Quality of sleep greatly affects a person's physiological well-being. Traditional sleep monitoring systems are expensive in cost and intrusive enough that they disturb the natural sleep of clinical patients. In our previous work, we proposed a non-intrusive sleep monitoring system to first record depth video in real-time, then offline analyze recorded depth data to track a patient's chest and abdomen movements over time. Detection of abnormal breathing is then interpreted as episodes of apnoea or hypopnoea. Leveraging on recent advances in graph signal processing (GSP), in this paper we propose two new additions to further improve our sleep monitoring system. First, temporal denoising is performed using a block motion vector smoothness prior expressed in the graph-signal domain, so that unwanted temporal flickering can be removed. Second, a graph-based event classification scheme is proposed, so that detection of apnoea / hypopnoea can be performed accurately and robustly. Experimental results show first that graph-based temporal denoising scheme outperforms an implementation of temporal median filter in terms of flicker removal. Second, we show that our graph-based event classification scheme is noticeably more robust to errors in training data than two conventional implementations of support vector machine (SVM).