Recently, sparse representation-based classification (SRC) has been widely studied and has produced state-of-the-art results in various classification tasks. Learning useful and computationally convenient representations from complex redundant and highly variable visual data is crucial for the success of SRC. However, how to find the best feature representation to work with SRC remains an open question. In this paper, we present a novel discriminative projection learning approach with the objective of seeking a projection matrix such that the learned low-dimensional representation can fit SRC well and that it has well discriminant ability. More specifically, we formulate the learning algorithm as a bilevel optimization problem, where the optimization includes an $\ell _{1}$ -norm minimization problem in its constraints. Through the bilevel optimization model, the relationship between sparse representation and the desired feature projection can be explicitly exploited during the learning process. Therefore, SRC can achieve a better performance in the transformed subspace. The optimization model can be solved by using a stochastic gradient ascent algorithm, and the desired gradient is computed using implicit differentiation. Furthermore, our method can be easily extended to learn a dictionary. The extensive experimental results on a series of benchmark databases show that our method outperforms many state-of-the-art algorithms.

中文翻译：

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通过双层优化的基于稀疏表示的分类的最优判别投影

最近，基于稀疏表示的分类（SRC）得到了广泛的研究，并在各种分类任务中产生了最先进的结果。从复杂的冗余和高度可变的视觉数据中学习有用且计算方便的表示对于 SRC 的成功至关重要。但是，如何找到与 SRC 一起使用的最佳特征表示仍然是一个悬而未决的问题。在本文中，我们提出了一种新颖的判别投影学习方法，其目标是寻找一个投影矩阵，使得学习到的低维表示能够很好地拟合 SRC 并且具有很好的判别能力。更具体地说，我们将学习算法表述为双层优化问题，其中优化在其约束中包含 $\ell _{1}$ -norm 最小化问题。通过双层优化模型，可以在学习过程中明确利用稀疏表示和所需特征投影之间的关系。因此，SRC 可以在变换后的子空间中获得更好的性能。可以使用随机梯度上升算法求解优化模型，并使用隐式微分计算所需梯度。此外，我们的方法可以很容易地扩展到学习字典。在一系列基准数据库上的大量实验结果表明，我们的方法优于许多最先进的算法。可以使用随机梯度上升算法求解优化模型，并使用隐式微分计算所需梯度。此外，我们的方法可以很容易地扩展到学习字典。在一系列基准数据库上的大量实验结果表明，我们的方法优于许多最先进的算法。可以使用随机梯度上升算法求解优化模型，并使用隐式微分计算所需梯度。此外，我们的方法可以很容易地扩展到学习字典。在一系列基准数据库上的大量实验结果表明，我们的方法优于许多最先进的算法。