The article presents a method to facilitate the solution process of matrix factorization by applying a gradient to the energy landscape. This is achieved by using a rectified linear type cost function, which is readily available in modern annealing machines.

Matrix factorization is an important tool in various decision processes, as it allows for the identification of factors that influence these processes. The 0/1 matrix factorization, in particular, defines matrix products using logical AND and OR as product-sum operators. This arrangement allows for the representation of instances and their characteristics in rows and columns, providing valuable insights into the decision-making factors.

While the theoretical framework of Simulated Annealing (SA) enables finding a minimum solution to the matrix factorization problem, practical implementation can be challenging due to the presence of many plateaus with flat slopes in the energy landscape. The search for the optimal solution becomes time-consuming in such cases.

The proposed method addresses this challenge by introducing a gradient to the energy landscape. By applying a rectified linear type cost function, the method enhances the search process and enables finding a solution more efficiently. The use of modern annealing machines further facilitates the implementation of this approach.

A notable aspect of the proposed method is the ability to update the cost function’s gradient during the search process. This allows for quick adjustments and improvements to the solution, making it more flexible and adaptive to changing conditions.

The effectiveness of the method has been confirmed through numerical experiments conducted with both noise-free artificial and real data. The results demonstrate the method’s ability to efficiently find solutions in a variety of scenarios.

In conclusion, the proposed method presents a promising approach to improving the efficiency of matrix factorization in decision processes. By incorporating a gradient to the energy landscape and utilizing a rectified linear type cost function, this method offers a practical solution to overcoming the challenges posed by plateaus with flat slopes. The ability to update the cost function’s gradient during the search process further enhances its performance, making it a valuable tool for both theoretical and practical applications.

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