Ultra Low-Power and Real-time ECG Classification Based on STDP and R-STDP Neural Networks for Wearable Devices

Ultra Low-Power and Real-time ECG Classification Based on STDP and R-STDP Neural Networks for Wearable Devices

Abstract

This paper presents a novel ECG classification algorithm for real-time cardiac monitoring on ultra low-power wearable devices. The proposed solution is based on spiking neural networks which are the third generation of neural networks. In specific, we employ spike-timing dependent plasticity (STDP), and reward-modulated STDP (R-STDP), in which the model weights are trained according to the timings of spike signals, and reward or punishment signals. Experiments show that the proposed solution is suitable for real-time operation, achieves comparable accuracy with respect to previous methods, and more importantly, its energy consumption is significantly smaller than previous neural network based solutions.

Cardiac monitoring, Electrocardiogram (ECG) classification, Machine learning, Spiking neural network (SNN), Low power consumption, Wearable devices

I Introduction

Cardiovascular diseases (CVDs) account for a large proportion of global deaths [1]. Early detection, as in many other diseases, plays a very crucial role in the process of stopping or controlling the progression of CVDs. Cardiac arrhythmias are widely used as signs for many of these diseases. Since the arrhythmias are reflected into electrical activities of the heart, they can be detected by analyzing Electrocardiogram (ECG) signals.

Visual inspection of recorded ECG signals during a visit to the cardiologist is the traditional form of arrhythmia detection. However, due to their intermittent occurrence, specially in early stages of the problem, arrhythmias are difficult to detect from a short time window of the ECG signal. Therefore, continuous ECG monitoring is crucial in early detection of potential problems [2].

In recent years, personal wearable devices have been introduced as cost-effective solutions for continuous ECG monitoring in daily life. Previous works include ECG monitoring solutions that are low-power but only extract the R peak or the QRS complex and do not further process the ECG signal [3, 4, 5, 6]. Many others analyze the signal and perform ECG classification, but transmit the signal to a connected smartphone or a remote cloud server for performing the computations associated with ECG classification algorithms [7, 8]. Besides privacy concerns [9], employing such solutions for continuous cardiac monitoring is limited by the availability, speed and energy consumption of the wireless connection. Other solutions include offline analysis of recorded ECG signals [10, 11]. Our approach, on the other hand, is to continuously monitor the ECG signal in real-time and on the wearable device itself.

In this approach, the ECG signal is continuously monitored without any connection to or any assistance from other systems. However, the main limiting factor is that wearable health monitoring devices should be small, and thus, may not utilize powerful processors or large batteries. Therefore, computational costs and energy consumption of ECG classification algorithms are important for real-time operation on small and low-power wearable devices [2].

Classical algorithms were mainly based on morphological features, such as the QRS complex, and signal processing techniques such as Fourier transform and wavelet transform [12, 13, 14, 15]. Such features show significant variations among different individuals and under different conditions, and therefore, are not sufficient for accurate arrhythmia detection [16, 17]. Many solutions have been proposed based on artificial neural networks, and especially in recent years, deep convolutional neural networks (CNN) and recurrent neural networks (RNN) [18, 19, 20, 21, 17, 22]. Neural network algorithms automatically extract the features from data, and hence, provide higher accuracy. This is because neural network based feature extraction is inherently more resilient to variations among different ECG waveforms [17]. However, the downsides of employing deep neural networks are high computational intensity and large power consumption.

Spiking neural networks (SNN) are the third generation of neural networks and provide the opportunity for ultra low-power operation [23, 24, 25, 26, 27, 28]. In this type of neural networks, the information is processed based on propagation of spike signals through the network as well as the timing of the spikes. Every neuron consumes energy only when necessary, that is only when it sends or receives spikes. In recent years, neuromorphic processors have been introduced for low-power implementation of SNN-based algorithms. Examples include IBM TrueNorth [26], Intel Loihi [27] and Qualcomm Zeroth [28].

This paper proposes a novel SNN-based ECG classification algorithm for real-time operation on ultra low-power wearable devices. The overall view of the proposed solution is shown in Fig. 1. The heartbeat signal is split into a small number of overlapping windows, which are then encoded into spike signals. The patterns in the generated spikes are automatically extracted in the STDP layer with assistance from a Gaussian layer and an inhibitory layer. Finally, the extracted features are classified in the R-STDP layer. STDP stands for spike-timing dependent plasticity which means the timings of the spikes are used to train the weights in this layer. R-STDP stands for reward-modulated STDP which means reward or punishment signals are used to train the weights, in addition to the spike timings. All the above layers are performed in the spike domain, and therefore, energy consumption is reduced significantly. In addition, the learning rules in training STDP and inhibitory layers are optimized in order to better fit the ECG classification domain. Experiments show that the proposed solution is suitable for real-time operation, achieves comparable classification performance with respect to previous methods, and more importantly, its energy consumption is significantly smaller than previous neural network based methods.

Previous SNN-based solutions that process ECG signals employ non-SNN algorithms for pattern extraction [29], or do not fully analyze the ECG signal, for instance, extract the heart rate [30], apply a band-pass filter to the input ECG signal [31], or detect perturbations in the signal [32].

It is noteworthy to mention that SNNs have previously been employed in many areas in computer vision. Examples include digit recognition [33, 34] and visual categorization [35, 36, 37]. This is mainly because the spiking neuron models are inspired from neuroscience studies on the brain’s visual cortex. SNNs have also been applied to non-vision applications including robot path planning and control [38, 39] and classification of EEG spatio-temporal data [40].

The rest of this manuscript is organized as the following. Section II provides a brief introduction to the neuron model and other basic concepts related to spiking neural networks. Section III presents our proposed SNN-based ECG classification algorithm. Section IV presents the results of experimental evaluations as well as comparisons with previous works in term of classification performance, network type, and energy consumption. Section V concludes the paper.

Fig. 1: Overall view of the proposed solution.

Ii Neuron Model

The employed neuron model and other basic concepts in spiking neural networks (SNN) are briefly explained in this section. SNNs are the third generation of neural networks which are inspired by the nerve cells in the brain. In contrast to the second generation neural networks such as multi-layer perceptrons, here the concept of time is deeply incorporated into the operational model [41]. In specific, the neurons communicate through electrical signals called spikes. For example in Fig. 2, neuron sends nine spikes to neuron at different times. The information is encoded in the timing of the spikes, not in their amplitude.

A neuron fires at time , i.e., generates a spike on its output at time , only when its membrane potential reaches a specific threshold value . When neuron fires, is decreased to and the generated spike travels to neuron and causes an increase in , i.e., the membrane potential of neuron . This is shown in Fig. 2. Since neurons do not fire all the time, the energy consumption is significantly smaller than other types of neural networks [26].

A connection from neuron to is called a synapse. For this synapse, is called pre-synaptic neuron, and is called post-synaptic neuron. A weight is associated with every synapse.

Different brain-inspired mathematical models exist for SNNs. We employ one of the most popular models called Leaky Integrate-and-Fire (LIF) model [41] which operates based on the following equation. This differential equation describes how is changed at time .

(1)

The index iterates through all neurons whose outputs are connected to neuron . The term is equal to either one or zero, and represents whether neuron has generated a spike at time . Hence, the term is zero when no spike is received by neuron at time . When one or multiple spikes are received at time , the term causes an increase in . In addition, a leaky current causes membrane potential to tend to the rest value with time constant . To summarize, does not change at time , if it is equal to its rest value and no spike is received. Otherwise, is non-zero, and thus, changes at time .

According to the above operational model, synaptic weight impacts spike propagation from neuron to . A larger means a spike generated by neuron is more likely to trigger a spike by neuron . This is because affects . As a result, the larger the weight the higher the firing rate of neuron .

Fig. 2: In this example, neuron sends nine spikes to neuron . As a result, the membrane potential of neuron , i.e., , is increased and reached to twice. Hence, two spikes are fired on its output.

Iii Proposed SNN-Based ECG Classification

Our proposed SNN-based method for classification of ECG beats is presented in this section. Fig. 1 illustrates an overall view of the proposed solution. The input ECG signal is first segmented into heartbeats. The heartbeat is split into a small number of windows, which are then encoded into spikes. The patterns in the generated spikes are automatically extracted in the STDP layer with assistance from two other layers, namely the Gaussian and the inhibitory layers. Finally, the extracted features are classified in the R-STDP layer. The formulations which govern the STDP and the inhibitory layers are optimized to better fit ECG classification problem. The details are discussed in the following.

Iii-a Segmentation

Heartbeat segments are formed as  seconds of the input ECG signal before an peak and  seconds after. peak is a specific point in the ECG waveform as shown in Fig. 1. There exist many ultra low-power and highly accurate methods for peak detection [4, 5].

Since the peak has a much larger amplitude compared to other parts of the heartbeat, it becomes the dominant pattern in the STDP layer and basically causes the effect of other patterns to be highly reduced. In order to avoid this issue and efficiently capture all the patterns, every heartbeat is split into overlapping windows as shown in Fig. 1. The windows are processed separately in the pattern extraction step. Let’s denote the heartbeat signal as and the portion of which falls in window as . The number of samples in is given by the following equation.

(2)

Iii-B Spike Encoding

There is an encoder cell for every sample from every window . Every cell encodes its input into a series of spikes as the following. Spike generation is random and follows the Poisson process. The spike firing rate of this random Poisson process is set proportional to , i.e., the amplitude of sample from window , plus a small bias. The higher the amplitude, the higher the rate of spike firing of the corresponding cell [42].

In fact, since the amplitude can be both positive or negative, two encoder cells are employed for every sample, not one. Spikes are generated by the first encoder cell if the signal is positive, and by the second cell if negative. This is inspired by the nerve cells in the Retina [43].

The output of every encoder cell is connected to one synapse, and the generated spikes are fed into this synapse. Therefore, the total number of output synapses for a window is equal to

(3)

These synapses are split in two groups. As shown in Fig.1, the number of windows in the next layers is equal to . The positive encoder cells are connected to the synapses in the odd windows, and the negative encoder cells are connected to the synapses in the even windows.

(a)
(b)
(c)
Fig. 3: Learning rule for the synaptic weights in the STDP layer. (a) The usual STDP learning rule. (b) Proposed learning rule. (c) The value of in (b) is between and .

Iii-C Gaussian Layer

The purpose of this layer is to adjust the number of spikes in order to help the STDP-based pattern extraction that is discussed later in Section III-D.

Every window is processed separately as the following. As shown in Fig.1, input synapse in window is connected to one neuron and its synaptic weight is set to . As a result, the neuron adjusts the spike firing rate by a factor of . In specific, we have

(4)

where and denote the rate of spikes on the input and on the outputs of the neuron, respectively.

Since the windows overlap, an ECG peak which falls on the side of a window also appears in the middle of a neighbor window. In order to reduce the effect of side peaks, a Gaussian kernel is employed in setting the value of . In specific, is set as

(5)

where and . Note that denotes the window length. The mean is chosen such that the Gaussian function be centered at the middle of the window. The variance is chosen such that the effect of a side peak is reduced but not completely neglected.

The term is a trainable variable which is different for different values of , i.e., different windows. It is initialized as , and then trained as the following. The next layers operate more efficiently if all windows in this layer generate equal average number of spikes. Let denote the average number of spikes fired by the neurons in window in this layer. The larger the value of , the larger the value of .

Therefore, in training we would like to have reach the same target rate for all . Since the neuron behavior (Section II) is non-linear, to achieve the desired rate, is initialized to , then, the train data is fed to the network, and is iteratively updated as the following.

(6)

Iii-D STDP-Based Pattern Extraction

Spike-timing dependent plasticity (STDP) [44] is employed here to extract the patterns in the ECG signal. STDP is an unsupervised learning procedure. Every window is processed separately as the following. Let denote the synaptic weights in window in this layer. The synaptic weights, also known as plasticity, are trained according to the timing patterns of the spikes in pre- and post-synaptic neurons. In specific, consider a synapse in this layer which connects pre-synaptic neuron to post-synaptic neuron . If the spike time of the pre-synaptic neuron, denoted as , is earlier than the spike time of the post-synaptic neuron, denoted as , then the weight is increased. This is called long-term potentiation (LTP). Similarly, when is earlier than , the weight is decreased. This is called long-term depression (LTD).

The smaller the time difference, the larger the amount of change in the synaptic weight. This is shown in Fig. 2(a). Here, , and . As shown in the figure, is maximum when , and it is exponentially decreased with larger values of . The mathematical equation for the STDP learning rule is

(7)

where, and are learning rates, and is the time constant. Note that and are positive and negative constant values, respectively.

Analysis of the Learning Rule: The learning rule in (7) creates a form of positive feedback which pushes the synaptic weights towards or . The reason is described in the following. When a synaptic weight is increased, the term in (1) will be larger for the next time, and therefore, the next spike from neuron is more likely to cause a new spike by neuron . This further increases . Since this positive feedback is likely to happen many times, the probability that this weight is pushed towards is very high. Similar situation happens in decreasing the weights, and thus, some of the weights are pushed towards . Note that spikes arrive randomly, and hence, during the STDP training, a weight is both increased and decreased many times, depending on the values of . However, the net effect will be either positive or negative. Therefore, the weights are pushed towards or .

Optimized Learning Rule: In computer vision applications, the negative weights are usually clipped to zero and the positive weights to a constant . The synaptic weights that are close or equal to form the detected patterns in the input image [33, 34, 35, 36, 37]. In ECG classification, however, the clipping alone is not sufficient, and thus, we also optimize the STDP learning rule as

(8)

where, is equal to

(9)

The corresponding curves are shown in Fig. 2(b) and 2(c). The intuition behind this optimization is discussed in the following. Consider the toy example shown in Fig. 4, in which three pre-synaptic neurons , , and are connected to a post-synaptic neuron . Consider the three input signals shown in Fig. 4. Neuron generates a very small number of spikes for all the three input signals. This is because the signal amplitude is zero, and hence, the encoder cell which is connected to neuron fires at a very low frequency. On the other hand, for all the three input signals, neuron generates many spikes. This is because the signal amplitude is large, and hence, the encoder cell which is connected to neuron fires at a high frequency. Since the generated spikes cause neuron to fire as well, the synaptic weight is increased many times. This also decreases because the spike frequency of is much lower, and is negative in some cases. Therefore, in both the learning rules (7) and (8), and are trained as and , respectively. Basically, neuron is trained to be sensitive to a zero amplitude at location and a large peak at location in the input ECG signal.

Now, let’s study training of the synaptic weight . Note that spike generation by the encoder cells follows a random process. Hence, it is possible that neuron fires before . In addition, note that the weights are initialized to random values. Hence, it is possible that be initialized to a larger value than . Therefore, the learning rule in (7) may train as . It is also possible, depending on the random settings, that be trained as . This random training to either zero or is not desired because it lowers the capability of the network in capturing complex ECG arrhythmia patterns that have various amplitudes in different locations of the input signal.

The proposed learning rule in (8), however, trains differently. Since the three input signals in this example have different amplitudes at location , we would like to be trained as somewhere between and . This is achieved in the proposed learning rule, because as increases, is increased as well, i.e., LTD is amplified (Fig. 2(b)). Hence, although is decreased less often than increased, i.e., the likelihood of negative is smaller than positive , the net effect of decreasing is amplified by making LTD stronger than LTP. As a result, the synaptic weight is trained as desired.

As shown in Fig. 2(c), the curve has a sharp slope near . Hence, LTP is amplified quickly with a small increase in . This helps to suppress the effect of minor variations in the input ECG signal by lowering the probability that such variations can contribute to the captured patterns. This is because it quickly becomes difficult for them to be able to increase the weights. However, once a weight has been increased enough, i.e., a real pattern has been captured, the difficulty stays nearly the same, i.e., the curve does not increase much because it has a very small slope.

Fig. 4: Toy example to demonstrate the intuition behind optimized STDP learning rule in (8).

Iii-E Inhibitory Layer

In order to prevent similar or same patterns from possessing the attention of all neurons in the STDP layer, inhibitory neurons are added to the network as shown in Fig. 1. Inhibitory layer makes the STDP layer more efficient in capturing different patterns [45].

As shown in Fig. 1, there is exactly one inhibitory neuron for every neuron in the STDP layer. When a neuron in the STDP layer fires, its corresponding inhibitory neuron fires as well and prevents the firing of all the other neurons in the same window in the STDP layer. This is achieved through backward synapses with negative weights which carry the fired spikes from inhibitory neuron to all neurons in the STDP layer and decrease their membrane potentials.

The negative synaptic weights are trained as the following. When neurons from the same window in the STDP layer fire at about the same time, is decreased. The inhibitory learning rule is

(10)

where, learning rates and are positive and negative constant values, respectively. When spikes from neurons and in the STDP layer are within time units from one another, is decreased by . Otherwise, it is increased by . Note that is clipped to zero, so it always holds a negative value [46].

Optimized Learning Rule: When the divergence among the existing patterns are small, the inhibition becomes too strong, which in turn decreases the number of spikes and incapacitates STDP training. To prevent this, we propose to modify the learning rule as shown in (11) and illustrated in Fig. 5.

(11)

In the proposed learning rule, is a smaller negative value as becomes a larger negative value. This modification guarantees that the negative weights do not grow too strong.

Fig. 5: Proposed learning rule for the backward synapses in the inhibitory layer. Note that is always kept negative.

Asymmetric Structure: Our additional strategy for preventing the repercussion of sameness in the detected patterns is to employ an asymmetric structure in the inhibitory layer. In specific, in every epoch, some of the inhibitory neurons are randomly inactivated. This basically distributes the authority among the neurons in the STDP layer. The core idea is inspired by the dropout technique in deep convolutional neural networks [47]. Note that inhibitory neurons are only present during the training stage, and they are inactivated during the inference (test) stage.

Iii-F Classification via R-STDP

This layer classifies the patterns which are previously extracted in the STDP layer. Here, reward-modulated STDP (R-STDP) is employed as the classifier. R-STDP operates not only based on spike timings but also a modulator signal. In the brain, the modulator signal can be a reward or punishment depending on Dopamine secretion [48].

As shown in Fig. 1, in our proposed solution, R-STDP is used for training synaptic weights in the final layer. Every neuron in this layer predicts one of the output classes, e.g., the normal class or an arrhythmia class. For an input ECG heartbeat, the neuron that fires more often is considered as the winner, i.e., its corresponding class is considered as the predicted class for the input ECG heartbeat. Unlike STDP, R-STDP follows a supervised learning procedure. During the training stage, if the prediction of a winner neuron is correct, a reward signal is applied to all its input synapses. In other words, the reward is applied to all synaptic weights , where represents all the pre-synaptic neurons from all windows that are connected to neuron , i.e., the winner neuron. Similarly, if the prediction is incorrect, a punishment signal is applied.

Different learning rules exist for employing R-STDP. Here, we use the following equations which are inspired from the method in [37].

(12)
(13)

In the above equations, and are learning rates in the reward situation, while and are learning rates in the punishment situation. As shown in (12), in the reward situation, i.e., when the prediction is correct, a positive reward proportional to is given to the synapses whose pre-synaptic neurons spike before the winner neuron, i.e., those with . A negative reward proportional to is given to all the other connected synapses, i.e., those with . As shown in (13), the negative and positive signals are reversed in the punishment situation, i.e., when the prediction is incorrect.

The term highly increases the probability that the trained weights stay near zero or . This is because is zero at and . Basically, once a weight is pushed to either of the two sides, it becomes more difficult to change it. Unlike in pattern extraction in the STDP layer, this is desired in classification in the final layer. This is because we would like a captured pattern from the STDP layer to have either no or full contribution to the prediction of an output class.

Iii-G Training Method

As shown in Fig. 1, there are four trainable layers in the proposed model. Since STDP is unsupervised but R-STDP is supervised, the layers are trained successively. In specific, first the Gaussian layer is trained. Next, the STDP and inhibitory layers are trained simultaneously, and finally, the R-STDP layer is trained.

All weights in the entire network need to be positive, and therefore, negative weights are clipped to zero. However, the backward synapses in the inhibitory layer need to have negative weights, and therefore, only for these synapses, positive weights are clipped to zero.

Iv Experimental Evaluation

Iv-a Classification Performance

The proposed solution is implemented based on Brian2 which is a Python package for evaluation of spiking neural networks [49].

The proposed solution is evaluated and compared with previous works using MIT-BIH ECG arrhythmia database. The ECG signals in this database are independently labeled by two or more cardiologists. Two groups of ECG signals called DS1 and DS2 are available in this database. DS1 includes representative samples of different ECG signals and artifacts that an arrhythmia detector might encounter in routine clinical practice. DS2 includes complex arrhythmia patterns [50].

In order to provide thorough and fair comparisons, we employ the exact same data as the previous works. In specific, the following patients from the DS2 group are used as test data: 200, 201, 202, 203, 205, 207, 208, 209, 210, 212, 213, 214, 215, 219, 220, 221, 222, 223, 228, 230, 231, 232, 233 and 234. This is the same set of data employed in [19, 17, 22]. To train the model for each of the above patients, two sets of data are combined, in specific, randomly selected representative heartbeats from all arrhythmia classes in DS1, plus the first five minutes of the patient’s own ECG signal. Employing the first five minutes of the patient’s own ECG signal is in compliance with AAMI standards [51] and has been used in many previous works [18, 19, 17, 22]. Note that the first five minutes are skipped in the test data. The result is shown in Table I. It compares the proposed solution with previous works, in terms of accuracy and network type.

Iv-B Real-time Operation and Energy Consumption

The neurons’ operating time step is  ms, i.e., the operating frequency is  KHz. Every heartbeat signal is provided to the network for  ms. At the end of this time duration, the network provides its classification result. This configuration supports up to beats per minute, and therefore, it is suitable for real-time operation.

Once the proposed model is trained, it is simulated according to the method presented in [52, 25] in order to estimate its energy consumption in classifying the ECG signals. The input ECG signals are applied to the network and the neurons are allowed to fire. When a neuron fires a spike, we consider that  pJ (pico Joules) of energy is consumed [25]. The connected output synapses transfer this spike to other neurons. For every spike transfer, i.e., every synaptic event,  pJ of energy is counted [25]. The simulation results show that the energy consumption is  J (micro Joules) per beat. This is significantly smaller than previous neural network based solutions.

Accuracy Type
Hu et al.[18] 94.8 MLP
Kachuee et al.[21] 93.4 CNN
Kiranyaz et al.[17] 98.6 FFT, CNN
Saadatnejad et al.[22] 99.2 Wavelet, RNN
Ince et al.[19] 97.6 Wavelet, MLP
Kolagasioglu et al.[29] 95.5 Wavelet, SNN
Lee et al.[14] 97.2 Wavelet
Proposed 97.9 SNN
TABLE I: Comparing the proposed solution with previous works in terms of accuracy and network type.

V Conclusion

This manuscript proposed an ECG classification algorithm in which both the pattern extraction and the classification steps are implemented based on spiking neural networks. In addition, the learning rules are optimized to better fit the ECG classification domain. As a result, the achieved accuracy is comparable to previous methods while the energy consumption is significantly smaller. Hence, the proposed method is suitable for ultra low-power wearable ECG monitoring devices.

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