Abstract--A multiple instance dictionary learning approach, Dictionary Learning using Functions of Multiple Instances (DL-FUMI), is used to perform beat-to-beat heart rate estimation and to characterize heartbeat signatures from ballistocardiogram (BCG) signals collected with a hydraulic bed sensor. DL-FUMI estimates a "heartbeat concept" that represents an individual's personal ballistocardiogram heartbeat pattern. DL-FUMI formulates heartbeat detection and heartbeat characterization as a multiple instance learning problem to address the uncertainty inherent in aligning BCG signals with ground truth during training. Experimental results show that the estimated heartbeat concept found by DL-FUMI is an effective heartbeat prototype and achieves superior performance over comparison algorithms. I. INTRODUCTION Increasingly more and more devices for realtime heart rate monitoring are becoming available. However, the majority of these devices are intrusive and require continual interaction. For example many heart rate monitoring systems require a user to physically wear the system ( e.g., as a watch, chest strap, electrodes, finger sensor, etc.) and/or charge batteries frequently. In contrast, devices that use ballistocardiography can provide an unintrusive and, thus, relatively low maintenance, comfortable alternative for heart rate monitoring. These sensing systems record the motion of the human body generated by the sudden ejection of blood into the large vessels at each cardiac cycle [1]. Such motion contains rich information and has gained revived interest due to recent development in measurement technology [2, 3] and a growing interest in managing chronic health conditions through passive sensors in the home [4].

A multiple instance dictionary learning method using functions of multiple instances (DL-FUMI) is proposed to address target detection and two-class classification problems with inaccurate training labels. Given inaccurate training labels, DL-FUMI learns a set of target dictionary atoms that describe the most distinctive and representative features of the true positive class as well as a set of nontarget dictionary atoms that account for the shared information found in both the positive and negative instances. Experimental results show that the estimated target dictionary atoms found by DL-FUMI are more representative prototypes and identify better discriminative features of the true positive class than existing methods in the literature. DL-FUMI is shown to have significantly better performance on several target detection and classification problems as compared to other multiple instance learning (MIL) dictionary learning algorithms on a variety of MIL problems.