Representation learning in intraoperative vital signs for heart failure risk prediction

Classification of unlabeled time series into existing classes is a traditional data mining task. All classification methods start by establishing a classification model based on labeled time series. In this case, “labeled time series” means that we build the model using a training dataset with the correct classification of observations or time series. The model is then used to predict a new, unlabeled observations or time series. Prediction of heart failure risk is summarized as a multidimensional time series classification problem. TSC is an important and challenging problem in data mining. With the increase of time series data availability, hundreds of TSC algorithms have been proposed [15, 16]. The time series classification problem is generally composed of extracting time series feature representation and machine learning classification algorithm. The methods used in this paper are the decision tree algorithm [17, 18], gradient boosting machine algorithm [19, 20], logistic regression algorithm [21], Bayesian algorithm [22], SVM [23], random forest [24] and popular deep learning methods [25, 26].

Piecewise Approximate Aggregation was originally a time series data representation method proposed by Lin et al. [27]. It can significantly reduce the dimensionality of the data while maintaining the lower bound of distance measurement in Euclidean space. Assume that the original time series is C = {x_1,x₂, …x_N}, the sequence defines that the PAA is \( \overline{\boldsymbol{C}}=\left\{{\overline{\boldsymbol{x}}}_{\mathbf{1}},{\overline{\boldsymbol{x}}}_{\mathbf{2}}\dots .{\overline{\boldsymbol{x}}}_{\boldsymbol{w}}\right\} \). Figure 1 shows the PAA of patient heart rate time series in this article. The Formula as Eq. 1.

Symbolic Aggregate Approximation [27] was a time-series data representation method that Lin et al. extended the PAA-based method to obtain the symbol and time series features in the discretized symbol representation of the PAA feature representation of a time series. Figure 2 shows the sax representation of the patient’s heart rate. The red line shows the data that has been aggregated with the PAA. For each coefficient, we assign the literal associated with the area.

Latent Dirichlet Allocation [28] was proposed by Blei David in 2003 to estimate the subject distribution of the document. It gives a probability distribution to the topics of each document in the document set, so that by analyzing some documents to extract their topic distribution, you can cluster topics or classify text based on the topic distribution. See Formula 2 and Fig. 3. Here k is the number of topics (fixed on initialization of the LDA model), M is the number of documents, N is the number of words in the document, which itself is represented by the vector w as a bag-of-words. The β_k is the multinomial distribution words that represent the topics and is drawn from the prior Dirichlet distribution with the parameter η. Similarly, the topic distribution θ_d is drawn from a Dirichlet prior with the parameter α. The z_ij is the topic which is most likely to have generated w_ij, which is the j-th word in the i-th document. In this paper, the topic model is used to extract the text features of patient’s sign monitoring data. Specifically, the time series of vital signs is converted into symbols by SAX, these symbols are then transformed into human-readable text using high-level semantic abstraction. Finally, LDA model is used to extract text topics of patients for heart failure prediction. See below for details in section 3.

The time series grid representation is an algorithm for converting time series data into images, which introduces a m × n grid structure to partition time series. According to the characteristics of time and value, the points in time series are assigned to their corresponding rectangles. The grid is then compiled into a matrix where each element is the number of points in the corresponding rectangle. The matrix form not only can reflect the point distribution characteristic of the sequence, but also improve the computational efficiency by using the sparse matrix operation method. See the algorithm for details [29]. Figure 4 demonstrates the schematic diagram of converting patient’s heart rate, diastolic blood pressure, systolic pressure, and pulse pressure difference time series data into a grid representation.

In recent year, deep learning (DL) models have achieved a high recognition rate for computer vision [30, 31] and speech recognition [32]. A Convolutional Neural Network is one of the most popular DL models. Unlike the traditional feature-based classification framework, CNN does not require hand-crafted features. Both feature learning and classification parts are integrated in a model and are learned together. Therefore, their performances are mutually enhanced. Related CNN algorithms can be found in [33]. The two most essential components of CNN are the convolution (Conv) layer and pooling (Pool) layer. Figure 5: a shows that the convolution layer realizes the convolution operation, and extracts the image features by calculating the inner product of the input image matrix and the kernel matrix. The other essential component is the pooling layer, also known as the sub-sampling layer, which is primarily responsible for simpler tasks. Figure 5: b shows that the pooling layer only retains part of the data after the convolution layer. It reduces the number of significant features extracted by the convolution layer and refines the retained features. In this paper, CNN is used to extract the image features of the vital signs monitoring data from surgical patients.

This section mainly demonstrates how to use the different time series feature representation of vital signs during surgery to predict the risk of postoperative heart failure using the relevant techniques described above. First a general overview over the workflow is given and shown in Fig. 6. Then each of the components are described in more detail in individual subsections.

The overall workflow of our presented method consists of three representation techniques towards heart failure which are described in more detail in the following Sections. They are:

Statistical representation of vital signs data: Statistical analysis of vital signs monitoring data of surgical patients to extract features for heart failure prediction.

Text representation of vital signs data: Firstly, the time series of vital signs is converted into symbols by the SAX, these symbols are then transformed into human-readable text using high-level semantic abstraction. Finally, the LDA model is used to extract text topics of patients for heart failure prediction.

Image representation of vital signs data: The vital sign monitoring time series data of the surgical patient is converted into a grid image by using the grid representation, and then the convolutional neural network is directly used to identify the grid image for heart failure prediction.

Perioperative heart failure prediction is based only on vital signs monitoring data of intraoperative patients. Indicators include heart rate (HR/hr), systolic blood pressure (NISYSBP/nisysbp), diastolic blood pressure (NIDIASBP/nidiasbpe), SpO2 (spo2), and pulse pressure difference (PP/pp). Learning window: defined as the duration of continuous monitoring during surgery, predictive window: defined as the patient’s perioperative period. As shown in Fig. 7.

In order to capture the various statistical feature of patient monitoring data trends, and mine intraoperative patient monitoring data from multiple dimensions in this paper, the mean (mean), variance (std), minimum (min), maximum (max), 25% (perc25), 50% (perc50), 75% (perc75) quantile, skewness (skew), kurtosis (kurt) and derivative variables of the first order difference (diff) of each monitoring index were calculated. That is, a total of 90 statistical parameters are obtained as derivative variables. The individual characteristic derivative variables are shown in Table 1, and the calculation is shown in Eq. 3. Finally, the classifier is used to predict heart failure. Specifically, the meaning of Feature variables in Table 1 are connected the abbreviation use “_” to add abbreviation together. For example: “mean_hr” means the mean of heart rate (hr), “min_diff_hr” means the minimum of the first order difference of heart rate, and “perc25_nisysbp” means that 25% of systolic blood pressure.

The second method in this paper is based on the textual features of patient monitoring data for heart failure prediction. The specific process is shown in Fig. 8. These include the following steps:

The advantage of textualization is that the results of the analysis are easier for humans to understand. Though the alphabetization of Symbols obtained from the SAX pattern extraction give a representation of the shape of the data within the time frame, the SAX strings are not intuitively understood and still have to be interpreted. Furthermore, by considering the statistics of the time frame in the abstract process, we are able to represent more information in the text than just the shape. Therefore, we use a rule-based engine that uses the SAX patterns and the statistical information of the time frame to produce text that is understandable to humans. The general form of the rules is given in Eq. 4 where < pattern > is the SAX pattern, < l > is the level, < f > is the feature, < mod > is a modifier for the pattern movement and < pm > is the pattern movement. Eq. 5 shows the possible values that the individual output variables can take.

<l > = [‘low’,‘medium’,‘high’].

<f > = The values are shown in Table 1.

<pm> = [‘decreasing’,‘increasing’,‘steady’,‘peak’,‘varying’].

The heart rate, diastolic blood pressure, systolic blood pressure, spo2 and pulse pressure difference of the surgical patients are converted into text semantics. See Fig. 9. The patient text topic is extracted through the LDA, and finally the risk of heart failure is predicted by the classifier.

Although deep learning is now well developed in computer vision and speech recognition, it is difficult to build predictive models when it comes to time series. Reasons include that Recurrent neural networks are difficult to train and there are no existing trained networks for time series. But if we turn the time series into pictures and then we can take advantage of the current machine vision for time series. Therefore, we convert the vital sign data of the patient into grid image by using the grid representation, and then the convolutional neural network is directly used to identify the grid image for heart failure prediction in this paper. See Fig. 10.

The grid representation is a compression technique that we convert a time series to a matrix format. Given a time series X = { x_t, t = 1, 2,..., T}, the length of which is T, and a grid structure, which is equally partitioned into m × n rectangles and the number of row and column are m and n, respectively, we are able to produce a grid representation as where a_ij is the number of data points located in the i-th row and the j-th column so it should be an integer and satisfies a_ij ≥ 0. See the algorithm for details [29]. A good representation method should retain as much information as possible of the initial time series when compressing it. Time series contain not only time and value information but also point distribution information. The m × n grid structure can meet these requirements, so a method of representing time series is introduced. In this paper, the values of m and n that we used for the similarity measure are dependent on the structure of CNN. We designed a small network structure because of the small dataset, and all samples used the same m and n.

The converted time-series grid image (see Fig. 4) is fused at the channel level as input to the convolutional neural network for heart failure prediction.

The data used in this paper is from the Department of Anesthesiology, Southwest Hospital. All data were gathered from the surgical patients from June 2018 to October 2018. A total of 14,449 operations include 99 cases of postoperative heart failure, 46 cases of liver failure, 61 cases of death, renal failure 54,49 cases of respiratory failure and 31 cases of sepsis. The remaining is uncomplicated patients. 15 out of 99 patients with heart failure had incomplete monitoring data. These patients were removed from the experiment and the remaining 84 patients were positive. 168 cases of negative data were randomly selected from the normal data set for the experiment. The training set is 80% and testing set is 20%, we used 10-fold cross validation in the experiment. Particularly, we divided the training set into training set (9 sets) and validation set (1 set), then used the test set to evaluate our model. The data screening diagram is as Fig. 11.

The statistical features have a total of 90 variables, and the data has to be selected before prediction. In order to reduce calculation complexity, features with lower importance should be removed. In this paper, the correlation was analyzed that calculating the Pearson CorrelationCoefficient of each feature, then the features with importance of 0 were removed. Figure 12 shows the correlation of each feature, in which the regions with dark color tend to have a strong correlation and vice versa.

Models were built from these statistical features using 8 different classifiers: Adaboost, Decision Tree (DT), Support Vector Machine (SVM), Logistic regression (LR), naive Bayes (NB), Random forest (RF), Multiple perception machine (MLP), Gradient Boosting Decision Tree (GBDT). Because the sklearn library of python includes these machine learning methods, we used the sklearn library to build these models. The core principle of AdaBoost is to fit a sequence of weak learners (i.e., small decision trees) on repeatedly modified versions of the data. All the predictions are then combined by weighted majority voting (or summation) to produce the final prediction. The data modification for each so-called boosting iteration involves applying weights to each of the training sample. The parameter of Adaboost was: n_estimators is 100. Decision Tree is to create a model that predicts the value of a target variable by learning simple decision rules inferred from the data features, where “DecisionTreeClassifier” of scikit-learn is a class capable of performing multi-class classification on a dataset. The parameters of DT were: criterion is “gini”, min_samples_split is 2, min_samples_leaf is 1, min_weight_fraction_leaf is 0.0. SVM is a set of supervised learning methods used for classification, regression and outliers detection. SVM in scikit-learn supports both dense (“numpy.ndarray” and convertible to that by “numpy.asarray”) and sparse (any “scipy.sparse”) sample vectors as input. The parameter of SVM was: kernel is “rbf”. In the model of Logistic regression, the probabilities describing the possible outcomes of a single trial are modeled using a logistic function. Logistic regression is implemented in LogisticRegression. This implementation can fit binary, One-vs-Rest, or multinomial logistic regression with l2. Naive Bayes methods are a set of supervised learning algorithms based on Bayes theorem, whose “naive” assumption is the conditional independence between each pair of features of a given class variable value. Random forests achieve a reduced variance by combining diverse trees, sometimes at the cost of a slight increase in bias. In practice the variance reduction is often significant hence yielding an overall better model. In RF, each tree in the ensemble is built from a sample drawn with replacement (i.e., a bootstrap sample) from the training set. Furthermore, when splitting each node during the construction of a tree, the best split is found either from all input features or a random subset of size max_features. The parameter of RF was: n_estimators is 100. The MLP is a supervised learning algorithm that learns a function f(·) : R^m → R^o by training on a dataset, where m is the number of dimensions for input and o is the number of dimensions for output. Given a set of features X= x₁, x₂, x₁, …x_m and a target y, it can learn a non-linear function approximator for either classification or regression. It is different from logistic regression, in that between the input and the output layer, there can be one or more non-linear layers, called hidden layers. The parameter of MLP was: hidden_layer_sizes is (5, 2). The GBDT is a generalization of boosting to arbitrary differentiable loss functions. GBDT is an accurate and effective off-the-shelf procedure that can be used for both regression and classification problems. The module “sklearn.ensemble” provides methods for both classification and regression via gradient boosted regression trees. The parameter of the GBDT was: n_estimators is 200. The other parameters of these models were the default parameters, see the Appendix for details. The results are shown in Table 2, and the Receiver Operating Characteristic (ROC) is shown in Fig. 13.

Figure 9 provides a general overview of our experimental process. First, we convert the patient’s vital signs monitoring data for 3 min into alphabetic symbols and convert consecutive 3 alphabetic symbols to text based on the rule engine. The LDA was used to unsupervised cluster all patient’s text representation into 5 topics. We chose 5 topics after varying the number from 2 to 10, because it was noted that validation set accuracy did not improve after 5, so that each patient’s vital signs monitoring data is represented by a 5-dimensional vector, summing to 1. Finally, we performed heart failure prediction based on the representation of the topic probability distribution using the same classifier and parameters as the Statistical Representation. The experimental results are shown in Table 2, and the ROC curve of the experiment is shown in Fig. 14.

In this experiment, we first convert the patient’s heart rate, diastolic blood pressure, systolic blood pressure, spo2, and pulse pressure difference into the grid image, and fuse the five images in the channel layer as input to the convolutional neural network (see the network structure designed in the previous section. See Fig. 11) to extract image features. Finally, heart failure is classified by softmax.

See Formula 6, where L is the length of the monitoring time series data, and (m, n) is the width and length of the grid image. The converted image has an associated length and width. Five grid maps of each patient simultaneously input into a convolutional neural network for heart failure recognition. The experimental results are shown in Table 2, and the ROC curve of the experiment is shown in Fig. 15. Figures 16 and 17 show the loss and accuracy of training and validation of convolutional neural networks.

Predictive results of various feature representations are presented in Table 2. These results demonstrate the GBDT classifier achieves the best results in the prediction of heart failure by statistical feature representation. The sensitivity, specificity and accuracy are 83, 85, 84% respectively; the NB classifier achieves the best results in the prediction of heart failure by text feature representation. The sensitivity, specificity and accuracy are 84, 73, 79% respectively; The sensitivity, specificity and accuracy of classification prediction based on convolutional neural network in image feature representation experiments also reached 89, 78 and 89%, respectively. It can be seen from Figs. 14, 15 and 16 that the AUC values based on the three feature representation algorithms are 0.92, 0.82, 083 respectively. Therefore, from the overall results, the patient’s intraoperative vital signs monitoring data has the ability to capture the precursory information of heart failure during the perioperative period.

Among the three feature representations, the method based on statistical representations achieves the best results. Because we did a lot of feature engineering before the model prediction, we removed the low-importance features and only retained the relevant features. In addition, the total sample size of the experiment is only 252 cases (positive: 84, negative: 168). Small sample size based on traditional feature engineering can achieve better results in classification. However, the method of text and image feature representation based on LDA and convolution neural network is likely to have the problem of under-fitting in the small sample training data set. Therefore, there should be a lot of room to improve the experimental results.