Visualising Convolutional Neural Network Decisions in Automated Sleep Scoring ?

Abstract

Current sleep medicine relies on the supervised analysis of polysomnographic recordings, which comprise amongst others electroencephalogram (EEG), electromyogram (EMG), and electrooculogram (EOG) signals. Convolutional neural networks (CNN) provide an interesting framework for automated sleep classi cation, however, the lack of interpretability of its results has hampered CNN's further use in medicine. In this study, we train a CNN using as input Continuous Wavelet transformed EEG, EOG and EMG recordings from a publicly available dataset. The network achieved a 10-fold cross-validation Cohen's Kappa score of = 0:71 0:01. Further, we provide insights on how this network classi es individual epochs of sleep using Guided Gradient-weighted Class Activation Maps (Guided Grad-CAM). The proposed approach is able to produce ne-grained activation maps on time-frequency domain for each signal providing a useful tool for identifying relevant features in CNNs.

Keywords

• Convolutional Neural Networks
• Guided Backpropagation
• Polysomnography

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Sleep is a fundamental biological process critical for the maintenance of physical and mental health. Associations between sleep disruption and various morbidities have been often reported, with some parainsomnias preceding serious neural disorders by many years [ 24 ]. Therefore, sleep monitoring is a matter of utmost importance. Current clinical praxis heavily relies on the analysis of polysomnographic (PSG) recordings, which include electroencephalogram (EEG), electromyogram (EMG), and electrooculogram (EOG) amongst other physiological signals. These signals are then interpreted based on clinical guidelines, such as R&K [ 14 ] and the AASM [ 2 ], which divide sleep into a few stages according to speci c spectral content and characteristic waveform patterns (see Table 1). Manual scoring following these rules is the gold-standard in sleep medicine.

Stage

Wake N1 N2 N3 REM

Description

Presence of EEG alpha rhythm (8-12 Hz); EMG with high-amplitude due to movements; EOG presents eye blinking artifacts, also visible on EEG around 0:5 2 Hz.

Attenuated alpha rhythm, presence of theta signal (4-7 Hz) on EEG; Muscle tone and slow eye movements decrease on EMG and EOG.

EEG presents K-complexes, i.e. large low frequency negative peaks in the range < 1:5 Hz, and sleep spindles, i.e. bursts of oscillations in the sigma band (12-15 Hz).

Slow wave activity for EEG (0.5-3 Hz), EMG tone is low and eye movements unusual.

Rapid eye movements (REM) clearly visible in EOG; low-amplitude and mixed-frequency activity in EEG; muscle atonia on EMG.

In contrast to manual scoring, automated approaches provide objective means of classifying sleep stages. Traditional approaches make use of numerous handengineered features from the physiological signals in combination with classical machine learning methods, e.g. support vector machines or hidden Markov models. Throughout the past decade, Convolutional Neural Networks (CNNs) have been widely applied in elds such as computer vision and audio processing due to their ability to operate on raw data, not requiring the explicit de nition of features. In the last couple of years, some early works applying CNNs in the eld of sleep analysis began to emerge [ 22, 19, 3, 1, 12 ]. Despite the competitive performance achieved, due to the high degree of abstraction present in CNN hidden layers, interpretability is an issue that has hindered its further use in medicine.

Vilamala et al. [ 23 ] proposed to visualise CNN decisions in sleep analysis using sensitivity maps [ 13, 16 ]. For this purpose, the authors converted each sleep epoch of single-lead EEG signals into spectrograms by using the Multitaper Spectral Estimation. In order to convert spectra into RGB images (i.e. containing three colour channels), the authors arti cially mapped the spectrogram intensities using an arbitrary colourmap. This was performed so that pre-trained image detection CNNs could be applied. The network of choice in [ 23 ] was the well-known VGGNet [ 17 ], which contains 13 convolutional layers followed by 3 fully connected (FC) layers and 138 million parameters. VGGNet was netuned to the task of sleep scoring using the Physionet Sleep-EDF Database [ 8 ]. Despite presenting an interesting framework, [ 23 ] has a few limitations. First, the number and diversity of subjects available in the Sleep-EDF is limited to 20 young healthy subjects. Second, using a single EEG lead is restrictive as experts classify sleep stages based on multichannel and multimodal settings. Third, despite the abundance and availability of pre-trained image models, these networks were trained for a very di erent task than the one at hand. As shown in [ 25 ] the transferability of features decreases as the distance between the base task and target task increases. Moreover, these networks usually assume three colour input channels. The workaround applied in [ 23 ] to obtain RGB channels out of a single spectrum provides no additional information to the network.

In this work, we proposed a simple CNN architecture that is trained from scratch using a large publicly available database. As input to the CNN we provide EEG, EOG and EMG signals, which are standard in sleep analysis. For visualising this network's weighs we apply the Guided Gradient-weighted Class Activation Maps [ 15 ]. This allows a detailed class-speci c view of the network for each channel used as input, which may provide somnologists with additional interpretation tools for sleep analysis. 2

Data Material

Data was obtained from the Montreal Archive of Sleep Studies database (MASSDB) [ 11 ], a large publicly available dataset comprising single night PSG recordings of 200 healthy participants ageing between 18 and 76 years, including 98 males aged 42:7 19:4 years and 102 females aged 38:1 18:9 years. The database is divided into 5 cohorts all of which were used in this study. To avoid a saturation on the number of needed channels in a recording setup we restrict our setup to three channels commonly used in the speci c literature: a single central EEG lead (C4-A1 or C3-A2, where available), a di erential EOG (ROC-LOC) and/or EMG (CHIN1-CHIN2).

As the MASS-DB comprises di erent study protocols, annotations using R&K were converted into AASM guidelines by assigning S3 and S4 stages to N 3, while fS0; S1; S2g were relabelled as fW; N 1; N 2g, respectively. Three of the MASS-DB cohorts contained 20s-epochs and were converted into 30s by including 5s of signal before and after each segment. A total of 228,870 epochs are available from the MASS-DB, being 13.6% W, 17.6% REM, 8.5% N1, 47.2% N2, 13.3% N3. To avoid biasing the network to either state, we undersampled each subject recording to the minority class, which results into 59,848 samples. 3

Methods

Various CNN models have been proposed for the task of sleep stage classi cation, most of which operate on raw single-channels (EEG or EOG). For instance, [ 19 ] proposed a network with two branches of 4 convolutional layers with distinct receptive elds aiming to generate feature maps with low and high frequency content. In [ 22 ], the authors propose a two-layer CNN model where after the rst 1-dimensional convolution, lters are reshaped (stacked) and processed by a 2D convolution. In [ 3 ] a spatial ltering technique is applied to multiple EEG, EOG and EMG channels. Each group of signals is treated in separate CNN pipelines as images by applying two-layers of 2D convolutions. The study also con rms that multiple channels and sensors provide an increase in detection accuracy, similar results were obtained in [ 1 ].

Sleep stages are largely de ned based on the spectral content of its signals (see AASM de nitions in Table 1). Therefore, it is reasonable to make use of time-frequency transforms as in [ 23 ]. Similarly to [ 23 ], the Short-Time Fourier Transform (STFT) coupled with a compact CNN network was successfully applied in [ 12 ]. Time-frequency representations are also bene cial for visualisation purposes, as one can observe time events at multiple frequency scales. Therefore, in this study we aim at generating time-frequency transforms for each epoch and modality of signal (EEG, EOG and EMG) as described in the following Section 3.1. The proposed network is further explained in Section 3.2. 3.1

Preprocessing

All recordings were sampled at fs = 100 Hz and divided in 30 s epochs following the AASM standard [ 2 ] for sleep scoring. Recordings were high-pass ltered using zero-phase 100th order FIR lters with 0.1 Hz cuto frequency for EEG/EOG signals and 10 Hz for EMG.

As presented in [ 21 ], Wavelet transforms are particularly suitable for analysing non-stationary signals (such as EEG), whereas STFT assumes periodicity and is signicantly a ected its window size, which makes it fundamentally impossible to correctly determine the onset of rapid events such as sleep spindles. Therefore, based on [ 21 ], we apply the Continuous Wavelet Transform (CWT) with Morlet basis function as time-frequency transform to each 30 s epoch using Matlab's cwt() function with default parameters. The resulting scalograms (dimensions 101 (30 fs)) were further reduced by using bilinear interpolation to 30 300 maps. The resulting time-frequency representations were then normalised to the range [0; 1], which serve as input to the proposed network. 3.2

Network Architecture

The proposed network is detailed in Fig. 1. As mentioned, the network assumes as input scalograms for each channel, i.e. input dimensions 30 300 3. The rst two convolutional layers use valid padding and convolutional strides of (1,2) to reduce the input dimensions, thus decreasing the total number of parameters in the following layers. The following block performs convolutions on 3 3, 5 5 and 7 7 windows in a similar fashion as the nave Inception block [ 20 ] and in [ 12 ] (shown in Fig. 1). The main idea of this block is to learn features at multiple temporal and frequency resolutions. At last, global average pooling is performed to reduce the spatial dimensions of each channel. Global pooling is directly followed by the softmax layer which outputs classes scores. The network contains a total of 9.0M parameters.

3x3 convolutions

3x3 convolutions

7x7 convolutions

7x7 convolutions Previous Layer 5x5 convolutions

5x5 convolutions

Filter concatenation

2x2 maxpooling Dropout (50%) (a) Layer Type Input Convolution 2D Batch Normalisation Activation Dropout Convolution 2D Batch Normalisation Activation Dropout Inception-like Block Concatenate MaxPool 2D Dropout Global Average Pool Dense #Filters Operation Size Output Dim.

- - (30,300,3) 64 (10 10) (21,146,64) - - (21,146,64) - ReLU (21,146,64) - 50% (21,146,64) 128 (10 10) (12,69,128) - - (12,69,128) - ReLU (12,69,128) - 50% (12,69,128) 256 (3 3),(5 5),(7 7) 3 (12,69,256) - - (12,69,768) - (2 2) (6,34,768) - 50% (6,34,768) - - (768) 5 Softmax 5 (b) The proposed model was developed in Keras/Tensor ow. Training was performed in 100 epochs, with batch size 64 and categorical cross entropy as loss function. Adam[ 9 ] optimiser was used with default parameters (learning rate lr = 10 3, 1 = 0:9 and 2 = 0:999). L2 norm regularisation was applied to the last layer with value = 10 5. To assess the performance of this network, a 10-fold crossvalidation procedure was carried out on the balanced MASS-DB. Results are evaluated in terms of sensitivity (SE), positive predictive value (PPV), accuracy (ACC), F1-score (F1) and Cohen's Kappa score ( ). 3.4

Visualising CNNs

Deep visualisation is an active eld of research. Current methods for visualising CNN weights with 2-dimensional data input (e.g. images or time-frequency representations) can be divided into gradient-based and activation maximisation.

Gradient-based methods aim at highlighting pixels of an input image I that have the most impact on the prediction score Sc for a given class c. In order to assess the rate of change in Sc with respect to small changes in image intensity, [ 16 ] proposed backpropagating the partial derivatives @Sc=@I across the network. Therefore positive values on the gradient indicate an increase on the output score for that class. As the class score function is highly non-linear function of image I, rst-order Taylor expansion is used to linearize this function [ 16 ]. Extensions of the backpropagation method focus on modifying to the original gradient function and result in qualitative improvements to visualisation [ 15 ]. Example of such methods include the Deconvolutional Networks [ 27 ], that modi es the backward pass of ReLU by clipping negative gradients, and Guided Backpropagation [ 10, 18 ], on which activations are masked during both deconvolution and forward pass. This group of techniques can be used for visualising the last layer [ 16 ], or on each of the hidden neurons [ 4, 26 ]. These approaches are attractive due to their simplicity, however despite producing ne-grained visualisations, these methods are not class-discriminative as optimisation process tends to produce images that are hardly recognisable [ 15 ]. In order to produce more natural-looking images, some studies suggested biasing optimisation with natural image priors [ 10 ] or using regularisation techniques [ 26 ].

Activation maximisation methods focus on directly visualising the activation of some speci c layer of a network given an input image. One approach is to estimate the importance of input pixels by visualising the probability of the correct class being chosen as a function of a mask occluding parts of the image, the so-called occlusion/perturbation sensitivity [ 27, 5, 23 ]. Another approach is to focus on the activation of the last layer before any FC layer, where higherlevel visual concepts are captured. An example of such approach is are Class Activation Maps (CAMs) [ 28 ]. In order to retain the tensorial shape any attening operation is substituted by global average pooling followed directly by the softmax (i.e. disregarding any FC layers). Based on the class scores Sc, wc k corresponding weights to class c for unit k, and Akxy = Px;y fk(x; y) activation map of unit k in the last layer a class-speci c heatmap Lc can be achieved for the image such as [ 28 ]:

Selvaraju et al. [ 15 ] proposed a generalisation of CAM by introducing the main concept of backpropagation from gradient-based approaches downstream from any Ak, i.e.

c LCAM (x; y) =

X wkcAkxy k kc = where kc is the partial linearization of the network from feature map Ak and Z1 Px Py represents the global average pooling operation perform over these feature maps. The Gradient-weighted CAM (Grad-CAM) then performs a weighted combination of forward activation maps followed by a ReLU:

c LGrad CAM (x; y) = ReLU

X k kcAkxy

Grad-CAM enjoys the bene ts from CAMs and produce class-discriminative localisation of image regions, while imposing fewer restrictions on the network's architecture. In fact, it can be used in any CNN-based architecture. However, Grad-CAM only produces an averaged heatmap for the image so that the channel information is lost. In order to show ne-grained gradient visualisations, [ 15 ] further proposed combining Guided Backpropagation and Grad-CAM by (1) (2) (3) point-wise multiplication of both bi-linear interpolated Grad-CAM and Guided Backpropagation heatmaps.

In this contribution, we aim at better understanding how the network classi es sleep stages regarding each signal modality (i.e. EEG, EOG and EMG). For this purpose, after pre-training the proposed CNN presented in Section 3.2, Guided Grad-CAM is applied to randomly selected segments of the MASS-DB. We qualitatively evaluate these Wavelet scalograms and heatmaps regarding their physiological meaning. 4

Results and Discussion

The results for the 10-fold cross-validation procedure using the proposed model and balanced MASS-DB set are described in Fig. 2. Despite having less than 10% the number of parameters of VGGNet, the proposed CNN is able of performing automated sleep staging when trained from scratch, resulting Kappa score of = 0:71 0:01. As usual in the literature, N1 stage classi cation performed worst as the state shares characteristics with wakefulness state. Moreover, the transition from wake to N1 is described as challenging and has been reported as a major source of inter-rater variability [ 6 ]. Our analysis di er from the one presented in [ 23 ] in that the database used in this study is larger and the di erent classes have been balanced. Similar results for the imbalanced MASS-DB were obtained in [ 19 ].

Figures 3 and 4 demonstrate the application of Guided Backpropagation and Guided Grad-CAM using the proposed trained model to segments of Wake, REM and N2 stages respectively. These stages were chosen for illustrating the visualisation method, due to their more distinguishable characteristics (e.g. presence of spindles/K-complexes on N2). A total of 100 randomly selected epochs from all cohorts and subjects were visually inspected from which Figs. 3 and 4 were selected. Overall Guided Grad-CAM produced cleaner heatmaps than Guided Backpropagation as described in [ 15 ]. More importantly, Guided Grad-CAM produces channel-speci c maps, which are relevant when analysing multimodal data such as PSG recordings.

The presented results show that relevant CNN feature maps (i.e. weights) often correspond to regions of interest for particular sleep stages. For instance Fig. 3(a) presents high sensitivity around EEG alpha bands (i.e. 8-12 Hz), which is characteristic for both Wake stage. During the wake stage, the patterns for EOG and EMG seem erratic spreading along various frequency bands (Fig. 3(a)) whereas during REM (Fig. 3(b)) weighs lower frequent EOG bands. Usually the N2 stage is the mostly recognisable one, comprising K-complexes (negative peaks followed by positive peaks with duration > 0.5 s) and sleep spindles (bursts of oscillatory waves in the sigma band, i.e. 11-15 Hz). Comparing Fig. 4(a) and (b) we notice that the Guided Grad-CAM weighs heavily such patterns. These conclusions are similar to the ones found in [ 23 ], except we notice coherent physiological information across the di erent input channels used in this study.

These exemplary epochs demonstrate the potential of such visualisation approaches for further interpreting how CNN weighs di erent sleep patterns and could greatly enhance the interaction of domain experts [ 23 ]. Nevertheless, conclusions must be carefully drawn as the method only provide a partial understanding of the network (e.g. not including FC layers). Moreover, as more aesthetically pleasing notions of image saliency are sought, di erent backpropagation heuristics (e.g. regularisation) are applied [ 5 ]. Further limitations of this method include i) epoch-speci city i.e. output depends on input representation/epoch; ii) the visualisation tool is not model-agnostic as each network will inevitably produce di erent outcomes. In this study we applied data from healthy subjects, future works should focus on comparing these results with feature maps generated from pathological data that may provide clinically relevant insights. Additionally, PSG analysis often takes into consideration surrounding epochs. The proposed CNN model treats each epoch independently, however, it is bene cial to consider the temporal/transition information contained in this signal. This can achieved by using Recurrent Neural Networks or soft-attention techniques. 5

Conclusion

In this contribution we shed a light onto how CNNs are able to distinguish sleep stages. For this purpose we trained a small CNN network from scratch which takes as input CWT scalograms from 3 di erent sensors (EEG, EOG and EMG). Further, we visualise regions of interest for the trained network by applying the Guided Grad-CAM method. The proposed approach is able to produce negrained activation maps on time-frequency representations of each individual signal providing a useful tool for identifying relevant features in CNNs. ) z ) z EEG Scalogram

EOG Scalogram alpha rhythm (8-12 Hz) and EOG erratic content in (a). In (b) EEG contains mixedfrequencies, low frequency EOG is considered relevant but not EMG. 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 ) z (b) Respective time signal with characteristic spindles and K-complexes. network seems to detect both K-complexes (low frequency content) and sleep spindels (11-13 Hz).

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