# Energy-Efficient Respiratory Anomaly Detection in Premature Newborn Infants

Ankita Paul1 1 Department of Electrical and Computer Engineering, Drexel
University, Philadelphia, PA 19104
2 Department of Mathematics and Computer Science, Ursinus College,
Collegeville, PA 19426  Md. Abu Saleh Tajin1 1 Department of Electrical and
Computer Engineering, Drexel University, Philadelphia, PA 19104
2 Department of Mathematics and Computer Science, Ursinus College,
Collegeville, PA 19426  Anup Das1 1 Department of Electrical and Computer
Engineering, Drexel University, Philadelphia, PA 19104
2 Department of Mathematics and Computer Science, Ursinus College,
Collegeville, PA 19426  William Mongan2 and Kapil Dandekar1 1 Department of
Electrical and Computer Engineering, Drexel University, Philadelphia, PA 19104
2 Department of Mathematics and Computer Science, Ursinus College,
Collegeville, PA 19426

###### Abstract

Precise monitoring of respiratory rate in premature newborn infants is
essential to initiating medical interventions as required. Wired technologies
can be invasive and obtrusive to the patients. We propose a Deep Learning
enabled wearable monitoring system for premature newborn infants, where
respiratory cessation is predicted using signals that are collected wirelessly
from a non-invasive wearable Bellypatch put on the infant’s body. We propose a
five-stage design pipeline involving data collection and labeling, feature
scaling, deep learning model selection with hyper parameter tuning, model
training and validation, and model testing and deployment. The machine
learning model used is a 1-D Convolutional Neural Network (1DCNN) architecture
with 1 convolution layer, 1 pooling layer, and 3 fully-connected layers,
achieving 97.15% classification accuracy. To address energy limitations of
wearable processing, several quantization techniques are explored and their
performance and energy consumption are analyzed for the respiratory
classification task. Results demonstrate a reduction of energy footprints and
model storage overhead with a considerable degradation of the classification
accuracy, meaning that quantization and other model compression techniques are
not the best solution for respiratory classification problem on wearable
devices. Hence,to improve classification accuracy, yet reduce the energy
consumption we propose a novel Spiking Neural Network (SNN)-based respiratory
classification solution, which can be implemented on event-driven neuromorphic
hardware platforms. To this end, we propose an approach to convert the analog
operations of our baseline trained 1DCNN to their spiking equivalent. We
perform a design-space exploration using the parameters of the converted SNN
to generate inference solutions having different accuracy and energy
footprints. We select a solution that achieves an accuracy of 93.33% with 18x
lower energy compared to the baseline 1DCNN model. Additionally, the proposed
SNN solution achieves similar accuracy as the quantized model with a 4x lower
energy.

###### Index Terms:

Wearable, Respiratory Classification, Deep Learning, Spiking Neural Network
(SNN)

##  I Introduction

A premature newborn infant is one who is born more than three weeks before the
estimated due date. Common health problems of these infants include Apnea of
Prematurity (AOP), which is a pause in breathing for 15 to 20 seconds or more
[1] and Neonatal Respiratory Distress Syndrome (NRDS), which is shallow
breathing and a sharp pulling in of the chest below and between the ribs with
each breath [2]. Precise respiratory monitoring is often necessary to detect
AOP and NRDS in premature newborn infants and initiate medical interventions
as required [3]. Wired monitoring techniques are invasive and can be obtrusive
to the patient.Therefore, non-invasive respiratory monitoring techniques are
recommended by pediatricians to increase comfort of infants and facilitate
continuous home monitoring [4].

We study the use of wearable technologies in respiratory monitoring of
infants. To this end, we use the Bellypatch (see Fig. 1), a wearable smart
garment that utilizes a knitted fabric antenna and passively reflects wireless
signals without requiring a battery or wired connection [5, 6, 7]. The
Bellypatch fabric stretches and moves as the infant breathes, contracts
muscles, and moves about in space; the physical properties of the radio
frequency (RF) energy reflected by the antenna change with these movements.
These perturbations in RF reflected properties enable detection and estimation
of the infant’s state, including respiration rate [8], heart rate [9],
movement of the extremities [10], and detection of diaper moisture [11].

Figure 1: (left) A smart-fabric Bellyband and (right) Bellypatch can be
integrated into wearable garments to enable wireless and passive biomedical
monitoring in infants.

The Bellypatch operates in the 900 MHz Industrial, Scientific, and Medical
(ISM) frequency band using Radio Frequency Identification (RFID)
interrogation. An RFID interrogator emits an interrogation signal multiple
times per second (often 30-100 interrogations per second). In typical RFID
technology deployments, only a single interrogation response is needed for
inventory purposes; however, many interrogations are sent to overcome
collisions among the responding RFID tags and other signal interference or
loss. We exploit this redundant interrogation to sample the state of the
antenna each time it is successfully interrogated. Specifically, we observe
changes in the received signal strength indicator (RSSI), phase angle, and
successful interrogation rate to estimate respiratory properties of the
wearer’s state as well as other biosignals. The use of passive RFID enables a
wireless and unobtrusive wearable device that requires no batteries to
operate; the interrogation signal itself is sufficient to power the worn RFID
tag for each interrogation. However, path loss, multipath fading, and
collision mitigation among the tags in the field require signal denoising and
interpolation of the received signal as well as intelligent algorithms for
signal processing and estimation. Because these biomedical estimates require
real-time or near-real-time processing, and may take place on low-power
embedded or portable systems, it is desirable to utilize techniques that place
minimal constraints on power consumption, online training, and processing
latency.

To this end, we propose a deep learning-enabled respiratory classification
approach. At the core of this approach is a five stage pipeline involving data
collection and labeling, feature selection, deep learning model selection with
hyper parameter optimization, model training and validation, and model testing
and deployment. We use a Laerdal SimBaby programmable infant mannequin (see
Figure 1) to collect respiratory data using the sensors attached on the
Bellypatch. We use a 1-D Convolutional Neural Network (1DCNN) for
classification of the features extracted from the SimBaby sensor data. The
1DCNN model consists of 1 convolution layer, 1 polling layer, and 3 fully-
connected layers, achieving 97.15% classification accuracy (see Section VI-A).
This is higher than state-of-the-art accuracy obtained using machine learning
techniques such as Support Vector Machine (SVM), Logistic Regression (LR), and
Random Forest (RF), all of which are proposed for respiratory classification
of infants. Hyper parameters of this 1DCNN model are selected using a Grid
Search method, which is discussed in Section III-D and the model parameters
are trained using the Backpropagation Algorithm [12].

We show that the energy consumption of our baseline 1DCNN model is
considerably higher, which makes it difficult to implement the same on the
Bellypatch due to its limited power availability. Therefore, we propose
several quantization approaches involving limiting the bit-precision of the
model parameters. We show that in order to achieve a significant reduction in
energy, the model accuracy can be considerably lower. Therefore, model
quantization may not be the best solution to implement respiratory
classification on the Bellypatch.

Finally, we propose a novel Spiking Neural Network (SNN) [13] enabled
respiratory classification solution, which can be implemented on event-driven
neuromorphic hardware such as TrueNorth [14], Loihi [15], and DYNAPs [16]. We
perform design-space exploration using SNN parameters, obtaining SNN solutions
with different accuracy and energy. We select a solution that leads to 93.33%
accuracy with 18x lower energy than the baseline 1DCNN model. This SNN-based
solution has similar accuracy as the best performing quantized CNN model with
4x lower energy.

Overall, the SNN-based approach introduces two additional stages in our design
pipeline – model conversion and SNN parameter tuning, making the overall
approach, a seven-stage pipeline. Using this seven stage design pipeline, we
show that the accuracy is significantly higher than all prior solutions, with
considerably lower energy, making this solution extremely relevant for the
battery-less Bellypatch.

The remainder of this paper is organized as follows. Related works on
respiratory classification are discussed in Section II. The five-stage design
pipeline is described in Section III. Model quantization techniques are
introduced in Section IV. The SNN approach to respiratory classification is
formulated in Section V. The proposed approach is evaluated in Section VI and
the paper is concluded in Section VII.

##  II Related Work

Recently, machine learning-based respiratory classification techniques have
shown a significant promise as enabler for continuous respiratory monitoring
of newborn infants. To this end, a Support Vector Machine (SVM)-based
classifier is proposed in [17] achieving 82% classification accuracy. A
Logistic Regression-based classifier is proposed in [18] achieving
classification accuracy of 87.4%. An Ensemble Learning with Kalman filtering
is proposed in [18] achieving 91.8% classification accuracy. All these
techniques are proposed for respiratory classification using pulseoximeter
data collected from infants, making these approaches relevant state-of-the-art
for our work. In Section VI, we compare our approach to these state-of-the-art
approaches and show that the proposed approach is considerably better in terms
of both classification accuracy and energy. Thermal imaging is also proposed
recently for repiratory classicication from infant [19]. The authors reported
a precision and recall score of 0.92. We achieve a score of 0.98. Respiratory
classification using acoustic sensors are proposed in [20]. An accuracy of
95.7% is reported. We achieved an accuracy of 97.15%.

Beyond respiratory classification, deep learning enabled techniques have been
used extensively for health informatics [21]. For instance, sleep apnea
classification is proposed using deep convolutional neural network (CNN) and
long short term memory (LSTM) in [22], achieving an accuracy of 77.2%. A deep
learning approach using InceptionV3 CNN model is proposed in [23] to detect
Alzheimer disease using brain images. Authors reported an area-under-curve
(AUC) score of 0.98. CNN models are used in [24] to detect metastatic breast
cancer in women. Authors reported an AUC score of 0.994. A CNN-based
Arrhythmia classification is proposed in [25]. Authors reported significant
improvement in classification accuracy over state-of-the-art.

Finally, many recent SNN-based techniques have shown comparable and in some
case, higher accuracy than their deep learning counterparts with significantly
lower energy. An unsupervised SNN-based heartrate estimation is proposed in
[26]. Authors reported 1.2% mean average percent error (MAPE) with 35x
reduction in energy. A spiking CNN architecture is proposed in [27] to
classify heart-beats in human. Authors reported 90% reduction in energy with
only 1% lower accuracy than a conventional CNN. SNN-based epileptic seizure
detection is proposed in [28]. Authors reported an accuracy of 97.6% with a
considerable reduction in energy.

To the best of our knowledge, this is the first work that uses SNN for
respiratory classification in infants and show that SNNs can achieve high
accuracy (93.33% in our evaluation) with a considerable reduction in energy
(18x lower energy).

##  III Design Pipeline

Figure 2 shows a high-level overview of the proposed respiratory
classification approach using Deep Learning techniques. The design pipeline
comprises of five stages – 1) data collection, 2) feature selection, 3) deep
learning model selection, 4) model training and validation, and 5) model
testing and deployment. These stages are clearly indicated in the figure. Once
a trained model is obtained using this approach, the model is used for
respiratory classification of streaming pulseoximeter data collected from the
sensors on the Bellypatch. This is shown at the bottom-left corner of Figure
2.

Figure 2: Design pipeline for respiratory classification using Deep Learning.

In the following, we describe the design pipeline stages.

###  III-A Data Collection and Labeling

####  III-A1 Data Collection

In this work, we use a Laerdal SimBaby programmable infant mannequin. The
mannequin was programmed to breathe at a rate of 31 breaths per minute for
variable time intervals, then to stop breathing for 30 seconds, 45 seconds,
and 60 seconds, alternating between these states for a period of one hour. An
RFID investigator (Impinj Speedway R420) was used to poll the Bellypatch
wearable RFID tag and the antenna with a 900 MHz band RFID signal coming from
the SimBaby. The RFID interrogator was also used to measure properties of the
backscattered signal reflected from the RFID tag. The interrogator was
positioned 1 feet from the mannequin, oriented above, astride, and at the
feet. Interrogations were performed with a frequency of 90 Hz. RFID properties
considered for model features include the Received Signal Strength Indicator
(RSSI), phase angle, Doppler shift, interrogation frequency, and timestamp.

Each of these properties is affected in-band by the frequency of the original
signal emitted by the interrogator. Under United States Federal Communications
Commission (FCC) regulations, RFID interrogations must iterate (or channel
hop) over 50 frequency channels in the 900 MHz band. In addition to perturbing
the raw measurement observations at the interrogator, channel hopping poses
challenges in computing higher order features from changes in the observed
phase, because these features depend on observing changes in successive values
of the phase under the assumption that they were observed from the same
interrogation frequency. As a result, the observed Doppler shift is used to
identify fine movements of the RFID tag, either in space or because of a
strain force applied to the surrounding knit antenna.

The received signal strength from an interrogation is influenced by several
factors as defined by the Radar Cross Section (RCS) formula in Equation 1
[29]. Specifically, the RCS relates changes in received signal power
($P_{Rx}$) to the interrogation power ($P_{Tx}$), the reader and tag gains
($G_{reader}$ and $G_{tag}$, respectively), the return loss (R), and the
interrogation wavelength $\lambda$ [18].

$\footnotesize P_{Rx}=P_{Tx}\cdot G_{reader}^{2}\cdot G_{tag}^{2}\cdot
R\cdot\left(\frac{\lambda}{4}\cdot\pi\cdot r\right)^{4}$ (1)

Some of these terms can be controlled by the interrogator configuration: for
example, the interrogation transmitter power and antenna reader gain at the
interrogator; however, the interrogation frequency changes due to channel
hopping, and the receiving antenna gain ($G_{tag}$) changes as the wearer
stretches the antenna or moves about in space. Thus, the observed RSSI alone
confounds several artifacts about the state of the transmission along with the
state of the wearer. As a result, a higher order feature $\zeta$ is computed
from the RSSI measure by accounting for the interrogation frequency.

We manipulate the RCS equation to arrange those terms related to wearer state
on one side, and set them equal to those terms related to the interrogator
configuration, as shown in Equation 2. Thus, we observe that the changes in
the gain of the tag $G_{tag}$ (resulting from movement or a strain force on
the antenna), the distance r between the interrogator and the tag (resulting
from movement), and return loss $R$ (resulting from movement, strain force,
fading or multipath interference) are proportional to the interrogation
wavelength lambda and observed $RSSI$ measure $P_{Rx}$, along with the
interrogation power $P_{Tx}$ and the reader gain $G_{reader}$, which are held
constant at the interrogator and interrogating antenna [5]. We define $\zeta$
as the terms of RCS model indicative of the changes in the tag, such as
movement, strain force, or interference.

$\zeta=G_{tag}^{-2}\cdot r^{4}\cdot R^{-1}=P_{Tx}\cdot G_{reader}^{2}\cdot
P_{Rx}^{-1}\cdot\left(\frac{\lambda}{4\pi}\right)^{4},$ (2)

We remove a residual term
$\delta=-10log_{10}\frac{f^{4}}{(f-(0.5*10^{6}MHz))^{4}}\approx-0.00941$ to
compensate for a sawtooth artifact resulting from quantization of the observed
RSSI as the interrogation frequency changes among 50 discrete channels per FCC
regulations in the United States.

In summary, we chose the following features for consideration during wireless
respiratory state classification.

  * •

Feature 1: Reflected signal strength as measured at the interrogator, $\zeta$
(RSSI)

  * •

Feature 2: Tag velocity as a function of the observed Doppler shift at the
interrogator ($P_{Rx-deoscillated}$)

We normalized RFID signal strength (RSSI) data by frequency and calculated the
tag velocity to utilize the signal for respiratory analysis. The resulting
time-series data was filtered, and signal processed to determine the mean
power spectral density, derived from the amplitude of the oscillatory behavior
observed in the signal during short time windows.

Figure 3 illustrates the two features ($P_{Rx-deoscillated}$ and RSSI) over a
time window of 1.2 seconds.

Figure 3: Variation of the two features for 1.2 seconds.

####  III-A2 Data Labeling

In case of supervised learning of human-activity recognition from sensor data
it is necessary to appropriately label the output. The dataset contained
approximately 1685 samples per minute, obtained for 60 minutes resulting in
approximately 1 sample generated every 0.03 seconds. This indicated that the
RFID interrogation frequency was approximately 28 Hz per RFID tag. For each
sample we have two features — RSSI and $P_{Rx-deoscillated}$ .

The observations were broken into time windows of 1 second with no overlap.
Hence, each time window contained approximately 28 samples, with two sets of
observations from the 2 features. We manually labeled the data collected from
the two features as ‘1’ when the SimBaby is in breathing state and ‘0’ when it
is in a non-breathing state. Over a period of one hour, we collect and label
the dataset to form train and test samples representing binary respiratory
state (1: Breathing, 0: Non- Breathing state). Figure 4 shows the respiratory
state corresponding to the features of Figure 3 for 1.2 seconds.

Figure 4: Respiratory state corresponding to features shown in Fig. 3.

Since there are only two features and two output classes, the problem we aim
to solve is a bivariate time series binary classification one.

###  III-B Feature Scaling

From the time series features extracted from each time window we apply feature
engineering to make the input vectors suitable for the classifier. For
multivariate data, it is necessary to transform features with different scales
to have uniform distribution, to ensure optimal performance of the
classifiers. We first cleaned our feature set by filtering the missing values
(NaN). The data with the features and the labels were loaded from two csv
files and then we split the dataset 3:1 to form the training set and the
testing set. After splitting the dataset, we scale the features before we fit
it into our classifier, which is a one dimensional convolutional neural
network (1DCNN).

The two features in our dataset were scaled to a standard range, the
distribution of the values was rescaled, so the mean was 0 and the standard
deviation was 1. The method involved determining the distribution of each
feature and subtracting the mean from each feature. Then we divide the values
(after the mean has already been subtracted) of each feature by its standard
deviation.

The standard score ($Z$) of a sample is given by Equation 3.

$Z=\frac{x-\mu}{\sigma},$ (3)

where $x$ is the sample value, and $\mu$ and $\sigma$ are the mean and
standard deviation of all the samples, respectively. Feature standardization
transforms the raw values into the standard scale that helps the model to
extract salient signal information from the observations. After rescaling the
variables, we reshape the data according to dimension expected by the
convolution layer of the 1DCNN model.

###  III-C Deep Learning Model Selection

A Convolution Neural Network (CNN) is a class of deep learning that uses a
linear operation called convolution in at least one of their layers. Equation
4 represents a convolution operation, where $x$ is the input and $w$
represents the kernel, which stores parameters for the model. The output $s$
is called the feature map of the convolution layer.

$\footnotesize s(t)=\int x(a)w(t-a)da$ (4)

In CNN, the first layer is a convolution layer that accepts a tensor as an
input with dimensions based on the size of the data [30]. The second layer, or
the first hidden layer, is formed by applying a kernel or filter that is a
smaller matrix of weights over a receptive field, which is a small subspace of
the inputs. Kernels apply an inner product on the receptive field, effectively
compressing the size of the input space [12]. As the kernel strides across the
input space, the first hidden layer is computed based on the weights of the
filter. As a result, the first hidden layer is a feature map formed from the
kernel applied on the input space. While the dimension of the kernel may be
much smaller in size compared to the initial inputs of the convolution layer,
the kernel must have the same depth of the input space. The inputs and
convolution layers are often followed by rounds of activation, normalization,
and pooling layers [12]. The precise number and combination of these layers
are specific to the problem at hand.

For the proposed respiratory classification problem, our CNN model consists of
one convolution layer, which is activated by a rectified linear unit (ReLU).
The filter size is set to 64 and the kernel size to 1. This layer is followed
by a one dimensional Max Pooling layer with a pool size and stride length of
1, each. The next layer is a Flattenning layer followed by a Dropout layer.
The Dropout layer randomly sets input neurons to 0 with a rate of 0.01 at each
step during training time. This is done to prevent overfitting. The dropout
layer is followed by two fully connected hidden layers. The first hidden layer
consists of 200 neurons with ReLU activation, the second hidden layer contains
100 neurons with a Softmax activation function. Overall, the proposed CNN
model uses one-dimensional convolutions and therefore, this model is referred
to as 1DCNN. Figure 5 shows the proposed 1DCNN architecture along with the
dimension of each layer.

Figure 5: Our proposed 1DCNN architecture.

###  III-D Hyperparameter Optimization

In a CNN, the parameters in each layer whose values control the learning
procedure are called hyperparameters. Grid search is a hyperparameter tuning
technique that can build a model for every new combination of hyperparameters
that are specified in the search space and evaluates each model for that
combination. A machine learning algorithm $A_{\theta}$ can estimate a model
$M_{\theta}\in M$ that minimizes a loss function $\mathcal{L}$ with its model
regularization term $\mathcal{R}$ given by

$\footnotesize A_{\theta}(X_{\text{train}})=\underset{M_{\theta}\in
M}{\texttt{argmin}}\mathcal{L}(M_{\theta},X_{\text{train}})+\mathcal{R}(M_{\theta},\theta),$
(5)

where $X_{\text{train}}$ is the training dataset, $M$ is the set of all
models, $\theta\in\Theta$ is the chosen hyperparameter configuration, and
$\Theta=\\{\Theta_{1},\Theta_{2},\cdots,\Theta_{p}\\}$ is the p-dimensional
hyperparameter space of the algorithm. The optimal hyperparameter
configuration $\theta^{*}$ is calculated using the validation set as

$\footnotesize\theta^{*}=\underset{\theta\in\Theta}{\texttt{argmin}}\mathcal{L}(A_{\theta}(X_{\text{train}},X_{\text{validation}})=f_{D}(\theta),$
(6)

where $X_{\text{validation}}$ is the validation set and $f_{D}$ is the
misclassification rate.

The Grid search exhaustively searches through a grid of manually specified set
of parameter values provided in a search space to find the accuracy obtained
with each combination. We tuned the model based on the number of epochs
(ranging from 10 to 100) and the learning rate for the Adam optimizer (0.001,
0.01, 0.1, 0.002, 0.02, 0.2, 0.003, 0.03, 0.3). We evaluated the accuracy as a
performance metric for the different combinations. Figure 6 shows the
hyperparameter selection using Grid search, where the accuracy is reported for
different combinations of epochs and learning rate [31].

Figure 6: Hyperparameter selection.

Table I summarizes the hyperparameters of the 1DCNN.

TABLE I: Summary of hyperparameters for the proposed 1DCNN model. Learning rate |  0.001
---|---
Batch size |  5
Optimizer |  Adam
Data shuffle |  per epoch
Maximum epochs |  100

###  III-E Model Training and Validation

We trained our 1DCNN model with 75,834 samples and used repeated k-fold cross-
validation with 10 splits to validate our model performance. To improve the
estimated performance, we repeated the cross-validation procedure multiple
times and reported the mean result across all folds from all runs. This mean
accuracy reported is expected to be a more accurate estimate of the true
unknown underlying mean performance of the model on the dataset instead of a
single run of k-fold cross-validation ensuring less statistical noise. We also
compute the standard error that provides an estimate of a given sample size of
the amount of error that is expected from the sample mean to the underlying
and unknown population mean. The standard error is calculated as

$\sigma_{\text{error}}=\frac{\sigma}{\sqrt{n}},$ (7)

where $\sigma$ is the sample’s standard deviation and $n$ is the number of
repeats. We obtained a validation classification accuracy of 87.78% with a
standard error of 0.002 (see Section VI for detailed evaluation). We defined
Early Stopping as a regularization technique at the very beginning of
declaring the model architecture. At end of every epoch the training loop
monitors whether the validation loss is no longer decreasing and once it is
found no longer decreasing, the training is terminated. We enabled the
patience parameter equal to 5 to terminate the training after epochs of no
validation loss decrease. This is another measure to prevent the model from
overfitting during training, alongside the addition of a Dropout layer.
Without Early Stopping the training would terminate only after the maximum
number of epochs is reached.

###  III-F Model Testing and Deployment

We deployed the trained model to test the performance on an unseen test set
generated from the simbaby to classify the respiratory states. The model was
tested on 25,279 samples and achieved an accuracy of 97.15%, F1 Score of 0.98,
AUC score of 0.98, sensitivity score of 0.96 and specificity score of 0.99.
These performance metrics are defined in Section VI-A.

##  IV Model Quantization

CNN models consume a considerable amount of energy due to their high
computational complexity. The high energy consumption is due to the large
model size involving several thousand parameters. It is therefore challenging
to deploy the inference, i.e., a trained CNN model on battery-powered mobile
devices, such as smartphones and wearable gadgets due to their limited energy
budget. To address this high energy overhead, energy-efficient solutions have
been proposed to reduce the model size and computational complexity. Some
common approaches include pruning of network weights [32] and low bit
precision networks [33]. We focus on the latter techniques. Specifically, we
implement both bit precision weights and activations to reduce model sizes and
computational power requirements. To perform the training of a CNN with low-
precision weights and activations we use the following quantization function
to achieve a k-bit quantization [34].

$Z_{q}=Q(Z_{r})=\frac{1}{2^{k}-1}\texttt{round}\left((2^{k}-1)Z_{r}\right),$
(8)

where $Z_{r}\in[0,1]$ is the full precision value and $Z_{q}\in[0,1]$ is the
quantized value obtained using the k-bit quantization.

The quantization of weights is given by

$w_{q}=Q\left(\frac{\texttt{tanh}(w_{r})}{2\cdot\texttt{max}\left(|\texttt{tanh}(w_{r})|\right)}+\frac{1}{2}\right),$
(9)

where $w_{r}$ is the original weight using full precision and $w_{q}$ is the
quantized value using k-bit quatization.

The quantization of activations is given by

$x_{q}=Q\left(f(x)\right),$ (10)

where $f(x)=\texttt{clip}(x_{r},0,1)$ is the clip function bounding the
activation function between 0 and 1.

In this paper we apply both bit precision techniques for both weights and
activations using quantization with the QKeras library, which is a
quantization extension to the Keras [35]. It enables a drop-in replacement of
layers that are responsible for creating parameters and activation layers like
the Conv 1D, Dense layers. It facilitates arithmetic calculations by creating
a deeply quantized version of a Keras model. We tag the variables, weights and
biases created by the Keras implementation of the model and the output of
arithmetic layers, by quantized functions. Quantized functions are specified
as layer parameters and then passed as a cumulative quantization and
activation function, QActivation. The quantized bits quantizer used above
performs mantissa quantization using the following equation.

$\displaystyle\text{mantissa quantization}=$ (11) $\displaystyle
2^{b-k+1}\cdot\texttt{clip}\left(\texttt{round}(x_{r}\cdot
2^{k-b-1}),-2^{k-1},2^{k-1}-1\right)$

where $x$ is the input given to the model, $k$ is the number of bits for
quantization, and $b$ specifies how many bits of the bits are to the left of
the decimal point.

We conduct our experiment to perform quantization of our Conv1D model using 2
bits, 4 bits, 8 bits, 16 bits, 32 bits and 64 bits. We observe the performance
accuracy increase with the increase of the quantization bits, with 2 bits
achieving an 88.93% compared to using all the 64 bits achieving 97.15% (see
the detailed results in Section VI-B).

The QTools functionality is used to estimate the model energy consumption for
the different bit-wise quantization implementations. It estimates a layer wise
energy consumption for memory access and MAC operations in a quantized model
derived from QKeras. This is helpful when comparing power consumption of more
than one models running on the same device. The model size is calculated as
the number of model parameters multiplied by the number of bits used in each
scenario. We observe that when we increase in the number of bits, the model
size increases, the accuracy increases but also does the consumption of energy
(pJ). This homogeneous replacement technique of Keras layers, with
heterogeneous per-layer, per-parameter type precision, chosen from a wide
range of quantizers, enabled quantization-aware training and energy-aware
implementation to maximize the model performance given a situation of resource
constraints, like detection of respiratory cessation on premature infants in
critical care conditions, which is crucial for high-performance inference on
wearables.

##  V SNN-Based Respiratory Classification

Spiking Neural Networks (SNNs), also known as the third generation of neural
networks, are interconnection of integrate-and-fire neurons that emulate the
working principle of a mammalian brain [13]. SNNs enable powerful computations
due to their spatio-temporal information encoding capabilities. In an SNN,
spikes (i.e., current) injected from pre-synaptic neurons raises the membrane
voltage of a post-synaptic neuron. When the membrane voltage crosses a
threshold, the post-synaptic neuron emits a spike that propagates to other
neurons. Figure 7 shows the integration of spike train from four pre-synaptic
neurons connected to a post-synaptic neuron via synapses.

Figure 7: Integration of spike trains at the post-synaptic neuron from four
pre-synaptic neurons in a Spiking Neural Network (SNN). Each spike is a
voltage waveform of ms time duration.

SNNs can implement many machine learning approaches such as supervised,
unsupervised, reinforcement, few-shot, and lifelong learning. Due to their
event-driven activation, SNNs are particularly useful in energy-constrained
platforms such as wearable and embedded system. Recent works demonstrate
significant reduction in memory footprint and energy consumption in SNN-based
heart-rate estimation [26], heartbeat classification [36, 27], speech
recognition [37], and image processing [38].

To integrate SNN-based respiratory classification into our design pipeline, we
introduce two additional stages – model conversion and SNN parameter tuning,
before the SNN model is deployed to perform classification from live data
collected from the SimBaby. Figure 8 shows the new design pipeline.

Figure 8: Seven stage pipeline, including the two new stages to process and
optimize the SNN model.

###  V-A Model Conversion

In this work, the 1DCNN architecture is converted to SNN in order to execute
it on a neuromorphic hardware such as Loihi [15]. The conversion steps are
briefly discussed below.

  1. 1.

_ReLU Activation Functions:_ This is implemented as the approximate firing
rate of a leaky integrate and fire (LIF) neuron.

  2. 2.

_Bias:_ A bias is represented as a constant input current to a neuron, the
value of which is proportional to the bias of the neuron in the corresponding
analog model.

  3. 3.

_Weight Normalization:_ This is achieved by setting a factor ${\lambda}$ to
control the firing rate of spiking neurons.

  4. 4.

_Softmax:_ To implement softmax, an external Poisson spike generator is used
to generate spikes proportional to the weighted sum accumulated at each
neuron.

  5. 5.

_Max and Average Pooling:_ To implement max pooling, the neuron which fires
first is considered to be the winning neuron, and therefore, its responses are
forwarded to the next layer, suppressing the responses from other neurons in
the pooling function. To implement average pooling, the average firing rate
(obtained from total spike count) of the pooling neurons are forwarded to the
next layer of the SNN.

  6. 6.

_1-D Convolution:_ The 1-D convolution is implemented to extract patterns from
inputs in a single spacial dimension. A 1xn filter, called a kernel, slides
over the input while computing the element-wise dot-product between the input
and the kernel at each step.

  7. 7.

_Residual Connections:_ Residual connections are implemented to convert the
residual block used in CNN models such as ResNet. Typically, the residual
connection connects the input of the residual block directly to the output
neurons of the block, with a synaptic weight of ‘1’. This allows for the input
to be directly propagated to the output of the residual block while skipping
the operations performed within the block.

  8. 8.

_Flattening:_ The flatten operation converts the 2-D output of the final
pooling operation into a 1-D array. This allows for the output of the pooling
operation to be fed as individual features into the decision making fully
connected layers of the CNN model.

  9. 9.

_Concatenation:_ The concatenation operation, also known as a merging
operation, is used as a channel-wise integration of the features extracted
from 2 or more layers into a single output.

We now briefly elaborate how an analog operation such as Rectified Linear Unit
(ReLU) is implemented using SNN. The output $Y$ of a ReLU activation function
is given by

$\footnotesize Y=\max{0,\sum_{i}w_{i}*x_{i}},$ (12)

where $w_{i}$ is the weight and $x_{i}$ is the activation on the
$i^{\text{th}}$ synapse of the neuron. To map the ReLU activation function, we
consider a particular type of spiking neuron model known as an Integrate and
Fire (IF) neuron model. The IF spiking neuron’s transfer function can be
represented as

$\footnotesize v_{m}(t+1)=v_{m}(t)+\sum_{i}w_{i}*x_{i}(t),$ (13)

where $v_{m}(t)$ is the membrane potential of the IF neuron at time $t$,
$w_{i}$ is the weight, and $x_{i}(t)$ is the activation on the $i^{\text{th}}$
synapse of the neuron at time $t$. The IF spiking neuron integrates incoming
spikes ($X_{i}$) and generates an output spike ($Y_{\text{spike}}$) when the
membrane potential ($v_{m}$) exceeds the threshold voltage ($v_{\text{th}}$)
of the IF neuron. Therefore, by ensuring that the output spiking rate
$Y_{\text{spike}}$ is proportional to the ReLU activation $Y$, i.e.,
$Y_{\text{spike}}\propto Y$, we accurately convert the ReLU activation to the
spike-based model. To further illustrate this, we consider the multi-layer
perceptron (MLP) of Figure 9a and its SNN conversion using rate-based encoding
(Figure 9b) and inter-spike interval (ISI) encoding (Figure 9c).

Figure 9: Example of converting an analog MLP to its spiking equivalent.
Figure 10: The NeuroXplorer framework [39].

In Figure 9a, neurons 1,2 and 3 are the input neurons and neurons 4 and 5 are
the output neurons. To keep the model simple, let us consider the case where
the activations of the input neurons 1,2 and 3 are equal to 1. Using Equation
12, we know that the output of neurons 4 and 5 are 0.6 and 0.3, respectively.
Figures 9b and 9c show the mapped SNN model, using rate-based and inter-spike
interval encoding schemes, respectively. In the rate-based model in Figure 9b,
the rate of spikes generated is expected to be proportional to the output of
neurons 4 and 5 in the MLP. In the case of the ISI-based SNN model, the inter-
spike interval of the spikes generated by neurons 4 and 5 is expected to be
proportional to the output generated in the MLP, as shown in Figure 9c.

###  V-B SNN Mapping to Neuromorphic Hardware

The SNN model generated using the conversion approach is analyzed in CARLsim
[40] to generate the following information.

  * •

_Spike Data:_ the exact spike times of all neurons in the SNN model.

  * •

_Weight Data:_ the synaptic strength of all synapses in the SNN model.

The spike and weight data of a trained SNN form the SNN workload, which is
used in the NeuroXplorer framework [39] to estimate the energy consumption.
Figure 10 shows the NeuroXplorer framework.

The framework inputs the 1DCNN model and estimates the accuracy and energy
consumption of the model on a neuromorphic hardware. Internally, NeuroXplorer
first converts the 1DCNN to SNN using the steps outlined in the before. It
then simulates the SNN using CARLsim. The extracted workload is first
decomposed using the decomposition approach presented in [41]. This is to
ensure that the workload can fit on to the resource-constraint hardware.

Typically, neuromorphic hardware are designed as tile-based architectures
[42], where each tile can accommodate only a limited number of neurons and
synapses. The tiles are interconnected using a shared interconnect such as
Network-On-Chip (NoC) [43] or Segmented Bus [44]. Therefore, to map an SNN
into a tile-based neuromorphic hardware, the model is first partitioned into
clusters, where each cluster consists of a proportion of the neurons and
synapses of the original machine learning model [45]. Each cluster can then
fit onto a tile of the hardware. Then the clusters are mapped to the tiles to
optimize one or more hardware metrics such as energy [46, 47], latency [48,
49, 50, 51, 52], circuit aging [53, 54, 55, 56, 57, 58], and endurance [59,
60, 61]. We use the energy-aware mapping technique of [47].

Once the clusters of the converted 1DCNN model is placed to the resources of
the neuromorphic hardware, we perform cycle-accurate simulations using
NeuroXplorer, configured to simulate the Loihi neuromorphic system. Table II
shows the hardware parameters that are configured in NeuroXplorer.

TABLE II: Major simulation parameters extracted from Loihi [15]. Neuron technology |  16nm CMOS (original design is at 14nm FinFET)
---|---
Synapse technology |  HfO2-based OxRRAM [62]
Supply voltage |  1.0V
Energy per spike |  23.6pJ at 30Hz spike frequency
Energy per routing |  3pJ
Switch bandwidth |  3.44 G. Events/s

###  V-C SNN Parameter Tuning

Unlike the baseline 1DCNN architecture, where model hyperparameters are
explored only during model training, SNNs allow parameter tuning on the
trained (and converted) model, such that the energy and accuracy space could
be explored to generate a solution that satisfies the given energy and
accuracy constraints of the target wearable platform. To explore such
exploration capabilities, we analyze the dynamics of SNNs.

The membrane potential of a neuron at time $t$ can be expressed as [13]

$u(t)=u_{0}+a\int_{0}^{t}D(s)\cdot w\cdot\sigma(t-s)ds,$ (14)

where $u_{0}$ is the initial membrane potential, $a$ is a positive constant,
$D(s)$ is a linear filter, $w$ is the synaptic weight and $\sigma$ represents
a sequence of $N$ input spikes, which can be expressed using the Dirac delta
function as

$\sigma(t)=\sum_{i=1}^{N}\delta(t-t_{i})$ (15)

The membrane potential of a neuron increases upon the arrival of an input
spike. Subsequently, the membrane potential starts to decay during the inter-
spike interval (ISI). When the neuron is subjected to an input spike train,
the membrane voltage keeps rising, building on the undissipated component.
When the membrane potential crosses a threshold ($V_{th}$), the neuron emits a
spike, which then propagates to other neurons of the SNN. The spike rate of a
neuron can be controlled using this threshold. If the threshold is set too
high, less spikes will be generated, meaning that the energy will be lower but
so is the accuracy because spikes encode information in SNNs. Therefore, by
adjusting the threshold, the design space of accuracy and energy can be
explored (see Section VI-C).

##  VI Results and Discussions

All simulations are performed on a workstation, which has AMD Threadripper
3960X with 24 cores, 128 MB cache, 128 GB RAM, and 2 RTX3090 GPUs. Keras [35]
is used to implement the baseline 1DCNN, which uses TensorFlow backend [63].
QKeras [64] is used for training and testing the quantized neural network.
Finally, CARLsim [40] is used for SNN function simulations.

We present our respiratory classification results organized into 1) results
for the baseline 1DCNN model (Section VI-A), 2) results using quantization
(Section VI-B) , and 3) SNN-specific results (Section VI-C).

###  VI-A Baseline 1DCNN Performance

In this section we evaluate the performance of the proposed 1DCNN specified
using the following metrics.

  * •

Top-1 Accuracy: This is the conventional accuracy and it measure the
proportion of test examples for which the predicted label (i.e., respiratory
state) matches the expected label. To formulate top-1 accuracy, we introduce
the following definitions.

    * –

True Positives (TP): For binary classification problems, i.e., ones with a
yes/no outcome (such as the case of respiratory classification), this is the
total number of test examples for which the value of actual class is yes and
the value of predicted class is also yes.

    * –

True Negatives (TN): This is the total number of test examples for which the
value of actual class is no and value of predicted class is also no.

    * –

False Positives (FP): This is the total number of test examples for which the
value of actual class is no but the value of predicted class is yes.

    * –

False Negatives (FN): This is the total number of test examples for which the
value of actual class is yes but the value of predicted class is no.

$\text{Top-1 Accuracy}=\frac{TP+TN}{TP+FP+FN+TN}$ (16)

  * •

F1 Score: To formulate F1 score, we introduce the following definitions.

    * –

Precision: This is the ratio of correctly predicted positive observations to
the total predicted positive observations, i.e.,

$\text{Precision}=\frac{TP}{TP+FP}$ (17)

    * –

Recall: This is the ratio of correctly predicted positive observations to the
all observations in actual class, i.e.,

$\text{Recall}=\frac{TP}{TP+FN}$ (18)

F1 Score conveys the balance between the precision and the recall. It is
calculated as the weighted average of precision and recall, i.e.,

$\text{F1
Score}=\frac{2*(\text{Recall}*\text{Precision})}{(\text{Recall}+\text{Precision})}$
(19)

  * •

AUC: In machine learning, a receiver operating characteristic (ROC) curve is a
graphical plot that illustrates the diagnostic ability of a binary classifier
as its discrimination threshold is varied. The area under curve (AUC) measures
the two-dimensional area underneath the ROC curve. AUC tells how much the
model is capable of distinguishing between classes. Higher the AUC, the better
the model is at predicting yes classes as yes and no classes as no.

  * •

Sensitivity: This is the true positive rate, i.e., how often the model
correctly generates a yes out of all the examples for which the value of
actual class is yes. Sensitivity is formulated as

$\text{Sensitivity}=\frac{TP}{TP+FN}$ (20)

  * •

Specificity: This is the true negative rate, i.e., how often the model
correctly generates a no out of all the examples for which the value of actual
class is no. Specificity is formulated as

$\text{Specificity}=\frac{TN}{TN+FP}$ (21)

Table III compares the classification performance using the proposed 1DCNN
against three state-of-the-art approaches – 1) Support Vector Machine (SVM)
classifier of [17], 2) Logistic Regression (LR) classifier of [18], and 3)
Random Forest classifier of [18]. We make the following four key observations.

TABLE III: Comparison with State-of-the-Art Approaches. Classification Technique | Top-1 Accuracy | F1 Score | AUC | Sensitivity | Specificity
---|---|---|---|---|---
SVM | 92.34% | 0.91 | 0.92 | 0.93 | 0.92
LR | 91.60% | 0.91 | 0.90 | 0.90 | 0.92
RF | 93.40% | 0.92 | 0.90 | 0.92 | 0.93
1DCNN (proposed) | 97.15% | 0.98 | 0.98 | 0.96 | 0.99

First, the proposed 1DCNN has the highest top-1 accuracy of all the evaluated
techniques (higher top-1 accuracy is better). The top-1 accuracy of 1DCNN is
better than SVM by 5.2%, LR by 6.0%, and RF by 4.0%.

Second, the proposed 1DCNN has the highest F1 score of all the evaluated
techniques (higher F1 score is better). The F1 score of 1DCNN is higher than
SVM by 7.7%, LR by 7.7%, and RF by 6.5%.

Third, the proposed 1DCNN has the highest AUC of all the evaluated techniques
(higher AUC score is better). The AUC score of 1DCNN is higher than SVM by
6.2%, LR by 8.5%, and RF by 8.5%.

Fourth, the proposed 1DCNN has the highest sensitivity of all the evaluated
techniques (higher sensitivity score is better). The sensitivity score of
1DCNN is higher than SVM by 3.2%, LR by 6.7%, and RF by 4.3%.

Finally, the proposed 1DCNN has the highest specificity of all the evaluated
techniques (higher specificity score is better). The specificity score of
1DCNN is higher than SVM by 7.6%, LR by 7.6%, and RF by 6.4%.

The reason for high performance using the proposed 1DCNN model is two-fold.
First, we perform intelligent feature selection from the data collected using
sensors on the SimBaby programmable infant mannequin. Second, we perform
hyperparameter optimization with neural architecture search to generate a
model that gives the highest classification accuracy using the selected
hyperparameters.

To give further insight to the improvement, Figure 11 shows the confusion
matrix obtained for the training and test sets. We observe that the proposed
1DCNN model has very low false positives and false negatives, which are
critical for respiratory classification in premature newborn infants.

Figure 11: Confusion matrix for the 1DCNN model.

###  VI-B Quantization Results

Table IV reports the top-1 accuracy (%), energy (in pJ), and model size (in
bits) with 2-bit, 4-bit, 8-bit, 16-bit, and 32-bit precision for the model
parameters. For comparison, we have included results using the baseline 1DCNN,
which uses full 64-bit precision for the model parameters. We make the
following three key observations.

TABLE IV: Model Quantization Results. Quantization | Top-1 Accuracy | Energy (pJ) | Model Size (bits)
---|---|---|---
2-bit/parameter | 88.93% | 7,089 | 92,258
4-bit/parameter | 88.98% | 15,994 | 184,516
8-bit/parameter | 93.00% | 29,871 | 369,032
16-bit/parameter | 96.55% | 57,640 | 738,064
32-bit/parameter | 97.03% | 113,386 | 1,476,128
Baseline 1DCNN | 97.15% | 134,613 | 2,952,256

First, top-1 accuracy reduces with a reduction in the bit precision (higher
accuracy is better for respiratory classification in premature newborn
infant). With 2-bit, 4-bit, 8-bit, 16-bit, and 32-bit precision, the top-1
accuracy is lower than the baseline 64-bit precision by 8.5%, 8.4%, 4.3%,
0.6%, and 0.1%, respectively. The top-1 accuracy with 32-bit precision is
comparable to 64-bit precision.

Second, energy reduces with a reduction of the bit precision (lower energy is
better for respiratory classification in wearables due to limited battery as
we motivated in Section I). With 2-bit, 4-bit, 8-bit, 16-bit, and 32-bit
precision, energy is lower than the baseline 64-bit precision by 94.7%, 88.1%,
77.8%, 57.2%, and 15.8%, respectively. These results show the significant
reduction in energy achieved using quantization. Lower energy leads to longer
battery life in wearables. Finally, model size also reduces with a reduction
in the bit precision (lower model size is better for wearables due to their
limited storage availability). With 2-bit, 4-bit, 8-bit, 16-bit, and 32-bit
precision, energy is lower than the baseline 64-bit precision by 96.8%, 93.7%,
87.5%, 75.0%, and 50.0%, respectively.

We conclude that to reduce energy and model size for respiratory
classification in wearables, quantization techniques can lead to a significant
reduction in accuracy.

###  VI-C SNN-Related Results

Table V reports the top-1 accuracy and energy results using the proposed SNN-
based approach compared to the baseline 1DCNN, 2-bit, and 8-bit quantized
model. We make the following three key observations.

TABLE V: SNN Accuracy and Energy Results. Model | Top-1 Accuracy | Energy (pJ)
---|---|---
Baseline 1DCNN | 97.15% | 134,613
2-bit Quantized 1DCNN | 88.93% | 7,089
8-bit Quantized 1DCNN | 93.00% | 29,871
SNN | 93.33% | 7,282

First, the top-1 accuracy of the proposed SNN is only 4% lower than the
baseline 1DCNN model with 18x lower energy. Second, compared to 2-bit
quantized model, the top-1 accuracy is 5% higher, while the energy is only 2%
higher. Finally, compared to 8-bit quantized model, the top-1 accuracy is
comparable while the energy is 4x lower. We conclude that SNN-based
respiratory classification achieves the best tradeoff in terms of top-1
accuracy and energy. To achieve similar accuracy, SNN can lead to 4x reduction
in energy, which is a critical consideration for respiratory classification on
wearables. The following results are reported to give further insight into
these improvements.

####  VI-C1 SNN Accuracy Compared to 1DCNN

Figure 12 shows the Bland-Altman plot comparing the accuracy of SNN solution
against the baseline 1DCNN model. Bland–Altman plots are extensively used to
evaluate the agreement among two models, each of which produced some error in
their predictions. As can be seen from the plot, the average accuracy
difference between the 1DCNN and the converted SNN is 7.3%, while the minimum
and maximum accuracy difference are 2.1% and 12.5%, respectively.

Figure 12: Bland-Altman plot comparing the accuracy of different SNN solutions
against the baseline 1DCNN model.

####  VI-C2 Design Space Exploration with SNN Parameters

We perform design-space explorations to identify SNN model parameters that
give the best tradeoff in terms of energy and accuracy.

In spiking neural networks, a spike is not fired by a neuron unless the
specified activation threshold voltage is attained. This implies, the larger
the firing threshold voltage, the more selectively a neuron is fired while
communicating between each layer. To demonstrate this, Figure 13 shows the
variation in accuracy as a function of the activation threshold ($V_{th}$)
(see Section V-C).

Figure 13: Accuracy impact with varying the activation.

In the figure, we vary the activation threshold, across different number of
test samples. We observe that for smaller number of test samples, as we
increase the threshold voltage for firing spikes, the performance accuracy
varies highly. But for larger size of test samples, the performance accuracy
does not vary as much, when we increase the threshold voltage.

For larger test sample sizes (500, 1000, 2000 etc.) the performance accuracy
varies between 92% and 94%. When we use small sample sizes (e.g., 100 and 200)
the prediction accuracy varies between 86% and 92%. We observe that the firing
threshold is most ideal when set within 1-3mV for smaller test samples and
within 1-5mV for larger test samples.

##  VII Conclusions

We propose a Deep Learning enabled wearable monitoring system for premature
newborn infants, where respiratory cessation is predicted using signals that
are collected wirelessly from a non-invasive wearable Bellypatch put on the
infant’s body. To this end, we developed an end-to-end design pipeline
involving five stages – data collection, feature scaling, model selection,
training, and deployment. The deep learning model is a 1D convolutional neural
network (1DCNN), the parameters of which are tuned using a grid search
methodology. Our design achieved 97.15% accuracy compared to state-of-the-art
statistical approaches. To address the limited energy in wearable settings, we
evaluate model compression techniques such as quantization. We show that such
techniques can lead to a significant reduction in respiratory classification
accuracy in order to minimize energy. To address this important problem, we
propose a novel Spiking Neural Network (SNN)-based respiratory classification
technique, whicch can be implemented efficiently on an event-driven
neuromorphic hardware. SNN-based respiratory classification involves two
additional pipeline stages – model conversion and parameter tuning. Using
pulseoxiometer data collected from a Laerdal SimBaby programmable infant
mannequin, we demonstrate 93.33% respiratory classification accuracy with 18x
lower energy compared to the conventional 1DCNN model.

We conclude that SNNs have the potential to implement respiratory
classification and other machine learning tasks on energy-constrained
environments such as wearable systems.

Our research results are based upon work supported by the National Science
Foundation Division of Computer and Network Systems under award number
CNS-1816387. Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the author(s) and do not necessarily
reflect the views of the National Science Foundation. Research reported in
this publication was supported by the National Institutes of Health under
award number R01 EB029364-01. The content is solely the responsibility of the
authors and does not necessarily represent the official views of the National
Institutes of Health.

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