This paper introduces a novel approach to supervised dictionary learning, focusing on learning discriminative sparse representations for signals from different classes using a shared dictionary and multiple class-decision functions. The authors propose a generative/discriminative model that combines sparse coding with classification, allowing for the simultaneous learning of a dictionary and decision functions. The linear variant of the model is interpretable in a probabilistic framework, while the general version can be interpreted in terms of kernels. An optimization framework is presented to learn all components of the model, and experimental results on handwritten digit and texture classification tasks demonstrate the effectiveness of the proposed method. The paper also discusses the trade-off between generative and discriminative components and provides insights into the discriminative power of the learned dictionaries.This paper introduces a novel approach to supervised dictionary learning, focusing on learning discriminative sparse representations for signals from different classes using a shared dictionary and multiple class-decision functions. The authors propose a generative/discriminative model that combines sparse coding with classification, allowing for the simultaneous learning of a dictionary and decision functions. The linear variant of the model is interpretable in a probabilistic framework, while the general version can be interpreted in terms of kernels. An optimization framework is presented to learn all components of the model, and experimental results on handwritten digit and texture classification tasks demonstrate the effectiveness of the proposed method. The paper also discusses the trade-off between generative and discriminative components and provides insights into the discriminative power of the learned dictionaries.