording pollutants value $| V | = S$ , $ε$ is a set of edges and $M$ is the weighted adjacency matrix. The edge weights are calculated by using the equation.

\begin{aligned} W_{i j} = {\begin{cases} \sum p r e v (p_{i j}) & i f i a n d j a r e p r e s e n t i n a p a t t e r n p \\ 0, & o t h e r w i s e \end{cases} \end{aligned}

(2)

Where $p r e v (p_{i j})$ is the prevalence of the pattern in which $i$ and $j$ are present together. All such prevalence value is added up to give edge weight for the nodes.

Table 7

Graph construction algorithm.

	Algorithm: Graph Construction
	Input:	C-STCOP patterns $(p)$ , prevalence of a pattern prev(p), vertices $V$ .
	Output:	Undirected graph $G$ .
1:	Function:	Graph construction $(p, p r e v, V)$
2:		Create a $V \times V$ matrix M filled with 0
3:		While $(p \neq \emptyset)$ do
4:			For $(i, j)$ in M do
5:			Calculate Edge weight $W_{i j} = \sum p r e v (p_{i j})$
6:			M[i][j]: $= W_{i j}$
7:			M[j][i]: $= W_{i j}$
8:			End
8:			Return M
10:		End While
11:	End

Figure 3.

Illustration of graph construction from sample C-STCOP.

An algorithm for Graph Construction is given in Table 7. The algorithm begins by creating a zero matrix of size $V \times V$ . If the prevalent pattern set is not empty then the algorithm proceeds to compute the edge weight for nodes using Eq. (2). The resultant undirected graph is an adjacency matrix computed using the prevalent C-STCOP patterns.

An illustration of graph construction for three C-STCOP patterns is given in Figure 3. The first pattern is 5-9-15-16-23 and its prevalence value is 0.08. The station ID is used for denoting stations in the patterns. This value is assigned as edge weight to all the vertices involved in the pattern. The second pattern is 2-5-7-8-13 with a prevalence value of 0.07 and this value is assigned as edge weight to all the vertices. The third pattern considered is 15-23-25 and when assigning this prevalence value as edge weight to 15-23 and 23-15 the new prevalence value is added up with the existing value. The resultant graph constructed from using all the C-STCOP patterns obtained for the set parameters $c o c o = 0.05$ , $pi =$ 0.1, $Δ t =$ 7 day, $r =$ 25 km is visualized in Figure 4 and Table 8 provides statistics of the graph depicted in Figure 4.

Figure 4.

Spatio-temporal graph constructed using the C-STCOP patterns.

Table 8

Graph statistics.

ID	Station	Number of edges
0	Alipur	2
1	AnandVihar	6
2	AshokVihar	7
3	Bawana	2
4	DrKarniShootingRange	4
5	DTU	4
6	DwarkaSector8	0
7	IHBASDilshadGarden	3
8	Jahangirpuri	4
9	JawaharlalNehruStadium	8
10	MajorDhyanChandNationalStadium	7
11	MandirMarg	6
12	Mundka	0
13	Najafnagar	3
14	Narela	0
15	NehruNagar	8
16	OkhlaPhase2	6
17	Patparganj	0
18	PunjabiBagh	6
19	Pusa	5
20	RKPuram	7
21	Rohini	4
22	Shadipur	1
23	Sirifort	8
24	SoniaVihar	0
25	SriAurobindoMarg	6
26	VivekVihar	0
27	Wazirpur	6

4.3. STCOP-DCRNN

The spatiotemporal dynamics of air pollution are modelled using STEEP. The spatiotemporal association considers the interconnectedness of pollution levels across different monitoring stations over time. It recognizes that pollution levels at one location can be influenced by the pollution levels at nearby or geographically distant locations, as well as by the temporal dynamics and trends in those locations. Therefore, by incorporating spatiotemporal association, time series prediction models can capture the spatial interactions and dependencies among monitoring stations, enabling more accurate and comprehensive predictions of air pollution levels. The proposed model recognizes that local factors and spatiotemporal relationships with neighbouring locations influence pollution levels. Consequently, the model captures the spatio-temporal association between the monitoring stations using the diffusion convolution process on the constructed graph. The temporal dependencies among time series are captured by the sequence-to-sequence architecture of the encoder-decoder.

4.3.1. Diffusion convolution

The diffusion convolution process is used on the graph that is constructed in Section 4.2. The standard convolutional neural network (CNN) usually handles grid-structured data in image processing. The convolution process uses a filter to examine the image and extract necessary features. For example, if a 3 $\times$ 3 ilter is used to convolve on a 6 $\times$ 6 image to output a 4 $\times$ 4 image. It proceeds by multiplying the 3 $\times$ 3 filter matrix with the first 3 $\times$ 3 size on the image and then shifts the column followed by row shifting to add up the 4 $\times$ 4 image. The diffusion convolution process extends this idea to the graph constructed [26, 35]. The diffusion convolution is the diffusion process with different steps on the graph. In a $k$ -step diffusion process, $k$ denotes the distance to the centre point. A transition matrix $T$ is computed at each step $i$ by diffusing attention to neighbors, which are $k$ -step away from the centre point. The filter later adds up the transition matrices with a probability $θ$ , which is learned during the training step. The diffusion convolution operation $◼_{G}$ on the graph signal $X \in R^{S \times F}$ using a filter $f_{θ}$ is defined as given below:

\begin{aligned} X_{:, p} ◼_{G} f_{θ} = \sum_{k = 0}^{K - 1} (θ_{k} (T^{k}) X_{:, p}) \end{aligned}

(3)

Where $θ_{k}$ are the parameters of the filter such that $θ_{k} \in R^{K \times 2}$ and $T^{k}$ is a transition matrix. The transition is defined as $T^{k} = D^{- 1} A$ , where $D$ denotes the diagonal degree matrix $d_{i i} = \sum_{j} a_{i j}$ , and $A$ represents the adjacency matrix. Equation (3) defines the diffusion convolution function performed in the diffusion convolutional layer.

4.3.2. RNN

The temporal dependency is addressed by using the recurrent neural network (RNN). The Gated Recurrent Unit (GRU) is an improved version of the customary recurrent neural network (RNN) [4]. GRU uses an update and reset gate to handle the vanishing gradient problem. The matrix multiplication in GRU is replaced by the diffusion convolution operation $◼_{G}$ , which results in the DCRNN model.

\begin{aligned} r^{(t)} & = σ (Θ_{r} ◼_{G} [I^{(t)}, O^{(t - 1)}] + b_{r}) \\ z^{(t)} & = σ (Θ_{z} ◼_{G} [I^{(t)}, O^{(t - 1)}] + b_{z}) \\ C^{(t)} & = t a n h (Θ_{c} ◼_{G} [I^{(t)}, (r^{t} ⊙ O^{(t - 1)}] + b_{c}) \\ O^{(t)} & = z^{(t)} ⊙ O^{(t - 1)} + (1 - z^{(t)}) ⊙ C^{(t)} \end{aligned}

(4)

Here $◼_{G}$ represents the diffusion convolution operation as mentioned in Eq. (1). $Θ_{r}, Θ_{z}, Θ_{c}$ are the corresponding filter parameters. $I^{(t)}$ , $O^{(t)}$ denotes the input and output state at time $t$ . $r^{(t)}$ , $z^{(t)}$ are the reset gate and update gate at time $t$ . The operation $⊙$ is the Hadamard product that calculates the element-wise product for two matrices. $C^{(t)}$ denotes the current memory content at time $t$ . $b_{r}, b_{z}, b_{c}$ are the corresponding bias for reset gate, update gate, and current state.

A sequence-to-sequence architecture is employed for performing multi-step ahead forecasting. i.e., if a PM_2.5 vector of 6 hours is fed to an encoder, then the decoder takes the last state as input and produces the subsequent sequence. Throughout the training phase, the encoder is provided with historical time series data, and its final state is used to initialize the decoder. During the testing phase, the forecasted results are compared with the ground truth for evaluating the model.

5. Experimental setup

The air quality data, weather data, and C-STCOP patterns were used for building the STEEP model. Delhi, India, was used as the study area, as explained in Section 3. The Spatio-temporal data was stored in the PostgreSQL database using the PostGIS extension. The experiments were conducted in an intel core i5 desktop with 16 GB RAM and 500 GB SSD.

In this research work, the PM_2.5, AT, RH, and WS observation from 2019 to 2020 was used for training and testing the model. The Spatio-temporal patterns obtained from C-STCOP were constructed as a graph. The C-STCOP patterns were used to construct the adjacency matrix/undirected graph. To compute the graph, the weight between each node using the patterns prevalence measure is calculated as per Eq. (2). The matrix was normalized to get values between the range 0–1 to be set as the edge weights of the nodes. This graph and the time series data are used for evaluating the model. K-fold cross-validation was employed with a value of 10 for k. 70% of the data was used for training purposes, 20% for testing, and 10% for validation. For the $k$ – step Diffusion convolution process, a 3-hop neighborhood of each station was considered and repeated 200 times during the training process to get the best suitable state. The encoder and decoder have 2 recurrent layers, each with 64 units. The experimental setup details is given in Table 9. The STCOP-DCRNN model was evaluated using the Mean absolute error (MAE), Root Mean Square Error (RMSE), and Mean Accuracy Percentage error (MAPE) metrics. The mean absolute error (MAE) measures the mean error between the ground truth and the predicted value. The RMSE tells the data distribution around the mean and indicates how well the model fits the data. The MAPE measures the accuracy of the model; the accuracy is recorded in terms of percentage. Formulas of these loss functions are given in Eqs (5)–(7):

\begin{aligned} M A E & = \frac{1}{n} \sum_{i = 1}^{n} | g_{i} - p_{i} | \end{aligned}

(5)

\begin{aligned} R M S E & = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} (g_{i} - p_{i})^{2}} \end{aligned}

(6)

\begin{aligned} M A P E & = \frac{1}{n} \sum_{i = 1}^{n} | \frac{g_{i} - p_{i}}{g_{i}} | \end{aligned}

(7)

Where $n$ is the total number of values, $g_{i}$ is the ground truth value and $p_{i}$ is the predicted value.

Table 9

Experimental settings.

Parameter	Value
Number of event instances	28
Pollutant	PM_2.5
Weather	AT, RH and WS
Time interval(h)	1
Training set	70%
Validation set	10%
Test set	20%
K-fold cross validation	10 fold
Prediction length ( $T^{'}$ , h)	[1,6,12,18,24]
History length ( $T$ , h)	24
Number of stations	28
Loss function	RMSE, MAE, MAPE

6. Result analysis

In this section the Result obtained by baseline methods and proposed STEEP is analysed.

6.1. Baseline methods

The baseline methods used for evaluating the proposed STEEP are explained in this section.

Linear Regression (LR): The linear relationship between input values and predicted values is analyzed by the LR. An autocorrelation exists among the predictions, i.e., the value of $X_{t + 1}$ is dependent on $X_{t}$ . This method works well for linear data. Autocorrelation among the data and some lag variables are used for time series analysis.

Gradient Boosting Machines (GBM): This model can find linear patterns that LR cannot discover. This algorithm aims to reduce errors by adding a weak learner to the tree-based method through a gradient descent-like procedure. At each step, a new weak learner is added to minimize the error leaving the old ones unchanged.

LSTM: They are unique forms of RNN that are specialized in handling the long-term dependencies problem. The LSTMs can remember information for a longer period of time, thus, suitable for sequence data and time series prediction.

DCRNN: This model uses the geographic distance between the stations to model a graph for spatial dependency. The distance between monitoring stations is recorded as edge weight between the nodes. The diffusion convolution recurrent neural network uses a sequence-to-sequence encoder-decoder architecture to predict time series [26].

GC-DCRNN: This model is an extension of the DCRNN. Here the similarity between the stations is computed based on the geographic factors surrounding the monitoring station to represent the spatial dependency [35].

Table 10
The comparative results of different models for predicting PM_2.5 values.

Horizon Metric LR GBM LSTM DCRNN GC-DCRNN STEEP

$h =$ 1 MAE 16.53 18.62 17.72 16.68 16.30 16.10

RMSE 36.37 38.44 38.70 39.20 37.10 35.33

MAPE% 0.25 0.24 0.24 0.25 0.23 0.23

$h =$ 6 MAE 30.20 31.50 31.15 30.75 29.53 28.08

RMSE 54.50 55.7 56.00 55.20 53.78 51.44

MAPE% 0.38 0.42 0.43 0.41 0.38 0.37

$h =$ 12 MAE 40.81 41.50 40.51 41.25 39.24 37.68

RMSE 66.12 69.50 70.00 68.21 67.37 64.97

MAPE% 0.50 0.52 0.54 0.53 0.49 0.48

$h =$ 18 MAE 48.02 50 49.58 48.66 47.38 45.68

RMSE 79.10 82.13 84.07 81.43 78.76 76.18

MAPE% 0.65 0.60 0.62 0.61 0.57 0.56

$h =$ 24 MAE 58 58.72 57.20 55.76 54.07 52.16

RMSE 90.22 92.05 94.01 93.51 88.35 85.25

MAPE% 0.73 0.74 0.75 0.70 0.66 0.66

Horizon	Metric	LR	GBM	LSTM	DCRNN	GC-DCRNN	STEEP
$h =$ 1	MAE	16.53	18.62	17.72	16.68	16.30	16.10
	RMSE	36.37	38.44	38.70	39.20	37.10	35.33
	MAPE%	0.25	0.24	0.24	0.25	0.23	0.23
$h =$ 6	MAE	30.20	31.50	31.15	30.75	29.53	28.08
	RMSE	54.50	55.7	56.00	55.20	53.78	51.44
	MAPE%	0.38	0.42	0.43	0.41	0.38	0.37
$h =$ 12	MAE	40.81	41.50	40.51	41.25	39.24	37.68
	RMSE	66.12	69.50	70.00	68.21	67.37	64.97
	MAPE%	0.50	0.52	0.54	0.53	0.49	0.48
$h =$ 18	MAE	48.02	50	49.58	48.66	47.38	45.68
	RMSE	79.10	82.13	84.07	81.43	78.76	76.18
	MAPE%	0.65	0.60	0.62	0.61	0.57	0.56
$h =$ 24	MAE	58	58.72	57.20	55.76	54.07	52.16
	RMSE	90.22	92.05	94.01	93.51	88.35	85.25
	MAPE%	0.73	0.74	0.75	0.70	0.66	0.66

Table 11

Comparison of running time for each model.

S. No	Model name	Total duration (minutes)
1	LR	0.54
2	GBM	3.13
3	LSTM	5.74
4	DCRNN	9.20
5	GC-DCRNN	13.43
6	STEEP	15.37

Table 11 gives the running time for each model in terms of minutes. It can be observed that the proposed STEEP model takes more time as it involves a pattern mining procedure followed by a time series prediction. But this concern can be overlooked as it gives better result in terms of MAE, RMSE and MAPE as seen in Table 10.

Figure 5.

MAE, RMSE, MAPE graph visualization.

Figure 6.

Graph constructed for the DCRNN model.

6.2. Discussion

This section evaluates the results obtained by the proposed STEEP for forecasting PM_2.5 values in Delhi. The PM_2.5, AT, RH, and WS data for 2019–2020 were used along with the C-STCOP patterns. The patterns were modelled into a graph, as explained in Section 4.2. Figure 4 shows the undirected graph constructed using the ST patterns obtained from the C-STCOP method.

The stations involved in the graph and the number of edges from each node or station is shown in Figure 4. It can also be observed that a few stations don’t have any edges, irrespective of nearness to neighboring stations. DwarkaSector8, Mundka, Narela, Patparganj, SoniaVihar, and VivekVihar are the stations that have no association with other stations as per the Spatio-temporal patterns generated by the C-STCOP algorithm. It implies that the PM_2.5 values recorded in these stations are not synonymous with other stations concerning spatial and temporal closeness. These stations exhibit a unique behavior as they are immune to the spatial and temporal dependency property. Generally, the ST patterns show the association between stations, which frequently exhibit spatial and temporal dependency. But, the above-mentioned stations have edges in Figure 6 as the spatial distance is only used to construct them. The main reason these stations show such behaviour is that they are located on the outskirts of Delhi. The other reason could be their geographic property, population, flora, and fauna. Expert studies are required to further analyse the reason supporting this characteristic. These stations have edges in the graph generated by the DCRNN model using a thresholded geographic distance matrix. Figure 6 shows the graph generated using 10 km as the neighbor threshold for the DCRNN model. From the graph, it can be seen that all the stations are present as nodes, as they have some stations as neighbors. The C-STCOP patterns capture the spatio-temporal association between the neighbors per the PM_2.5 recorded; therefore, using these closed ST patterns as knowledge for time series forecasting will give better results, and Table 10 and Figure 5 proves this.

Comparison of the baseline models and the proposed STEEP with respect to forecasted results is shown in Table 10. The best results are highlighted in bold, and it can be observed that the proposed STEEP gives the best result compared to the baseline approaches. The proposed model generates low RMSE, MAE, and MAPE values compared to the baseline approaches as shown in Figure 5. This emphasizes the importance of using the ST patterns as knowledge in time series forecasting. The usage of ST patterns has led to a low error rate and accurate results compared to the existing models that use geographic context information like GC-DCRNN and DCRNN. Table 10 shows that the STEEP model performed better than the baseline models across all the horizons, with an improvement of 8%–13%. This clearly shows the proposed model’s ability to utilize the Spatio-temporal patterns in predicting PM_2.5 values across all the horizons.

7. Conclusion

The surge in the availability of historical air pollution data and sophisticated computing resources has led to the development of various air quality prediction models. This work proposed a deep-learning model for forecasting PM_2.5 pollutants. The proposed STEEP model incorporates spatio-temporal association among the monitoring stations. Also, this model integrates diffusion convolution and a gated recurrent unit (GRU) model. The Spatio-temporal association is captured by constructing a graph based on the patterns obtained from the C-STCOP algorithm. The STEEP model was initially trained to validate the network parameters, and later the test dataset justified it. The experimental results demonstrated that the proposed model surpasses the baseline models in forecasting PM_2.5 value. The performance of the proposed model is better in forecasting across all horizons with respect to MAE, RMSE and MAPE. The STEEP achieves a consistent improvement of 8%–13% over the baseline approaches. The proposed model can be extended to use other types of ST patterns as knowledge in future studies.

Footnotes

Acknowledgments

This work was supported by the Council of Scientific & Industrial Research, India, under the scheme Direct- SRF with grant File No: 09/559(0141)/19-EMR-I.

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Spatio-temporal patterns assisted deep learning model for PM 2.5 prediction (STEEP)

Abstract

Keywords

1. Introduction

Table 1 Ambient air quality standard. Pollutants Time-weighted average The concentration of ambient air PM10 ( μ g/m3) 24 h 100 PM2.5 ( μ g/m3) 24 h 60 SO2 ( μ g/m3) 24 h 80 NO2( μ g/m3) 24 h 80 O3 ( μ g/m3) 8 h 100 CO (mg/m3) 8 h 02 NH3 ( μ g/m3) 24 h 400

3. Data

3.1. Study area

Table 5 Event modelling. Timestamp Event Latitude Longitude 02-01-2019 00:00 Alipur 28.79792 77.12327 03-01-2019 00:00 Alipur 28.79792 77.12327 04-01-2019 00:00 Alipur 28.79792 77.12327 20-01-2019 00:00 Anand Vihar 28.69177 77.13061 21-01-2019 00:00 Anand Vihar 28.69177 77.13061

4. Methodology

4.3.1. Diffusion convolution

6.1. Baseline methods

7. Conclusion

Footnotes

Acknowledgments

References

Table 5
Event modelling.

Timestamp Event Latitude Longitude

02-01-2019 00:00 Alipur 28.79792 77.12327

03-01-2019 00:00 Alipur 28.79792 77.12327

04-01-2019 00:00 Alipur 28.79792 77.12327

20-01-2019 00:00 Anand Vihar 28.69177 77.13061

21-01-2019 00:00 Anand Vihar 28.69177 77.13061