In this work, neuro-fuzzy systems are compared to standard machine learning algorithms to predict the hypertension risk level. Hypertension is a cardiovascular disease, which should be continuously monitored to avoid the worsening of its symptoms. Automatic techniques are useful to support the clinicians in this task, however, most of the machine learning techniques behave like black boxes, thus they are not able to explain how their results have been obtained. In the medical domain, this is a critical factor, and explainability is demanded. Neuro-fuzzy systems, that combine Neural Networks (NNs) and Fuzzy Inference Systems (FISs), are used to obtain explainable results. Moreover, to enhance the explanation, a feature selection method has been used to reduce the number of relevant features and thus the overall number of fuzzy rules. Qualitative analyses have shown comparable results between the machine learning methods and the neuro-fuzzy systems. However, the neuro-fuzzy systems are able to explain the hypertension risk level with only nine fuzzy rules, which are easy to interpret since they use linguistic terms.
Hypertension is cardiovascular disease, consisting of a rise in blood pressure, that increases
the risk for cerebral, cardiac, and renal events. Antihypertensive drugs are used to lower blood
pressure, thus reducing cardiovascular risk. However, despite the availability of several efective
drugs, hypertension and its concomitant risk factors remain uncontrolled in most patients,
whilst continuous monitoring would help in preventing major cardiovascular events [
As an alternative, machine learning methods, have been shown to be efective tools to support
medical decisions [
In this context, photoplethysmography (PPG) is a great ally for continuous monitoring of
vital signs parameters [
In this work, a dataset of photoplethysmographic signals was collected to perform a quality
assessment study of them and explore the intrinsic relationship between PPG waveform and
cardiovascular disease [
Specifically, interpretability for hypertension prediction is studied, since the results returned
by automatic processing need to be understood by physicians [
A feed-forward network or a set of interpretable fuzzy rules are suitable to represent the
reasoning behind a classification model learned from a neuro-fuzzy network. This leads to the
use of neuro-fuzzy networks suitable for classification tasks where the interpretability of the
model, as well as the accuracy, are desirable. A neuro-fuzzy system has been compared with
standard machine learning techniques since it combines the accuracy of neural networks with
the interpretability characteristic of fuzzy inference systems [
The paper is organized as follows. Section 2 describes the data and the algorithms that have been used to assess the hypertension stage. Section 3 reports the results of experiments aimed to compare the derived neuro-fuzzy model with other machine learning methods, in terms of classification performance and interpretability. In section 4 we draw conclusions and outline future works.
The goal of the work is to compare black-box machine learning algorithms with neuro-fuzzy
systems to verify whether the use of the latter approach is more efective than classical machine
learning algorithms, in terms of accuracy and interpretability. Indeed, neuro-fuzzy systems
generate IF-THEN rules that constitute a model that is comprehensible to the user.
2.1. Data
A dataset composed of 219 subjects, aged between 21 and 86 years (mean age 58), has been
used. The dataset collects the photoplethysmographic signals (PPG) together with the related
physiological signals of the patients, to study the presence of possible correlations between them
[
Moreover, while four diseases are described in the dataset, namely hypertension, diabetes, cerebral infarction, and cerebrovascular disease, this work focuses on hypertension disease. Four output classes Normal, Prehypertension, Stage 1, and Stage 2 have been defined for the prediction task. As Table 1 shows, the dataset is quite unbalanced, indeed, patients belonging to the two last classes (i.e. serious disease symptoms) are lower than those belonging to the first two classes (i.e. healthy subjects, and patients with low symptoms). 2.2. Classification algorithms To solve the decision task, classification algorithms have been used. In particular, two variants of neuro-fuzzy systems (with Gaussian and Triangular membership functions) have been compared with standard machine learning algorithms.
A neuro-fuzzy network, i.e. a neural network encoding a set of fuzzy IF-THEN rules in its
structure, was trained to learn fuzzy rules for assessing the level of hypertension from data. In
particular, the form of fuzzy rules adheres to a zero-order Takagi-Sugeno (TS) fuzzy model [
Given the collection of rules, the fuzzy model provides certainty degrees for each output class (risk level) by inference of fuzzy rules. The fuzzy knowledge base will contain fuzzy rules with the following structure: IF (1 is 1) AND ... AND ( is ) THEN (1 is 1) AND .... AND ( is ) for = 1, .., , where is the number of rules, are fuzzy sets defined over the input variables ( = 1, ..., ) and are fuzzy singletons expressing the certainty degree of the output class , = 1.... Gaussian and Triangular membership functions have been used to design the fuzzy sets in the two variants of the system.
The neuro-fuzzy architecture is inspired by ANFIS (Adaptive-Network-Based Fuzzy Inference
System) [
A Backpropagation learning procedure implementing the gradient descent on fuzzy rules parameters was used for the training of the neuro-fuzzy network.
Four standard classification algorithms have been used for comparison, namely Random
Forest (RF), Multilayer Perceptron (MP), Multiclass support vector machine (SVC), XGBoost
(XGB) [
Two sets of experiments have been conducted to compare the efectiveness of the neurofuzzy models, with the other classifiers, in terms of classification performance. Moreover, the interpretability of NFSs has been studied.
In the first one, all the features have been considered, while in the second one, a feature selection technique, based on ANOVA F-values 4, has been used.
This second experiment aimed to reduce the number of features, thus leading to more simple models, that is with a lower number of fuzzy rules. Of course, while increasing the interpretability of the neuro-fuzzy models, classification performance should be preserved or increased.
Since the dataset is unbalanced, to study the robustness of the diferent algorithms, in learning accurate models, three experimental setups have been considered, by using diferent splits for the training and test sets (60-40, 70-30, and 80-20).
Moreover, to evaluate which membership function is more suitable for the given problem, both Gaussian (NFG) and Triangular (NFT) membership functions have been compared.
Standard classification measures have been used to quantitatively evaluate the model performances, whilst both quantitative and qualitative evaluations have been discussed to evaluate the interpretability of the neuro-fuzzy systems.
Table 2 shows the qualitative evaluation of the neuro-fuzzy systems and the standard classiifers, without and with feature selection, varying the splits. Looking at the neuro-fuzzy models 3Python’s Scikit-Learn library: https://scikit-learn.org/ 4f_classif : https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.f_classif.html 80-20 70-30 60-40
NFT NFG MLP RF SVC XGBC NFT NFG MLP RF SVC XGBC NFT NFG MLP RF SVC XGBC (NFT and NFG), without feature selection, the Gaussian membership function returns better results than the Triangular one. Particularly, no significant diferences are observed varying the splits.
This is also confirmed by the confusion matrices in Figure 2. Heatmap representation has been used to easily identify misclassifications. It can be seen that by using the Gaussian membership function the results are more accurate and a low number of false positives and negatives are returned. As it could be expected, the first two classes are easier to predict, since more samples are available. For the same reason, the more are the data in the training set (e.g. 80%), the better are the classification results. However, we can observe that whilst the neuro-fuzzy systems with Gaussian membership function have a low misclassification rate, and it confuses adjacent classes, that, in the medical domain, means subsequent stages of the disease. On the contrary, a higher number of errors is returned by the Triangular membership function, as suggested by the dark colors in the cells outside the principal diagonal. Moreover, in some cases, non-adjacent classes are confused. This is the case of Stage 2 that is predicted as Stage 1 or Normal (Fig. 3f), which is a very serious error, since suggesting that the patient is healthy while he is not.
Looking at the other classifiers, without feature selection, we can observe that, again, the best results are obtained with more data in the training set (split 80-20). In all configurations, the model that performs worse is SVC. Then there is MLP, followed by the RF. Finally, the best results are returned by XGBC, for all the splits.
In this first part of the experiments the black-box machine learning models (RF, MLP, and (d) 80-20-Triangular XGBT), except for SVC, performed better than the neuro-fuzzy models, reaching in some cases an accuracy of 1.0 on the test set. However, as already said, they are not able to explain how predictions are derived. On the contrary, neuro-fuzzy models showed quite good results (the best accuracy achieved was 0.80), but they have the characteristic of being explainable and therefore a low decrease of accuracy could be preferred with an increase of explainability.
However, when using all the features, 2187 rules were returned by the neuro-fuzzy systems. This makes the system complex to understand, thus a feature selection process has been applied to reduce the number of rules and observe its influence on the classification performance.
Only two variables were selected as the most relevant by the feature selection process, namely SBD (Systolic Blood Pressure) and DBP (Diastolic Blood Pressure). The third section of Table 2 shows the qualitative results obtained by using these two features to learn the models.
The neuro-fuzzy models strongly improved their performance for all the splits. Particularly, the best improvements are obtained by the Triangular membership functions that return comparable results with the Gaussian membership function (the best accuracy is 0.93).
Figure 3 shows the confusion matrices of the neuro-fuzzy models. Almost all models are able to classify the normal hypertension class. As regards the classification of the other classes, also in this case the neuro-fuzzy models occasionally committed errors by confusing the adjacent class. The model with the most errors in classification has been the configuration with the Triangular membership function and with the split of the dataset into 60% for the training set and 40% for the test set (figure 3f).
Whilst the model based on neuro-fuzzy systems improved their performance, and a high reduction of accuracy is observed for MLP, the other classifiers were not afected by the feature selection.
However, it is worth pointing out that a strong reduction in the number of fuzzy rules has been obtained after the feature selection phase. Indeed, with 7 features 2187 fuzzy rules were returned (described by 3 membership functions each). With 2 features (again, with 3 membership functions each), the number of fuzzy rules has been drastically reduced to 9, as (d) 80-20-Triangular shown in figure 4. The antecedents of the rules contain the two fuzzy variables returned by the feature selection (SBD and DBP) with all the configurations of the three fuzzy terms emerged by the neuro-fuzzy computation (low, medium, and high), as shown in figure 5. The consequents contain the four risk levels with the relative memberships. Thus, from the first four rules it is easy to understand that, the hypertension risk is Normal, if: SBD is low, and DBP is low, or SBD is low and DBP is medium, or SBD is low and DBP is high, or SBD is medium and DBP is low.
Overall, whilst qualitative results are comparable to those obtained by the best machine learning models, the neuro-fuzzy systems are able to return interpretable results, that help clinicians in understanding and trusting the process behind the algorithms. (a) SBP-Post training (b) DBP-Post training
Four machine learning algorithms have been compared with two neuro-fuzzy systems (based on Gaussian and Triangular membership functions) for hypertension assessment. The experiments aimed to evaluate if the qualitative performance of the two NFS models were higher, or at least comparable, with those given by the ML methods, with the added value of the explainability that fuzzy logic allows.
Since the dataset is unbalanced, three diferent experimental settings have been used. Moreover, further experiments, with a reduced number of features, have been conducted, to enhance the explainability of the neuro-fuzzy systems.
Results have shown that, without feature selection, the Gaussian membership function obtains higher performance than the Triangular one, but still lower than the machine learning methods. However, by considering all the seven features in data, the number of rules is too high to be understandable. Thus, the two most relevant features have been selected, leading to a significant reduction of the number of rules (from 2187 to 9). Feature selection has also improved the performance of the neuro-fuzzy systems, while machine learning methods have preserved their quantitative values, or as for MLP they have been reduced.
Overall, experiments have shown that NFSs are useful support tools for hypertension risk assessment since while returning accurate results, they are also able to explain with linguistic terms how these results have been obtained. In the medical domain, this is crucial, since both patients and medical staf need to understand and trust the automatic tools. Future work will be devoted to better studying the model explainability. To this aim, diferent algorithms will be compared and domain experts will be involved in evaluating the explanations.
This work was partially supported by INdAM GNCS within the research project “Computational Intelligence methods for Digital Health”. All authors are members of the INdAM GNCS research group. G. Casalino and G. Castellano are with the CITEL - Centro Interdipartimentale di Telemedicina, University of Bari Aldo Moro.