IEEE Computational Intelligence Magazine - November 2020 - 36

optimum training of an RNN using time
series analysis of the signals used in training.
To train a supervised Artificial Neural Network (ANN), one needs to decide the features
and labels to be used for training. Here we discuss how these features and labels can be
selected systematically. As stated earlier, we
hypothesise that the number of confirmed cases of COVID-19
is a function of the variability of environmental conditions
(temperature and humidity), and the measures put in place by
the jurisdictions to control the spread of the virus (transmission
rates). The effectiveness of such measures is usually reflected by
the transmission rates varying with different lockdown phases.
As a result, there are four different time series introduced to the
training process in this paper: (1) temperature (T), (2) humidity
(H), (3) the number of confirmed cases (CC), and (4) the transmission rates (TR). Restated, this paper aims to construct an
RNN to predict the future number of CC signal based on its
previous observed numbers and the other aforementioned signals (T, H, and TR).

Before constructing an RNN, we propose to
pre-analyse the data to explore the nature of the
signals used for training.
and Tamil Nadu per day. As can be seen from the figures, the
transmission rate graphs resemble step functions. It is hypothesised that the effect of lockdown does not have immediate
effects on the transmission rate as it takes time for the entire
population to adapt their behaviour to the new set of rules. A
robust spline based smoothing technique is exploited to slightly
smooth these graphs. The so-called smoothing technique aims
at balancing the fidelity in the data by minimising the following goal function [21],
2
F ^St ^ t hh = St ^ t h - S ^ t h + rP ^St ^ t hh, 	(2)

	

where S(t) and St (t) represent respectively the original and
smoothed signals, and P (St (t)) is a penalty term that reflects the
roughness of the obtained smoothed signal (St (t)). The real positive scalar parameter r is the smoothing factor that controls the
degree of smoothness in St (t). A smoothing factor of r = 10
has been used to this end. Figures 2(c) and 2(d) show the
smoothed graphs of transmission rates for Maharashtra and
Tamil Nadu, respectively.
III. Signal Pre-Processing

This section presents the procedure of the proposed method,
aiming to obtain a computational model that can forecast the
number of confirmed cases of the COVID-19 in Maharashtra
and Tamil Nadu. RNN has been widely used for time series
forecasting; in this section we propose a novel framework for

A. Time Series Analysis of Features

Before constructing an RNN, we propose to pre-analyse the
data to explore the nature of the signals used for training. Since
the signals used in this paper have a stochastic nature, their stationary or non-stationary behaviour is first processed in this
section. This will result in more accurate training and ensure
much better prediction results. First, a brief definition of the
stationary and non-stationary time series is presented.
The first order autoregressive process AR(1) of a signal S(t)
is shown as
s t = z s t - 1 + e t (3)

	

where e t is a stationary white Gaussian noise process. Three
different scenarios can occur for the above AR(1) model: 1)

4,000

2,500
2,000

3,000

Confirmed Cases

No. of Confirmed Cases

3,500

2,500
2,000
1,500
1,000

1,500
1,000
500

500
0

0

10

20

30

40 50
Day
(a)

60

70

80

0

0

10

20

30

40 50
Day
(b)

60

70

80

FIGURE 1 The number of daily new confirmed cases of COVID-19 in Maharashtra and Tamil Nadu as of 24 March, 2020. (a) Maharashtra.
(b) Tamil Nadu.

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IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2020
IEEE Computational Intelligence Magazine - November 2020

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