## 1 Introduction  
Studies on Electronic Health Records (EHRs) [1] play an important role in modern society [2]. According to the International Organization for Standardization (ISO) definition [3], EHRs mean a repository of patient data in digital form, which includes diagnostic records, electronic medical images, patient history, allergies and laboratory test results, etc. Healthcare workers rely on EHRs to bill patients and evaluate the physical conditions of patients [4]. In addition, more and more studies focus on using machine learning to deal with EHRs for the large amount of data. In this paper, we study the clinical time series, which originates from sensors in intensive care units (ICUs) or is recorded manually. Under most circumstances, these records are multivariate, including heart rate, blood pressure, and weight, etc. Generally, researchers analyze the multivariate time series of EHRs to accomplish the following tasks: in-hospital morality classification [5], diagnosis classification [6] and length of stay classification problems [7]. Because it is unnecessary to record all variables at all times, resulting in massive missing values, one of the major challenges of clinical time series classification tasks is to deal with the massive missing data. Figure 1 shows an example of a clinical time series. It should be noted that the observation frequency is usually quite different between different variables. Traditionally, in order to do the classification task on clinical time series, we will impute the missing values in the time series first. After imputing the missing data or simply omitting it [8], we feed the processed data to the auto-regressive integrated moving average (ARIMA) model [9] and the Kalman filter [10], treating it as a normal time series classification problem [11; 12; 13]. Most people impute missing values with the mean value in the training set (mean imputation) or the last observation (forward imputation) for effectiveness and efficiency [14]. We can apply not only the simple methods mentioned above but also various advanced methods, such as matrix factorization [15], kernel methods [16], and the EM algorithm [17], to perform the imputation. However, missing data imputation only serves as an auxiliary function to improve classification accuracy, and some advanced methods may cause time-consuming and expensive computational problems without classification performance improvement. Moreover, many imputation methods may fail in dealing with such massive missing values [18]. Thus, the solutions of time series with no or few missing values and time series with massive missing values in classification tasks should be different. When most of the multivariate time series is missing, we need to find more features besides the time series itself. The missing values in clinical time series are caused by many reasons. The most important one is that it costs much money and time to ask healthcare workers to record every possible variable of the patients [19]. Usually, they only choose to record the variables related to the medical condition of the patients. For example, heart rate may be recorded more frequently when the patients have heart disease. In addition, when the condition of the patients get worse, the recording frequency becomes higher. Finally, automated monitoring devices might fail to record the variables sometimes, but it is rarer than the previous cases we discuss above. We define the information contained in whether to record the variable (missing mark) and how often to record it (missing rate) as a missing pattern of a variable in the multivariate clinical time series. Take the patients with heart disease as examples: we believe the missing pattern of variables related to heart conditions behaves differently from others. Moreover, we should process the missing patterns of different variables separately to fully exploit the information from the multivariate time series.