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We propose a fast and accurate patient-specific electrocardiogram (ECG) classification and monitoring system using an adaptive implementation of 1D Convolutional Neural Networks (CNNs) that can fuse feature extraction and classification into a unified learner. In this way, a dedicated CNN will be trained for each patient by using relatively small common and patient-specific training data and thus it can also be used to classify long ECG records such as Holter registers in a fast and accurate manner. Alternatively, such a solution can conveniently be used for real-time ECG monitoring and early alert system on a light-weight wearable device. The experimental results demonstrate that the proposed system achieves a superior classification performance for the detection of ventricular ectopic beats (VEB) and supraventricular ectopic beats (SVEB).