Obstructive sleep apnea (OSA) is a common but severely under-diagnosed sleep disorder that affects the natural breathing cycle during sleep with the periods of reduced respiration or no airflow at all. It is our long-term goal to increase the percentage of diagnosed OSA cases and reduce the time to diagnosis with user friendly and cost-efficient tools for sleep analysis at home. As a first step towards this goal, we study in this paper whether a small subset of those physiological signals that are used in classical OSA diagnosis in combination with automatic classification allows to detect apnea events. We study the performance of five data mining techniques to classify the epochs of data from the Apnea-ECG and MIT-BIH databases from PhysioNet as either disrupted or normal breathing. The data are only slightly preprocessed (rate reduction and normalization). We focus in this paper on respiratory signals from the nose, abdomen, chest, and oxygen saturation. We measure for any combination of these signals the accuracy, sensitivity, specificity, and the Kappa statistics of classification with artificial neural network, support vector machine, decision tree, K-nearest neighbor (KNN), and random forest. For Apnea-ECG, we achieve an accuracy of 96.6% with a combination of respiration data from the chest and nose as input data and an accuracy of more than 90% for all signal combinations. Interestingly, these good results are also achieved with the simple KNN technique. The results for MIT-BIH are lower, because of noise, smaller size, and some class imbalance. The accuracy does not significantly improves with the number of signals included in the signal combinations. We conclude that one signal might be sufficient to detect disrupted breathing, if the data set is of sufficient quality and size, and that respiration from the abdomen is the preferable choice when considering both classification performance and patient comfort.