Electrocardiography (ECG) signal recognition is one of the popular research topics for machine learning. In this paper, a novel transformation called tower graph transformation is proposed to classify ECG signals with high accuracy rates. It employs a tower graph, which uses minimum, maximum and average pooling methods altogether to generate novel signals for the feature extraction. In order to extract meaningful features, we presented a novel one-dimensional hexadecimal pattern. To select distinctive and informative features, an iterative ReliefF and Neighborhood Component Analysis (NCA) based feature selection is utilized. By using these methods, a novel ECG signal classification approach is presented. In the preprocessing phase, tower graph-based pooling transformation is applied to each signal. The proposed one-dimensional hexadecimal adaptive pattern extracts 1536 features from each node of the tower graph. The extracted features are fused and 15,360 features are obtained and the most discriminative 142 features are selected by the ReliefF and iterative NCA (RFINCA) feature selection approach. These selected features are used as an input to the artificial neural network and deep neural network and 95.70% and 97.10% classification accuracy was obtained respectively. These results demonstrated the success of the proposed tower graph-based method.