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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Sparse Uncorrelated Linear Discriminant Analysis for Undersampled Problems
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Sparse Uncorrelated Linear Discriminant Analysis for Undersampled Problems

机译：欠采样问题的稀疏不相关线性判别分析

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摘要

Linear discriminant analysis (LDA) as a well-known supervised dimensionality reduction method has been widely applied in many fields. However, the lack of sparsity in the LDA solution makes interpretation of the results challenging. In this paper, we propose a new model for sparse uncorrelated LDA (ULDA). Our model is based on the characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum ℓ1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as an ℓ1-minimization problem with orthogonality constraint. To solve this problem, we devise two algorithms: 1) by applying the linearized alternating direction method of multipliers and 2) by applying the accelerated linearized Bregman method. Simulation studies and high-dimensional real data examples demonstrate that our algorithms not only compute extremely sparse solutions but also perform well in classification.
机译：线性判别分析（LDA）作为一种众所周知的监督降维方法已广泛应用于许多领域。但是，LDA解决方案缺乏稀疏性，因此难以解释结果。在本文中，我们提出了一种稀疏不相关LDA（ULDA）的新模型。我们的模型基于广义ULDA所有解决方案的特征。我们通过从广义ULDA的所有最小维解中寻求最小ℓ1-范数的解，将稀疏性纳入ULDA转换。然后将该问题表述为具有正交约束的ℓ1最小化问题。为了解决这个问题，我们设计了两种算法：1）通过应用乘子的线性化交替方向方法，以及2）通过应用加速的线性化Bregman方法。仿真研究和高维真实数据示例表明，我们的算法不仅可以计算极为稀疏的解决方案，而且在分类方面也表现出色。

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