## 1 Introduction  
Heart disease is common and is associated with high mortality, as the end phase of many cardiovascular diseases is heart failure [1; 2]. Heart failure in the elderly has a prevalence greater than 10% [3] and is a frequent cause of hospitalization [4]; the annual mortality rate of heart failure is 10% as well [5; 6]. In addition, 30% to 40% of patients die within one year of being diagnosed with heart failure [7], and conditional four-year survivability is less than 50% [8]. Physiologically, heart failure is associated with dysfunction in the autonomic nervous system [9; 10]. Autonomic activity is traditionally evaluated by heart rate variability (HRV) [11; 12; 13]. HRV is the physiological phenomenon of variation in the time interval between two consecutive heartbeats. The beat-to-beat interval is usually determined by the time interval between two consecutive R-peaks observed in an electrocardiogram (ECG), which is knowns as an RR interval. RR intervals between normal heartbeats, which excludes missed beat detections and premature beats, are referred to as NN intervals. RR interval and NN interval time series are two common heart rate signals for evaluating HRV. HRV is analyzed from three perspectives--time domain, frequency domain, and nonlinear methods. All of these methods, however, characterize HRV based on a single temporal scale, which can result in a lack of data on features that can only be observed using alternate temporal scales. Multiscale entropy (MSE) [14; 15], developed from approximate entropy [16] and sample entropy [17], was thereby proposed as a method for measuring HRV across multiple temporal scales. Recently, many existing single-scale measures have been developed to multiscale measures, including multiscale fuzzy entropy [18; 19; 20], multiscale dispersion entropy [21; 22; 23; 24], multiscale distribution entropy [25; 26], multiscale permutation entropy [27; 28; 29], entropy of entropy, and average entropy [30; 31; 32]. Each specifically scaled measure reveals a particular feature of heartbeat signals. Measures at various scales representing multiple features form multidimensional HRV metrics. Machine learning is then employed to analyze multidimensional metrics and automatically discriminate between healthy people and those in heart failure, which has potential applications in diagnostic engines [33] for supporting physicians. Machine learning is widely used in analyzing multidimensional HRV metrics to detect heart failure [34; 35; 36; 37; 38; 39; 40; 41; 42], and most studies combine several different HRV measures. However, these HRV metrics are not applied to clinically diagnose heart failure, which means that the improvement of HRV analysis is still required. Besides, the use of MSE for discrimination between congestive heart failure (CHF) and healthy hearts in older people remains controversial [43; 44; 45; 46]. Relatively few studies have evaluated MSE with machine learning in the detection of heart failure. [PERSON] and [PERSON] [47] applied 40-dimensional MSE analysis and Fisher discriminant analysis to identify CHF, young healthy, and old healthy participants. Training accuracy reached 94% for the differentiation between CHF patients and old healthy participants. They also reported a positive predictivity of 76% and a specificity of 83%. In addition, they observed overtraining in using the 40 dimensions. [PERSON] and [PERSON] [48] used sequential forward feature selection to optimally choose a subset of 20 MSE scales, and reported sensitivities and specificities of 93.2 and 64.2% using linear discriminant analysis (LDA), 91.1 and 78.3% using quadratic discriminant analysis, and 95.6 and 64.7% using k-nearest neighbor (KNN), respectively. [PERSON] and [PERSON] [49] analyzed the RR interval time series and differential RR interval time series by MSE with scales ranging from 1 to 10 along with a support vector machine (SVM) classifier. Their reported accuracy was 75.9% for the analysis of the RR interval time series and 85.6% for the differential RR interval time series.