We present a novel methodology for automated feature subset selection from a
pool of physiological signals using Quantum Annealing (QA). As a case study, we
will investigate the effectiveness of QA-based feature selection techniques in
selecting the optimal feature subset for stress detection. Features are
extracted from four signal sources: foot EDA, hand EDA, ECG, and respiration.
The proposed method embeds the feature variables extracted from the
physiological signals in a binary quadratic model. The bias of the feature
variable is calculated using the Pearson correlation coefficient between the
feature variable and the target variable. The weight of the edge connecting the
two feature variables is calculated using the Pearson correlation coefficient
between two feature variables in the binary quadratic model. Subsequently,
D-Wave's clique sampler is used to sample cliques from the binary quadratic
model. The underlying solution is then re-sampled to obtain multiple good
solutions and the clique with the lowest energy is returned as the optimal
solution. The proposed method is compared with commonly used feature selection
techniques for stress detection. Results indicate that QA-based feature subset
selection performed equally as that of classical techniques. However, under
data uncertainty conditions such as limited training data, the performance of
quantum annealing for selecting optimum features remained unaffected, whereas a
significant decrease in performance is observed with classical feature
selection techniques. Preliminary results show the promise of quantum annealing
in optimizing the training phase of a machine learning classifier, especially
under data uncertainty conditions.
The proposed method is compared with commonly used feature selection techniques for stress detection.
Results indicate that QA-based feature subset selection performed equally as that of classical techniques.
However, under data uncertainty conditions such as limited training data, the performance of quantum annealing for selecting optimum features remained unaffected, whereas a signiﬁcant decrease in performance is observed with classical feature selection techniques.
Chronic effects of stress can cause physiological abnormalities such as hypertension, stroke, obesity, and diabetes, and psychological conditions such as cognitive impairments which might lead to the development of Alzheimer’s Disease in older adults  .
Monitoring and quantifying stress reliably is not a trivial task as stress is a complex phenomenon and is inﬂuenced by several factors such as environmental factors, mental workload, task-speciﬁc stressors, etc.
detecting stress. The most popular methods for detecting stress are through monitoring of physiological signals such as EDA (Electrodermal Activity), ECG (Electrocardiogram), PPG (Photoplethysmogram) , RESP (Respiration) and EEG (Electroencephalogra m).
• The proposed hybrid classical-quantum machine learning pipeline is used to solve the problem of selecting an optimum subset of features from a pool of physiological signals for detecting stress in automobile drivers.
This hybrid pipeline consists of a classical subroutine and a quantum subroutine.
We will discuss these subroutines in detail in this section.
A. Classical Subroutine
The classical subroutine executes the preprocessing and
feature extraction stages of the machine learning pipeline.
1) Preprocessing: In this module, the EDA signals from hand and foot, ECG, and RESP signals are normalized and ﬁltered using a low-pass Butterworth ﬁlter of order 5 and the signal components greater than 1 Hz for EDA, 40 Hz for ECG, and 10 Hz for Resp signals were cut off.
For the ECG signal, a total of 15 time-domain features and 6 frequency domain features were extracted.
The time-domain features comprised of the various statistical measure of the R peaks of ECG signal and the mean, maximum, minimum, and standard deviation of the heart rate extracted from the ECG signal.
To translate the problem, a binary quadratic model is initialized.
The nodes represent the features, and the strength of the connection between the nodes represents the interaction between the feature variables.
The values of the nodes are initialized with the biases obtained from the feature-target bias matrix from the training phase, and the strength of the connection between the nodes is initialized with the feature-feature weight matrix from the training phase.
The nodes that form the cliques with the lowest energy conﬁguration is hypothesized as the best performing optimum subset of features.
IV. RESULTS AND ANALYSIS In this section, we will discuss the performance of the QAbased feature selection technique with typically adopted feature selection techniques for stress detection such as Pearson correlation ranking-based feature selection, p-value based feature selection, and mutual-information-b ased feature selection.
B. Qualitative Evaluation In this section, we will perform a qualitative evaluation of the features selected using four techniques namely quantum annealing, mutual information, p-value, and Pearson correlation feature selection technique.
Fig. 3. Clockwise from top: (a) quantum annealing based selection, (b) mutual information based selection, (c) Pearson correlation based feature selection, and (d) p-value based feature selection.
フィギュア。 3. a) 量子アニールに基づく選択、(b) 相互情報に基づく選択、(c) ピアソン相関に基づく特徴選択、(d) p-値に基づく特徴選択。 訳抜け防止モード: フィギュア。 3. 上から時計回りに : (a) 量子アニールに基づく選択 b)相互情報に基づく選択、(c)ピアソン相関に基づく特徴選択 と (d ) p - value based feature selection である。
features. Figure 3 shows the contribution of speciﬁc signal sources in terms of the percentage of total features selected.
From Figure 3, we can visualize that quantum annealing based feature selection returned a more stable set of features from mainly two signal sources (ECG and RESP) for 100% training data and 30% training data.
The effectiveness of a particular feature selection algorithm will be estimated by the ability of the selected features to classify a feature sample in low, medium, and high stress classes using classical classiﬁcation.
The metric used to quantify the classiﬁcation performance is the F1-score.
Figure 4 shows the average F1score achieved when features were selected using the different training data sizes for QA-based feature selection technique, mutual-information-b ased feature selection, Pearsoncorrelation-b ased feature selection, and p-value-based feature selection.
This implies that the average F1-score did not drop signiﬁcantly as training samples were reduced.
Moreover, no signiﬁcant statistical difference (p-value>0.05) was observed between the F1-scores obtained under 30%, 20%, and 10% training data and the F1-score obtained when 100% of the training data was used for feature selection.
This implies that the performance of QA-based feature selection was not affected to a signiﬁcant extent under the presence of limited training data when the quantum-annealing-ba sed feature selection technique was used.
In the case of the mutual-information-b ased feature selection technique, the trend line follows a decreasing trend as training sizes are reduced.
Moreover, except for low stress, a signiﬁcant statistical difference (p-value<0.05) is observed between the F1-scores obtained under 30%, 20%, and 10% training data and the F1-score obtained when 100% of the training data was used.
An exception to this observation is the situation where p-valuebased features were used to detect low stress.
For the p-valuebased feature selection technique, no signiﬁcant statistical difference was observed between the F1-scores obtained under 30%, 20%, and 10% training data and the F1-score obtained when 100% of the training data.
However, the average F1score obtained using the p-value-based feature selection technique is signiﬁcantly lower than that obtained using quantum annealing and mutual-information-b ased feature selection technique.
Pearson-correlation- based feature selection tech-
(a) Quantum Annealing(b) Mutual InformationECG10% 20% 30% 100%1008060402001008 06040200RESPH-EDAF-E DA10% 20% 30% 100%10% 20% 30% 100%10% 20% 30% 100%% of ECG based features% of RESP based features% of H-EDA based features% of F-EDA based features% of selected features% of selected features% of training data used for selecting features(c) Pearson Correlation(d) P-Value
a)量子アニーリング(b) 相互情報ecg10% 20% 30% 100%1008040100804040 40200resph-edaf-eda1 0% 20% 30% 100%10% 20% 100%10% 20% 20% 100%10% 20% 100%10% 20% 20% 20% 30% 100%% of ecg based features% of h-eda based features% of f-eda based features% of select features% of selection features% of features(c) pearson correlation(d) p-value
Fig. 4. Clockwise from top: (a) quantum annealing based selection, (b) mutual information based selection, (c) p-value based feature selection, and (d) pearson correlation based feature selection .
The problem of selecting optimal features is formulated as selecting a clique with the lowest energy from a binary quadratic model.
The nodes forming the lowest energy clique are returned as the set of optimal feature space.
As a case study, QA-based feature selection was used to select the optimum feature subset for detecting stress in a driving scenario and compared with mutual information, Pearson coefﬁcient, and p-value based feature selection techniques.
However, future investigation on large-scale datasets and/Or on different application domain will help us understand how quantum-annealing-ba sed optimization techniques generally performs better than the classical techniques.
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Average F1-Scores0.00.20.40. 60.81.0LowMedHighLow LowLowMedMedMedHighH ighHighAverage F1-Scores0.00.20.40. 60.81.0(a) Quantum Annealing (b) Mutual Information(d) P-Value(c) Pearson CorrelationAll training data30% training data20% training data10% training dataTrend LineDecreasing Trend LineConstant Trend LineStress classes
A averageage F1-Scores0.00.20.40. 60.81.0LowHighLowMed MedHighHighAverage F1-Scores0.00.20.60. 81.0(a) Quantum Annealing (b) Mutual Information(d) P-Value(c) Pearson correlationAll training data30% training data20% training data20% training dataTrend lineDecreasing Trend LineConstant Trends LineStress class