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Reduced biquaternion is a four dimensional hyper–complex number which is commutative algebra and an extension of complex. Due to this property, the corresponding fast algorithm is designed in time frequency analysis which can better fit the convolution theorem than the non-commutative quaternion. In addition, the reduced biquaternion can be interpreted as a single point in 2-dimensional hyperbolic space with its algebraic structure which has more capacity and variable ability than the Euclidean space. However, the algebra properties of the reduced biquaternion have not yet been well explored in the deep convolutional neural network. In this paper, we develop a new deep network structure, namely reduced biquaternion valued convolutional neural network (RQV-CNN). The proposed RQV-CNN includes basic modules of reduced biquaternion convolution layer and fully connection layer. Extensive experiments on color image classification and color image denoising are conducted to evaluate the promising performance of the RQV-CNN framework. The results show that RQV-CNN outperforms the real-valued CNN (RV-CNN), complex-valued CNN (CV-CNN), and quaternion-valued CNN (QV-CNN) with same structures. The source code can be found at https://github.com/tasteimage/RQVCNN. [ABSTRACT FROM AUTHOR]