Daizhan Cheng

Changxi Li, Fenghua He, Hongsheng Qi et al.

Consider a multiplayer game, and assume a system level objective function, which the system wants to optimize, is given. This paper aims at accomplishing this goal via potential game theory when players can only get part of other players' information. The technique is designing a set of local information based utility functions, which guarantee that the designed game is potential, with the system level objective function its potential function. First, the existence of local information based utility functions can be verified by checking whether the corresponding linear equations have a solution. Then an algorithm is proposed to calculate the local information based utility functions when the utility design equations have solutions. Finally, consensus problem of multiagent system is considered to demonstrate the effectiveness of the proposed design procedure.

Qi Qi, Abdelhamid Tayebi, Daizhan Cheng et al.

In compressed sensing (CS), sparse signals can be reconstructed from significantly fewer samples than required by the Nyquist-Shannon sampling theorem. While non-sparse signals can be sparsely represented in appropriate transformation domains, conventional CS frameworks rely on the incoherence of the measurement matrix columns to guarantee reconstruction performance. This paper proposes a novel method termed Dimension-Keeping Semi-Tensor Product Compressed Sensing (DK-STP-CS), which leverages intra-group correlations while maintaining inter-group incoherence to enhance the measurement matrix design. Specifically, the DK-STP algorithm is integrated into the design of the sensing matrix, enabling dimensionality reduction while preserving signal recovery capability. For image compression and reconstruction tasks, the proposed method achieves notable noise suppression and improves visual fidelity. Experimental results demonstrate that DK-STP-CS significantly outperforms traditional CS and STP-CS approaches, as evidenced by higher Peak Signal-to-Noise Ratio (PSNR) values between the reconstructed and original images. The robustness of DK-STP-CS is further validated under noisy conditions and varying sampling rates, highlighting its potential for practical applications in resource-constrained environments.

Daizhan Cheng

A stationary value based algorithm (SVA) is provided to solve the nearest Kronecker product decomposition (KPD) problem of vector form hypermatrices. Using the algorithm successively, the finite sum KPD is also solved. Then the permutation matrix is introduced. Using it, the KPD of matrix form hypermatrices is converted to its equivalent KPD of vector forms, and then the SVA is also applicable to solve the same problems for vector form hypermatrix. Some numerical examples are presented to demonstrate the new algorithm and to compare it with existing methods.

Daizhan Cheng

The semi-tensor product (STP) of vectors is a generalization of conventional inner product of vectors, which allows the factor vectors to of different dimensions. This paper proposes a domain-based convolutional product (CP). Combining domain-based CP with STP of vectors, a new CP is proposed. Since there is no zero or any other padding, it can avoid the junk information caused by padding. Using it, the STP-based convolutional neural network (CNN) is developed. Its application to image and third order signal identifications is considered.

Daizhan Cheng

The matrix expressions for every parts of a transformer are firstly described. Based on semi-tensor product (STP) of matrices the hypervectors are reconsidered and the linear transformation over hypervectors is constructed by using projection. Its properties and calculating formulas are obtained. Using projection-based transformation of hypervector (PBTH), the framework of dimension-free transformer (DFT) is proposed by verifying each linear transformation in a transformer and replacing it by a proper PBTH, which allows the inputs and outputs being of arbitrary dimensions. Using balanced information about all entries, DFT must be more efficient in dealing with signals.