In this thesis, we explore a new framework for image classification with an emphasis on generating explainable prediction. Deep neural networks (DNN) have achieved unprecedented accuracy in image classification. However, DNNs are black-box classifiers notoriously hard to interpret. In some application areas, the lack of interpretation has prevented practitioners to embrace the machine learning system. On the other hand, easy to interpret classification methods, e.g., linear discriminant analysis or distance-based approaches, often fall much behind in accuracy. We hereby propose a method to learn the definition of a distance based on commonly used distances for different types of features. The new distance is subject to a so-called positive gradient constraint to ensure interpretability. This new method enables us to interpret the importance of different types of features with respect to particular image class or even individual images. In addition, the method provides insight into why a prediction decision is made. Comparisons have been made with DNN and other widely used classification algorithms. We find that the new approach is competitive in performance when the dataset is of small size.