In the two-process model of sleep regulation, slow-wave activity (SWA, i.e. the EEG power in the 0.5-4 Hz frequency band) is considered a direct indicator of sleep need. SWA builds up during non-rapid eye movement (NREM) sleep, declines before the onset of rapid-eye-movement (REM) sleep, remains low during REM and the level of increase in successive NREM episodes gets progressively lower. Sleep need dissipates with a speed that is proportional to SWA and can be characterized in terms of the initial sleep need, and the decay rate. The goal in this paper is to automatically characterize sleep need from a single EEG signal acquired at a frontal location. To achieve this, a highly specific and reasonably sensitive NREM detection algorithm is proposed that leverages the concept of a single-class Kernel-based classifier. Using automatic NREM detection, we propose a method to estimate the decay rate and the initial sleep need. This method was tested on experimental data from 8 subjects who recorded EEG during three nights at home. We found that on average the estimates of the decay rate and the initial sleep need have higher values when automatic NREM detection was used as compared to manual NREM annotation. However, the average variability of these estimates across multiple nights of the same subject was lower when the automatic NREM detection classifier was used. While this method slightly over estimates the sleep need parameters, the reduced variability across subjects makes it more effective for within subject statistical comparisons of a given sleep intervention.