High-dimensionality is a common characteristic of real-world data, which often results in high time and space complexity or poor performance of ensuing methods. Subspace learning, as one kind of dimension reduction method, provides a way to overcome the aforementioned problem. In this paper, we introduce multiobjective evolutionary optimization into subspace learning, and propose a Pareto-based sparse subspace learning algorithm for classification tasks. The proposed algorithm aims at minimizing two conflicting objective functions, the reconstruction error and the sparsity. A kernel trick derived from Gaussian kernel is implemented to the sparse subspace learning for the nonlinear phenomena of nature. In order to speed up the convergence, an entropy-driven initialization scheme and a gradient-descent mutation scheme are designed specifically. At last, a knee point is selected from the Pareto front to guarantee that we can obtain a solution with good classification performance, and yet as sparse as possible. The experiments and detailed analysis on real-life datasets and the hyperspectral images demonstrated that the proposed model achieves comparable results with the existing conventional subspace learning and evolutionary feature selection algorithms. Hence, this paper provides a more flexible and efficient approach for sparse subspace learning.

中文翻译：

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基于帕累托的稀疏子空间学习框架

高维度是现实世界数据的共同特征，通常会导致高时空复杂性或后续方法的性能不佳。子空间学习作为一种降维方法，为克服上述问题提供了一种途径。在本文中，我们将多目标进化优化引入子空间学习，并提出了一种基于Pareto的稀疏子空间学习算法进行分类任务。提出的算法旨在最小化两个有冲突的目标函数，即重构误差和稀疏性。从高斯核派生的核技巧被用于稀疏子空间学习，以解决自然界的非线性现象。为了加快收敛速度​​，专门设计了一个熵驱动的初始化方案和一个梯度下降突变方案。最后，从帕累托前面选择拐点，以确保我们可以获得具有良好分类性能且尽可能稀疏的解决方案。对现实数据集和高光谱图像进行的实验和详细分析表明，该模型与现有的常规子空间学习和进化特征选择算法取得了可比的结果。因此，本文为稀疏子空间学习提供了一种更灵活，更有效的方法。对现实数据集和高光谱图像进行的实验和详细分析表明，该模型与现有的常规子空间学习和进化特征选择算法取得了可比的结果。因此，本文为稀疏子空间学习提供了一种更灵活，更有效的方法。对现实数据集和高光谱图像进行的实验和详细分析表明，该模型与现有的常规子空间学习和进化特征选择算法取得了可比的结果。因此，本文为稀疏子空间学习提供了一种更灵活，更有效的方法。