IEEE Trans Image Process. 2017 Sep;26(9):4255-4268. doi: 10.1109/TIP.2017.2713948. Epub 2017 Jun 8.
For many image processing and computer vision problems, data points are in matrix form. Traditional methods often convert a matrix into a vector and then use vector-based approaches. They will ignore the location of matrix elements and the converted vector often has high dimensionality. How to select features for 2D matrix data directly is still an uninvestigated important issue. In this paper, we propose an algorithm named sparse matrix regression (SMR) for direct feature selection on matrix data. It employs the matrix regression model to accept matrix as input and bridges each matrix to its label. Based on the intrinsic property of regression coefficients, we design some sparse constraints on the coefficients to perform feature selection. An effective optimization method with provable convergence behavior is also proposed. We reveal that the number of regression vectors can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence. To examine the effectiveness of SMR, we have compared it with several vector-based approaches on some benchmark data sets. Furthermore, we have also evaluated SMR in the application of scene classification. They all validate the effectiveness of our method.
对于许多图像处理和计算机视觉问题，数据点以矩阵形式出现。传统方法通常将矩阵转换为向量，然后使用基于向量的方法。它们将忽略矩阵元素的位置，并且转换后的向量通常具有高维数。如何直接选择 2D 矩阵数据的特征仍然是一个未被研究的重要问题。在本文中，我们提出了一种名为稀疏矩阵回归（SMR）的算法，用于对矩阵数据进行直接特征选择。它采用矩阵回归模型接受矩阵作为输入，并将每个矩阵与其标签连接起来。基于回归系数的内在特性，我们对系数施加一些稀疏约束来执行特征选择。还提出了一种具有可证明收敛行为的有效优化方法。我们揭示了回归向量的数量可以被视为一个权衡参数，以平衡学习和泛化的能力。为了检验 SMR 的有效性，我们将其与一些基准数据集上的几种基于向量的方法进行了比较。此外，我们还在场景分类的应用中评估了 SMR。它们都验证了我们方法的有效性。
