The 0/1 matrix factorization defines matrix products using logical AND and OR
as product-sum operators, revealing the factors influencing various decision
processes. Instances and their characteristics are arranged in rows and
columns. Formulating matrix factorization as an energy minimization problem and
exploring it with Simulated Annealing (SA) theoretically enables finding a
minimum solution in sufficient time. However, searching for the optimal
solution in practical time becomes problematic when the energy landscape has
many plateaus with flat slopes. In this work, we propose a method to facilitate
the solution process by applying a gradient to the energy landscape, using a
rectified linear type cost function readily available in modern annealing
machines. We also propose a method to quickly obtain a solution by updating the
cost function's gradient during the search process. Numerical experiments were
conducted, confirming the method's effectiveness with both noise-free
artificial and real data.

0/1 矩阵因子分解应用逻辑 AND 和 OR 作为乘积求和运算符，以揭示影响各种决策过程的因素。通过将矩阵因子分解建模为能量最小化问题，并在理论上利用模拟退火方法实现在足够时间内找到最小解。我们利用现代模拟退火机器中可用的修正线性类型代价函数对能量景观应用梯度，从而提高解决过程的效率。在搜索过程中，我们还通过更新代价函数的梯度来快速获得解决方案。通过数值实验，验证了该方法在无噪声人工数据和真实数据上的有效性。

使用修正线性型代价函数，在模拟退火中生成能量景观的梯度，以有效解决 0/1 矩阵分解

Generating gradients in the energy landscape using rectified linear type  cost functions for efficiently solving 0/1 matrix factorization in Simulated  Annealing