On the stopping criteria for k -Nearest Neighbor in positive unlabeled time series classification problems

An Improved Self-Training Method for Positive Unlabeled Time Series Classification Using DTW Barycenter Averaging

Traditional supervised time series classification (TSC) tasks assume that all training data are labeled. However, in practice, manually labelling all unlabeled data could be very time-consuming and often requires the participation of skilled domain experts. In this paper, we concern with the positive unlabeled time series classification problem (PUTSC), which refers to automatically labelling the large unlabeled set U based on a small positive labeled set PL. The self-training (ST) is the most widely used method for solving the PUTSC problem and has attracted increased attention due to its simplicity and effectiveness. The existing ST methods simply employ the one-nearest-neighbor (1NN) formula to determine which unlabeled time-series should be labeled. Nevertheless, we note that the 1NN formula might not be optimal for PUTSC tasks because it may be sensitive to the initial labeled data located near the boundary between the positive and negative classes. To overcome this issue, in this paper we propose an exploratory methodology called ST-average. Unlike conventional ST-based approaches, ST-average utilizes the average sequence calculated by DTW barycenter averaging technique to label the data. Compared with any individuals in PL set, the average sequence is more representative. Our proposal is insensitive to the initial labeled data and is more reliable than existing ST-based methods. Besides, we demonstrate that ST-average can naturally be implemented along with many existing techniques used in original ST. Experimental results on public datasets show that ST-average performs better than related popular methods.

Renyi Distribution Entropy Analysis of Short-Term Heart Rate Variability Signals and Its Application in Coronary Artery Disease Detection

Coronary artery disease (CAD) is a life-threatening condition that, unless treated at an early stage, can lead to congestive heart failure, ischemic heart disease, and myocardial infarction. Early detection of diagnostic features underlying electrocardiography signals is crucial for the identification and treatment of CAD. In the present work, we proposed novel entropy called Renyi Distribution Entropy (RdisEn) for the analysis of short-term heart rate variability (HRV) signals and the detection of CAD. Our simulation experiment with synthetic, physiological, and pathological signals demonstrated that RdisEn could distinguish effectively among different subject groups. Compared to the values of sample entropy or approximation entropy, the RdisEn value was less affected by the parameter choice, and it remained stable even in short-term HRV. We have developed a combined CAD detection scheme with RdisEn and wavelet packet decomposition (WPD): (1) Normal and CAD HRV beats obtained were divided into two equal parts. (2) Feature acquisition: RdisEn and WPD-based statistical features were calculated from one part of HRV beats, and student’s t-test was performed to select clinically significant features. (3) Classification: selected features were computed from the remaining part of HRV beats and fed into K-nearest neighbor and support vector machine, to separate CAD from normal subjects. The proposed scheme automatically detected CAD with 97.5% accuracy, 100% sensitivity and 95% specificity and performed better than most of the existing schemes.

Early Classification of Time Series by Simultaneously Optimizing the Accuracy and Earliness

The problem of early classification of time series appears naturally in contexts where the data, of temporal nature, are collected over time, and early class predictions are interesting or even required. The objective is to classify the incoming sequence as soon as possible, while maintaining suitable levels of accuracy in the predictions. Thus, we can say that the problem of early classification consists of optimizing two objectives simultaneously: accuracy and earliness. In this context, we present a method for early classification based on combining a set of probabilistic classifiers together with a stopping rule (SR). This SR will act as a trigger and will tell us when to output a prediction or when to wait for more data, and its main novelty lies in the fact that it is built by explicitly optimizing a cost function based on accuracy and earliness. We have selected a large set of benchmark data sets and four other state-of-the-art early classification methods, and we have evaluated and compared our framework obtaining superior results in terms of both earliness and accuracy.