Arrhythmia Classifier Using Convolutional Neural Network with Adaptive Loss-aware Multi-bit Networks Quantization

Our original arrhythmia classification convolutional neural network is presented in Fig. 2. The network is composed of a number of basic blocks and two linear layers. A basic block layer includes a 1-D convolutional layer and a max-pooling layer, which the activation between them is ReLU. The basic blocks are used for feature extraction, while the linear layers play a role in classification.

The input is raw and long-duration ECG signals, composed of 3,600 sampling points in the duration of 10 s. The network achieves end-to-end detection and inferences the classification output without manual feature extraction or feature segmentation and data processing of the original signals.

When we design the network structure, we make a tradeoff between the network size and accuracy. Finally, we decide that the number of basic blocks should be 7 in that such depth can produce considerable output. At the same time, it retains the tiny size of the network parameters, which can be a consumption of memory and computation resources. Therefore, our proposed network is a 17 layer CNN, which will be discussed later in Sec. IV.B.

Even though the depth of the proposed network architecture is minimal, the arrhythmia detection network still presents the problem of memory and power consumption due to the high bitwidth of weights. Because the importance of different layers varies, it is reasonable to quantize different layers with adaptive bitwidth, which can significantly reduce the average bitwidth of the network. We adopt the adaptive 1-D loss-aware multi-bit networks(MBNs) quantization method to help us realize the compression of the original proposed network.

Different from the quantization methods that minimize errors to reconstruct full precision weights, 1-D ALQ minimizes errors caused by quantization on the loss function. During the progress, neither gradient approximation nor full maintenance is involved [20]. After we train the full precision ECGNet, quantization process can be started. For the sake of improving the compression speed, parallel computing is introduced. For a vectorized weight $\boldsymbol{w}\in\mathbb{R}^{N\times 1}$, $\boldsymbol{w}$ is divided into $m$ groups which are disjoint. Each group of weights is denoted by $\boldsymbol{w_{k}}\in\mathbb{R}^{n\times 1}$, where $N=n\times m$. Based on a binary basis, the quantized weights can be presented.

We use $I_{k}$ to denote bitwidth of group $k$, and $\boldsymbol{B_{k}}$ represents the matrix forms of the binary bases. Therefore, we can define average bitwidth.

Our target is to optimize the loss function of $\boldsymbol{w}_{k}$ so that it can help us reduce the average bitwidth $\bar{I}$, which is directly related to compression rate. Han et al. use a combination of pruning, quantization and Huffman encoding to realize the multiple compression, which has excellent performance [6]. Our 1-D ALQ combines pruning and quantization to achieve a better effect as well. Therefore, 1-D ALQ is composed of three steps, as shown in Fig. 3. Kernel weights are obtained according to the full-precision model parameters trained by the previously designed network. We perform flatten operation on the full-precision model parameters and then use the following three steps to achieve the final algorithm.

ECG signals can be acquired from the MIT-BIH Arrhythmia database [15], hosted at PhysioNet [3]. We extract 1,000 ECG signal fragments from this database sampled at a frequency of 360 Hz and lasted 10 seconds. 80% of data is used as the training set while the rest is used as the test set.

In the experiment, we normalize all the data, and then split the data index to ensure that the test set and training set are disjoint. In each experiment, all data were disordered and re-divided randomly to generate training sets and test sets for evaluating network performance.

Based on the design of the basic blocks and linear layer mentioned, we try different depths and numbers of convolution kernels. Considering the network’s memory size and classification accuracy as the evaluation criteria, we find that more convolution kernels are needed in the shallow region. Therefore, ideally, the deeper and narrower the convolution kernel is perfectly suited to our needs. At the same time, we also need to consider the subsequent quantization process to adjust the network structure appropriately. Studies have shown that the accuracy of the detection hardly increases after the number of Basic Blocks exceeds seven.

Finally, after taking multiple factors into consideration, we constructed a network with seven basic blocks and two linear layers. The memory size of the network is 316.3KB, and the accuracy rate is 93.75%. The detailed architecture design of the network is shown in Table 1.

As shown in Fig. 4, it is the normalized confusion matrix of the ECGNet above. As we can see, the accuracy of the detection is considerable that many of them reach 100% accuracy, only a few are less than 90% accuracy. For evaluating proposed network, the metrics are shown in (3)-(6), including the overall accuracy (OA), specificity (Spe) and sensitivity (Sen).

As Table 2 shown, comparing with three long-duration arrhythmia classifier [21, 25, 19], our network achieves an OA of 94.19%, obviously improving the overall accuracy. Moreover, the overall accuracy will be improved again after our [22] quantization method.

In this part, we realize the implementation compression of our ECGNet using adaptive loss-aware quantization as detailed in the last section. According to the study [12], the last layer and the second layer are more important layers for network structures like ours. Therefore, higher maximum bitwidth should be provided to these two layers. Other layers were offered with lower bitwidth. Table 3 illustrates the compression of the layers, respectively. As we expected, Softmax and Conv1D_2 acquire higher average bitwidth, respectively 2.0000 and 1.9896.

As discussed above, adaptive bitwidths are given according to the characteristics and importance order of each layer. As seen from Fig. 5, some layers of the current ECG network architecture are more important and therefore a higher bitwidth is gained. This method optimizes the model error as much as possible and retains the inference precision as much as possible.

As Fig. 6 presented, with the increase of pruning rate, the decreasing amplitude of bitwidth is different, which indicates the method of adaptive bitwidth mentioned above. Moreover, we find the rate of decline is decreasing and it tends to stabilize at some value in the end.

Although we can greatly reduce the average bit width using this method, extreme reliance on this method can cause an unsatisfactory result, which we can observe in Fig. 7. As the bitwidth decreases, the loss function increases. To a certain extent, we can use the methods mentioned in the previous section to recover or even improve our accuracy. But when we go too far, the loss function increases dramatically, making our method ineffective and resulting in poor performance, which cannot be employed at all. Therefore, for our model, we choose appropriate parameters to improve the compression rate as much as possible while ensuring the accuracy rate of detection.

Table 4 compares the performance of several existing methods and the proposed quantization method. All of the quantization methods are employed on the aforementioned convolutional neural network to ensure that the comparison is fair. As shown in Table 4, our quantization method reaches the highest OA of 95.84% with 2.34% improvement compared to the unquantized network. Furthermore, the memory occupied by the compressed network parameters is just 13.54 KB, which is only 4.28% of the original model’s space occupation. Binary Connect [17] compresses all weights to 1 bit while it has poor OA that is only 55.15%, which is too imprecise to be able to be deployed as an arrhythmia classifier. Pławiak et al. proposed DoReFaNet, reducing memory by 16 times and 10.67 times respectively for quantization to 2 and 3 bit. However, the degradation of accuracy is considerable as well. As for Accuracy-predominant [12], Memory-predominant [12] and INQ [9], although these compression methods successfully achieve compression with low accuracy loss, their overall accuracy are 1.41%,3.81%, 3.07% lower than proposed with prominent worse compression performance in compression rates, respectively. The comparison demonstrates that the proposed adaptive loss-aware quantization method has better performance, making it more suitable for deployment on hardware to achieve real-time heart rate detection.

In summary, after the proposed quantization method, the network has better accuracy than other models and significantly reduce the memory occupation for hardware-friendly oriented.

However, there are still some drawbacks introduced. After ALQ is quantized, our network weights have a coefficient, which is actually a design that adds extra overhead. Another problem is that the quantization of the activation layer is not considered, and relumax is not added, which may result in a loss of precision in hardware implementation. In future work, we have the chance to overcome these drawbacks, achieving a low-power arrhythmia detection ASIC chip that can be used on wearable devices.